Parity violation in compound nuclei: experimental methods and recent results

PARITY VIOLATION IN COMPOUND NUCLEI: EXPERIMENTAL METHODS AND RECENT RESULTS

G.E. MITCHELL, J.D. BOWMAN, S.I. PENTTILAG , E.I. SHARAPOV ElectriciteH de France, Div. R&D, MFTT, 6 Quai Watier, 78400 Chatou, France
Energy Conversion Department, Chalmes University of Technology, S-41296 GoK teborg, Sweden

AMSTERDAM } LONDON } NEW YORK } OXFORD } PARIS } SHANNON } TOKYO

Physics Reports 354 (2001) 157–241

Parity violation in compound nuclei: experimental methods and recent results G.E. Mitchella; b; ∗ , J.D. Bowmanc , S.I. Penttil,ac , E.I. Sharapovd a

North Carolina State University, Raleigh, North Carolina 27695-8202, USA b Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA c Los Alamos National Laboratory, Los Alamos, NM 87545, USA d Joint Institute for Nuclear Research, 141980 Dubna, Russia Received December 2000; editor : G:E: Brown

Contents 1. Introduction 1.1. Parity violation in compound nuclei 1.2. Brief review of the theoretical literature: 1960 –1990 1.3. Brief history of the experiments: 1980 –1990 1.4. TRIPLE Collaboration experiments: 1990 –2000 1.5. Theoretical developments: 1990 –2000 2. Experimental techniques 2.1. PNC neutron transmission and capture experiments 2.2. LANSCE short-pulse spallation neutron source 2.3. Polarized neutron beam line for PNC experiments 2.4. The neutron transmission detector 2.5. The -ray detector 2.6. Shape analysis of time-of-:ight data

159 159 160 163 165 167 168 168 170 171 174 177 180

2.7. Determination of resonance parameters and cross section asymmetries 3. Statistical analysis of parity violation in neutron resonances 3.1. General approach: MJ determined by Bayesian analysis 3.2. Extraction of rms matrix element for I = 0 targets 3.3 Extraction of rms matrix element for I = 0 targets 3.4. Level densities and neutron strength functions 3.5. Bayesian assignment of resonance parity 4. PNC asymmetries and spectroscopic results 4.1. Overview of the TRIPLE data 4.2. Bromine 4.3. Niobium 4.4. Rhodium

∗

Corresponding author. Tel.: +1-919-660-2638; fax: +1-919-660-2634. E-mail address: [email protected] (G.E. Mitchell).

c 2001 Elsevier Science B.V. All rights reserved. 0370-1573/01/$ - see front matter  PII: S 0 3 7 0 - 1 5 7 3 ( 0 1 ) 0 0 0 1 6 - 3

181 182 182 183 186 189 190 191 191 193 194 194

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4.5. Palladium 4.6. Silver 4.7. Cadmium 4.8. Indium 4.9. Tin 4.10. Antimony 4.11. Iodine 4.12. Xenon 4.13. Cesium 4.14. Lanthanum 4.15. Thorium 4.16. Uranium 5. Experimental average resonance parameters 5.1. Level densities

194 197 199 199 200 201 206 206 209 211 211 213 213 213

5.2. Neutron strength functions 5.3. Rms weak matrix elements 6. Sign eFect and oF-resonance PNC asymmetry in thorium 6.1. Distant doorway state models 6.2. Local doorway state models 6.3. Thorium data above 250 eV 6.4. OF-resonance PNC asymmetry in thorium 7. Summary and discussion 7.1. Weak spreading widths 7.2. Weak matrix elements 7.3. General summary Acknowledgements References

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Abstract The TRIPLE Collaboration studies of space-parity symmetry in the compound nucleus show numerous examples of parity violation in Br, Rh, Pd, Ag, Cd, In, Sn, Sb, I, Cs, Xe, La, U, and Th. The longitudinal cross section asymmetries have measured values in the range of 10−3 –10−1 for neutron energies from several eV up to 300 –2000 eV, depending on the target. The high density of states leads to enhancement of the parity violation by factors as large as 106 relative to parity violation in pp scattering. The high degree of complexity of the levels permits the use of statistical methods for determination of the root mean square weak matrix element M for each nucleus. This report is focused on the experimental results of the TRIPLE Collaboration studies. Parity violation has been observed in 75 resonances of 18 nuclides. The experimental data and analysis are presented for each nuclide studied. A nonstatistical anomaly (the sign correlation eFect) was observed in thorium. Statistical analysis techniques were developed and successfully applied to determine the rms weak matrix elements and the weak spreading widths w . The value of w obtained from our analysis is about 1:8 × 10−7 eV, which is in qualitative agreement with theoretical expectations. The individual weak spreading widths are consistent with a constant or slowly c 2001 Elsevier Science B.V. All varying mass dependence and there is evidence for local :uctuations.  rights reserved. PACS: 24.80.+y; 25.40.Ny; 11.30.Er; 27.60.+y; 27.90.+b Keywords: Parity violation; Weak interaction; Compound states; Neutron resonances; Nuclear spectroscopy; Polarized neutron beam; Rms matrix element; Spreading width; Statistical theory

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1. Introduction 1.1. Parity violation in compound nuclei Since the discovery of parity nonconservation by Lee and Yang [94] and its experimental veriKcation by Wu et al. [149], the study of parity violation has been a major activity in nuclear and particle physics. Parity violation is a characteristic feature of the weak interaction. Although nucleons must have a weak current because of their  decay, it has been diMcult to calculate the eFect on nucleon–nucleon interactions. The Standard Model speciKes the coupling of the electroweak bosons between quarks and leptons but does not bear directly on the weak interaction between physical hadrons. The strong interactions that bind nucleons in nuclei and quarks in nucleons modify the weak interactions of quarks as given by the standard model. Calculations of the coupling constants for the weak interaction between nucleons have been performed by many theorists. The most widely used formulation is that of Desplanques, Donoghue, and Holstein— the (DDH) parameters [48]. Although the strength of the weak interaction indicated by these calculations is very small relative to the strong force, about 10−7 , the weak force has been studied extensively through parity violating observables. Measurements have been performed in nucleon–nucleon scattering, in few-body systems, and in light nuclei. The parity violation results for light nuclei are summarized by Adelberger and Haxton [2]. The interpretation of these latter measurements requires the detailed wave functions of the nuclear states involved. The present review describes a quite diFerent experimental and analysis approach to parity violation studies in medium and heavy nuclei. There is a very large enhancement of parity violation in low-energy neutron scattering. The helicity dependence of the forward scattering amplitude for neutrons interacting with complex nuclei is enhanced enormously at weak p-wave compound nuclear resonances, by factors as large as 106 [138,4]. This remarkable enhancement is produced by the combination of the large density of compound nuclear resonances and by the very large ratio of the s- to p-wave neutron scattering amplitudes. Theoretical and experimental work on the stochastic nature of highly excited nuclear states by Wigner [148], Hauser and Feshbach [81], Porter and Thomas [116,117], Dyson [52], French [72], Mehta [103], Brody et al. [31], and Bohigas and Weidenm,uller [19] led to the conclusion that matrix elements of operators between compound-nuclear states could be treated as independent Gaussian random variables. The mean-squared matrix element of a particular operator in an energy interval small compared to the spreading width of the residual strong interaction is expected to be constant. The fact that the compound nucleus displays stochastic properties leads to a new analysis approach that does not require detailed information about the nuclear wave functions. In 1990 parity-violating asymmetries were measured for several states in 238 U. These data led the collaboration to develop statistical techniques to extract the mean-squared matrix element of the weak interaction directly from the experimental data, without determining the matrix elements between each pair of states [21]. The realization that the weak interaction mean-squared matrix element could be determined experimentally changed the study of parity violation in the compound nucleus from a qualitative to a quantitative subKeld. The complexity of the system allowed application of statistical methods to treat the hadronic weak interaction theoretically as well [146,62,142]. As has been noted many times before, e.g.,

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[62,106], these two features of large enhancement factors and stochasticity should occur not only for compound nuclei, but in general for any strongly interacting quantum system. Another factor that we would like to emphasize is the dual role of weak interaction studies. Naturally the understanding of the eFective weak interaction in nuclei is a basic many body problem of appreciable interest. However, the weak interaction can also be used to study strongly interacting hadronic systems. This role is accentuated in the present experiments which involve complex nuclei. The present article complements earlier reviews [24,68,106] of the TRIPLE work that were written at diFerent phases of the experimental activity. After a short review of the theoretical literature on parity violation in compound nuclei, we discuss the history of the parity violation measurements in p-wave neutron resonances and their analysis. Our review is intended to be a comprehensive compilation of the TRIPLE Collaboration experiments and results. We provide a description of the experimental techniques and introduce the framework for the statistical analysis of parity violation data. The main focus of the review is on presentation of the experimental data for parity-nonconserving (PNC) cross section asymmetries and resonance parameters, and the analysis and results for the weak matrix elements. The spirit of the review is to provide suMciently detailed information that any interested reader can perform independent evaluation and analysis. 1.2. Brief review of the theoretical literature: 1960 –1990 The opposite parity admixture in the total wave function of a quantum system =

( + )

+

( − )

(1)

is represented by the mixing coeMcient . For single-particle states (SP), with the weak matrix element VSP ∼ 1 eV of Michel [104] and a major shell spacing of ∼8 MeV, one estimates the single-particle value SP ∼ 10−7 . Enhancement of the mixing coeMcient for compound nuclear states was Krst suggested by Haas et al. [79]. Using standard Krst-order perturbation theory for

=

 + |H  | −  (E − − E + )

(2)

with the weak interaction Hamiltonian H  , they considered the weak matrix element between + and − states V + − ≡  + |H  | −  :

(3)

They argued that due to the random nature√ of the compound state wave function, the matrix element V + − should be suppressed by 1= N with respect to the single-particle value, where N ∼ 105 is the number of contributing excited states in the oscillator well model which they were using. On the other hand, the energy denominator in Eq. (2) decreases as 1=N . As a √ result, a net dynamical enhancement of order N relative to SP was estimated for the mixing coeMcient . Haas, Leipuner, and Adair searched unsuccessfully for an enhanced asymmetry

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A in the -ray yield 1 + A (˜n · ˜k ) after capture of polarized neutrons on cadmium. The Moscow group at the Institute of Theoretical and Experimental Physics (ITEP) [1] was the Krst to discover parity violation, while performing measurements of the asymmetry coeMcient A in cadmium. Their result A = −(3:7 ± 0:9) × 10−4 was explained by Shapiro in terms of the dynamic and structural enhancement mechanisms acting together in heavy nuclei [123]. As early as 1969, Karmanov and Lobov [86] suggested a possible enhancement of -ray circular polarization near p-wave resonances in heavy nuclei. For p-wave resonances, Forte [63] considered the enhancement of PNC eFects, especially parity-violating neutron spin rotation, for the case of a large single-particle component of the resonance amplitude. Such resonances are characterized by exceptionally large neutron scattering widths, e.g., for p-wave resonances in 124 Sn. Forte suggested a search for an enhanced thermal neutron spin rotation in tin (due to the tail of the 62-eV resonance in 124 Sn). Simultaneously, Karl and Tadic [87] proposed a valence model of parity-violating eFects in neutron elastic scattering by a spherical potential well. In subsequent experiments [64] at ILL, Grenoble, the PNC spin rotation angle and the longitudinal cross section asymmetry were observed in natural tin, but not in an enriched 124 Sn target. The tail of the extremely weak absorptive resonance at Ep = 1:3 eV in 117 Sn was suggested as responsible for the observed eFects in tin. In 1980, Sushkov and Flambaum [138] estimated the size of the individual weak matrix J between s- and p-wave resonances to be 1 meV. They predicted percent-size elements Vsp longitudinal asymmetries p √ J
Vsp + − −   ns p= =2 (4) + + − (Es − Ep ) np s of the + and − helicity cross sections + and − for p-wave absorption in compound-state resonances in 117 Sn, 139 La, and other nuclei. The large asymmetries of √ the total cross sections have their origin in the PNC-mixing of large s-wave neutron amplitudes ns into small p-wave  neutron amplitudes np , producing the so-called kinematical enhancement. SuMciently large matrix elements and small spacings (Es − Ep ) between the parity mixed resonances provide a second (dynamical) enhancement factor described above. The predicted large PNC asymmetries were soon observed by the Dubna team [3,4] (see Section 1.3). Development of the reaction theory for PNC eFects followed. Bunakov and Gudkov [32,33] constructed a theory in the framework of the microscopic shell-model approach to nuclear reactions, which was aimed at describing the energy dependence of PNC eFects over a broad energy range. Stodolsky [137] applied the K-matrix formalism, resulting in a successful explanation of the enhancement of PNC eFects near neutron threshold. The comprehensive formal reaction theory of Flambaum and Sushkov appeared in 1984 [57]. Later, Vanhoy et al. [145] developed a combined R-matrix and angular correlation formalism with an emphasis on the nuclear spectroscopic aspects of the parity violation experiments. This approach, which uses statistical tensors to describe the polarization states of the beam and target, was extended by Gould et al. [75] to identify the Cartesian components of all P- and TRI-symmetry violating terms in the total neutron cross section. These theoretical studies provided a consolidated description of the PNC eFects in neutron scattering and neutron-induced reactions over a broad energy range.

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Other studies [85,58,34,146,143] set the stage for the statistical approach to the problem of theoretical estimation of the rms weak matrix element in heavy nuclei—the problem which is directly connected to the physical mechanism of the parity mixing. We limit the introduction to a few comments intended to prepare the reader for the presentation of the experimental results. In the now standard approach, the large PNC eFects are produced by parity mixing between compound states. In this case the individual weak matrix elements of p-wave resonances are mean-zero random variables with variance MJ2 . In this statistical approach, obtaining the rms matrix elements MJ does not require knowledge of the wave functions of individual resonances. The weak mean-squared matrix element is introduced as an expectation value J 2 MJ2 = E(|Vsp | )

(5)

on the same footing as the level spacing DJ or the neutron strength function Sl . The mixing between the s- and p-wave resonances occurs only for resonances with the same spin J . The second approach, involving a ‘valence mechanism’, assumes the dominance of direct matrix elements of the PNC potential between s- and p-components of the single-particle amplitudes in the reaction entrance channel. The valence model was introduced for a potential well by Karl and Tadic [87] and developed for neutron resonances by Zaretskii and Sirotkin [155,156]. In this model the same single particle matrix element participates in all resonances, giving a calculable regular contribution of a Kxed sign to the individual matrix elements. However, from considerations of the strength of the weak nucleon–nucleon interaction [58,60,50], it was shown that the estimates obtained assuming the valence mechanism are about two orders of magnitude smaller than the observed PNC eFects in heavy nuclei. Numerous statistical estimates of the variance MJ2 can be summarized by the expression MJ2 = ca

DJ 2 V fa (A) ; DSP SP

(6)

where DJ is the average spacing for levels with spin J , VSP is the single particle weak matrix element, DSP is the single particle spacing, and fa (A) is a factor that is diFerently (but weakly) dependent on A in diFerent theoretical formulations, which are labeled by the index a. The constant ca is the numerical factor calculated in a given approach a. It is convenient to consider the quantity w = 2 MJ2 =DJ ;

(7)

which is expected to be nearly constant as a function of mass number A—a conjecture that must be conKrmed experimentally. This quantity has the magnitude of ∼1 × 10−7 eV and is known in the literature as ‘the weak spreading width’. Although widely used, the concept of a weak spreading width in the isolated resonance regime may seem unusual. The practical advantage of the weak spreading width is that it removes most of the level density eFects, thus making possible the comparison of PNC matrix elements measured in diFerent nuclei. This is similar to the procedure followed for isospin mixing in the compound nucleus [80]. The PNC strength arises explicitly in terms of the single particle matrix element in Eq. (6). The reviews by Flambaum and Gribakin [62] and by Desplanques [50] present the deKnitions of WSP used

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in the theoretical literature as well as the connection of WSP with the strength of the weak nucleon–nucleon interaction. Another way to express the strength of the weak interaction in the compound nucleus is through the relative size " of the symmetry breaking part of the Hamiltonian H = h(1) + V PC + "U PNC ;

(8)

where h(1) is the one-body part, and V PC and U PNC are the two-body parity-conserving and parity-breaking residual interactions (which have the same norm). The use of statistical spectroscopic methods to calculate matrix elements and level densities then leads to the relationship w = 2 cw "2

(9)

with the constant cw determined from the matrix elements of V PC , U PNC , and the noninteracting eigenvalue densities. The experimental value w ∼ 1 × 10−7 eV obtained for the Krst time by Bowman et al. [21] leads to " = 4 × 10−7 , assuming that the results of the cw calculations performed in [73] for the time-reversal noninvariant interaction can be applied for PNC interactions as well. The calculated value of cw was 100 keV, but diFers by a factor of three for the nuclei Er, Th, and U [73], suggesting the possible size of :uctuations in the spreading width due to nuclear structure. 1.3. Brief history of the experiments: 1980 –1990 As mentioned in Section 1.2, experiments on longitudinal asymmetries of neutron cross sections began in 1980 after the ILL measurements [64] on tin with polarized cold neutrons. In 117 Sn PNC eFects were observed: the spin rotation angle % = (3:7 ± 0:3) × 10−5 rad=cm and the cross section longitudinal asymmetry A = (9:8 ± 4:0) × 10−6 . The latter eFect was conKrmed with improved accuracy by the Gatchina group [90] with the result A = (6:2 ± 0:7) × 10−6 . The PNC asymmetry was shown to be entirely due to the capture component of the thermal neutron cross section. The tail of the 117 Sn absorptive resonance at Ep = 1:3 eV extending to the cold neutron energy of about 2 meV was suggested [64,138] as the cause of the observed PNC eFects. The longitudinal asymmetry of the total p-wave capture cross section is proportional to the imaginary part of the forward scattering amplitude, and therefore should increase dramatically at the p-wave resonance Ep = 1:3 eV. This resonance behavior was measured directly and the large size of the asymmetry conKrmed experimentally at JINR, Dubna, in 1981 [3] for the 1.3-eV resonance of 117 Sn and later [4,5] for p-wave resonances in 81 Br, 111 Cd, and 139 La. Weak matrix elements of ∼1 meV, and mixing coeMcients of ∼10−4 were inferred. These values agreed with the theory of parity mixed compound states [138]. Experiments at Dubna were performed using the IBR-30 pulsed reactor as a neutron source for time-of-:ight measurements. The reactor was operating at a mean power level of 20 kW with a neutron pulse width of 70
s and a 5-Hz pulse repetition rate. Transmission of longitudinally polarized neutrons was measured by a neutron detector located at the end of a 58-m :ight path. The neutron beam was polarized by transmission through a longitudinally polarized proton Klter. The neutron spin was reversed every 40 s by an adiabatic spin :ipper.

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The proton-Klter transmission technique for polarizing resonance neutrons was Krst developed at the Joint Institute of Nuclear Research (JINR) by another team [51]. Their method makes use of the large polarization cross section for neutron–proton scattering. Neutrons in the singlet spin state have a much larger scattering cross section than neutrons in the triplet state, and as a result the singlet neutrons are preferentially Kltered out of the beam after passing through a suMciently thick polarized proton target. The technique provides typical neutron beam polarizations of 70%. In order to improve the time-of-:ight resolution, the Dubna team later used a booster operation mode of the reactor with the 30-MeV electron accelerator. In this case the mean power level was 5 kW with pulse duration 4
s and 100-Hz repetition rate. Even in this mode of operation, the useful energy range for parity violation measurements was limited to an upper energy of ∼20 eV. A typical measuring time was 200 –300 h per target. The success of the Krst PNC measurements in neutron resonances stimulated other groups to develop similar polarization techniques at diFerent neutron sources. At the KIAE (Kurchatov Institute of Atomic Energy), Moscow, a linear electron accelerator with a uranium neutron-production target and a water-slab moderator was used. Pulse widths of 100 and 300 ns at repetition rates of 700 Hz provided the possibility of better neutron energy resolution. However, the low neutron :uxes set approximately the same upper energy limit as at Dubna. An innovation was a diFerent geometry: neutrons Krst passed through the target under investigation, then through a spin-:ipper, and Knally through a polarized-proton Klter acting as the analyzer. The neutron spin was reversed every 15 s. The neutrons were counted by a detector located 12 m from the neutron-production target. The same resonances in 117 Sn and 139 La were studied and the PNC eFect was conKrmed [15]. At KEK (High Energy Institute), Tsukuba, the pulsed neutron beam was generated by an 3-
A, 500-MeV proton beam on a uranium spallation target with subsequent moderation in a water slab. Although the proton burst width was 40 ns, the FWHM time spread introduced by the moderator was about 2
s at neutron energy 1 eV and 0:7
s at 10 eV. The KEK group Krst applied the total capture-yield detection method for measuring PNC eFects in neutron resonances with a -ray detector located at 7 m from the neutron source [99]. The proton polarization in the proton Klter was in the vertical direction and was rotated to the direction along the beam axis by a magnetic guide Keld. The longitudinal polarization direction of the beam was reversed every 4 s. The KEK group Krst achieved improved precision for the PNC cross section asymmetry of the 0.75-eV resonance in 139 La [100]. References to the latest KEK measurements are given in Section 4. The best possibility for conducting PNC experiments with resonance neutrons was at the LANSCE (Los Alamos Neutron Scattering Center) spallation neutron source installed after the proton storage ring. The 70-
A, 800-MeV proton beam is from the linear accelerator (then called the LAMPF linac). The beam consists of 125-ns FWHM wide pulses with a repetition rate of 20 Hz. The Krst use of this source for parity-violation measurements was reported by C. Bowman et al. [20]. For these LANL measurements on 139 La, an optically polarized 3 He Klter was developed as the neutron beam polarizer. The neutron transmission was measured at a :ight path of 11 m. For the next generation of parity-violation experiments, which were aimed at the measurement of many p-wave resonances, the TRIPLE Collaboration was formed. This opened a new page in the history of PNC experiments which we follow in the next subsection. For the Krst experiments a conventional polarized proton-Klter originally built by Keyworth et al. [88]

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was refurbished. Parity violation was studied in 238 U by Bowman et al. [21]. The formalism for extracting the weak interaction mean-squared matrix element M 2 directly from a set of measured asymmetries was introduced in this paper and the Krst experimental estimate of the weak spreading width was obtained. We conclude the presentation of the early parity violation studies in compound nuclei by noting several classes of PNC experiments with polarized thermal neutrons, such as parity violation in Kssion, PNC asymmetry of the total thermal neutron cross section, and parity violating -ray asymmetries in the integrated yields and in the individual -ray transitions. These experiments are reviewed by Danilyan [45] and KrupchitskiVi [92]. 1.4. TRIPLE Collaboration experiments: 1990 –2000 Although the Krst PNC results in p-wave resonances were very impressive, the Dubna data were restricted to one or two p-wave resonances per target in the neutron energy region up to ∼10 eV. The breakthrough came from the experimental program of the TRIPLE Collaboration which developed experimental techniques to perform measurements on a number of resonances for each nucleus studied. A seminal event for parity violation measurements in the compound nucleus was a meeting held in Chapel Hill, NC in 1987. The meeting was entitled ‘Tests of Time Reversal Invariance in Neutron Physics’ and almost all of the papers in the conference proceedings concern time reversal invariance [118]. However, a large part of the discussion at that workshop focussed on parity violation experiments. Following this meeting a new collaboration was formed—[T]ime [R]eversal [I]nvariance and [P]arity at [L]ow [E]nergies or TRIPLE. Although the original goal was the study of both time reversal and parity, the parity violation measurements were planned as the initial steps. The high intensity of epithermal neutrons available at the Los Alamos facility made it feasible to extend the neutron resonance PNC measurements to much higher neutron energies. The Krst TRIPLE measurements were performed in 1989 on 238 U by Bowman et al. [21,157] and on 139 La by Yuan et al. [152] with a single-lanthanum method and with the polarizationindependent double-lanthanum method. In the following year 232 Th [65,66] was measured with the same equipment; with additional experience the experimental procedures were improved. A number of statistically signiKcant PNC eFects were observed. This measurement produced the largest surprise of the entire series of measurements—all of the PNC eFects had the same sign! This result violated our basic view of the reaction mechanism. Our ansatz was that the compound nucleus is a statistical system described by Random Matrix Theory, and consequently the weak matrix elements should be random variables with mean zero. In addition to raising this key question concerning the statistical nature of the process, the observation of seven statistically signiKcant PNC eFects in 232 Th established empirically several important points. First the data were consistent with the rule that every resonance with the proper spin will show parity violation if the measurement is suMciently precise. This meant that an extensive study of a number of nuclei was indeed practical. Second was that the experimental system was not satisfactory for an extensive and careful study of PNC eFects in neutron resonances. Third was that the simple two-level approximation was not suMcient, and that the analysis must be extended to include the eFects of many s-wave resonances. In

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addition our resonance analysis—with an eFective single level approximation for Doppler, beam, and detector broadening—was not suMcient for the complicated resonance structures observed. It was also clear that the initial measurements should be repeated to conKrm or to reject the nonstatistical results in 232 Th. The new experimental system became operational in 1993—with a new polarizer, a new spin :ipper, and a new neutron detector. This system is described in Section 2. In addition, it became clear that we needed to study targets that were not available in the large quantities required for a standard transmission measurement. The solution was to extend the neutron spin transport system to the end of the :ight path and to locate the target at the end of the :ight path and surround it with a -ray detector array—the vastly increased detector solid angle makes measurements with small samples feasible. A prototype capture -ray detector was also tested during this time, prior to the fabrication of a Knal -ray detector array. The development of a new resonance analysis code FITXS that incorporated a multilevel formalism for the cross sections and a realistic instrumental resolution function was a major eFort by TRIPLE and took a long time. Fortunately the initial resonance analysis code gave results that were qualitatively correct for most of the p-wave resonances and even quantitatively correct for isolated resonances. Therefore we were able to obtain preliminary PNC results before we had a complete description of the beam and detector resolution functions. Our Krst measurements with the new experimental system repeated the transmission measurements on 238 U and 232 Th. A detailed description of the characteristics of each experiment— targetry, experimental method, and any special features, as well as the resonance parameters and the PNC longitudinal asymmetries—is given in Section 4. The new system yielded much better data and more PNC eFects, but essentially conKrmed all of the prior results with much better statistics. The nonstatistical sign eFect in 232 Th was conKrmed and extended to 10 PNC asymmetries in a row. In addition the spins of a number of p-wave resonances in 238 U were measured [78]. As expected, all of the resonances that showed parity violation had J = 1=2, and that none of the J = 3=2 resonances showed parity violation. During the 1993 run we also studied 107; 109 Ag, 115 In, and 93 Nb—all in transmission. In addition we studied an enriched target of 113 Cd with the prototype -ray detector. Since the total resonance width for these p-wave neutron resonances is essentially equal to the capture width, measuring the total -ray emission is equivalent to measuring the total cross section. In 1993 a workshop was held in Dubna entitled ‘Time Reversal Invariance and Parity Violation in Neutron Reactions’. Contrary to the Krst meeting on this topic, the majority of papers related to parity violation [76]. In 1994 the new -ray detector was commissioned. The -ray detector was essential for PNC measurements on targets that were not available in suMcient quantities for a transmission measurement. Another prime use of the -ray detector was the study of isotopically enriched targets for isotopic identiKcation. With the success of the new system, we observed many new resonances. For targets with more than one isotope, the transmission data often could not assign the weaker p-wave states to a speciKc isotope. The problem is illustrated by silver. Silver consists of two isotopes with approximately equal abundances. Since we observed many new resonances, additional measurements were required for their assignment to a speciKc isotope. This method worked so well that we applied a similar approach to antimony (again with two equally abundant isotopes) and to xenon and palladium (both with several isotopes).

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In 1995 there was a workshop held in Trento entitled ‘Parity and Time Reversal Violation in Compound Nuclear States and Related Topics’ [13]. It is interesting to note that in the title the order of Parity and Time Reversal is now reversed, and that the term ‘compound nucleus’ is included. Although the parity violation experiments proved extremely successful, the goal of time reversal invariance (TRI) studies at the LANSCE spallation source was not achieved. Although the general idea of utilizing resonance enhancement in experiments that test parity and time reversal invariance simultaneously received a great deal of attention, no practical experiment has yet been proposed and supported. Most of the diMculties center around targetry problems and eFects mimicking TRI violation. These issues are discussed at length in the literature and in the proceedings of the three workshops listed above. In 1995 the TRIPLE Collaboration studied parity violation with targets of natural xenon, antimony, iodine, and cesium via transmission, and 106 Pd and 108 Pd with the -ray detector. In 1996 PNC eFects were measured in 117 Sn and 103 Rh with the -ray detector, and with a natural palladium target in transmission. In 1997 enriched 104 Pd, 105 Pd, and 110 Pd targets were measured with the -ray detector to obtain spectroscopic information. With these measurements the experimental part of the TRIPLE program was completed. In 1997 the FITXS code became fully operational. Therefore the entire body of data was reanalyzed with the new analysis program to obtain the longitudinal asymmetries. The results for all of the data obtained by TRIPLE are listed in Section 4. 1.5. Theoretical developments: 1990 –2000 The study of parity violation in compound-nuclear reactions was advanced through application of statistical ideas by Bowman et al. [21] and by Weidenm,uller [146] to TRIPLE data on neutron resonances. In the TRIPLE approach [21], the root-mean-square matrix element MJ deKned by Eq. (5) is obtained by a Bayesian analysis, as described in Section 3, directly J . from the ensemble of measured asymmetries {p} without explicit reference to individual Vsp This solves the problem that the individual matrix elements cannot be determined when several neighboring s-wave resonances contribute to the asymmetry p in a given p-wave resonance. The individual matrix elements cannot be obtained because there are several unknowns and only one equation. However, as discussed in detail in Section 3, since all of the unknown matrix elements are sampled from the same underlying distribution, it is possible to obtain the variance, M 2 , of the matrix element distribution. Although the spirit of this statistical approach is straightforward and a value of M 2 was obtained for the spin I = 0 target 238 U [21], the extension to cases with nonzero spin and the incorporation of incomplete spectroscopic information becomes complicated, as Krst indicated by Bunakov et al. [35]. The most comprehensive description of the analysis for the spin I = 0 case was given by Bowman et al. [28]. The practical extraction of MJ from TRIPLE data in the Bayesian likelihood framework is described in Section 3. There were contrasting views on the use of this analysis method for PNC data. Bunakov [36] argued that one can only extract an upper limit for MJ when the spins of resonances for the I = 0 targets are unknown. The opposite point of view [29] was that reliable estimates can be obtained even in this case. The p-wave spin measurements by the IRMM group [78] settled the issue in favor of the TRIPLE approach. Further development of the Bayesian likelihood method and its

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application to extraction of fundamental symmetry breaking matrix elements was given by Davis [46,47]. The entire statistical ansatz rests on the fact that the compound nucleus is known to behave statistically—random matrix theory (RMT) describes the :uctuation properties of the spectra of highly excited nuclear systems. RMT is described in an early review by Brody et al. [31] and in the recent comprehensive review by Guhr et al. [77]. The most comprehensive theoretical examination of parity and time reversal violating eFects in the compound nucleus was provided by Flambaum and Gribakin [62]. Although they focus on the nucleus, Flambaum and Gribakin emphasize that the large enhancement arising from the close spacing of levels is generic and should apply to many complex many-body systems. Feshbach et al. provide reviews that focus more directly on the TRIPLE Collaboration data [55,56]. They consider symmetry violation in the compound nucleus within the framework of the Feshbach uniKed theory of nuclear reactions and approach the sign correlation issue from the optical model viewpoint. The observation of the nonstatistical ‘sign correlation’ eFect in 232 Th led to an enormous amount of discussion and speculation about the generality and the origin of the eFect [23,10,59,91,95,38,11,39,13,61,82,14,49,55]. To Krst order one can divide the attempted explanations into two general categories—the sign correlation either has some generic origin (such as a distant state, either single particle or specialized doorway) or is speciKc to thorium (such as a local doorway). A detailed discussion of the sign correlation eFect is given in Section 6. The attempts to relate the measured results for the weak interaction spreading width to the nucleon–nucleon force require a description of the complicated nuclear system and of the oneand two-body pieces of the nuclear force. The method of choice is statistical spectroscopy. This method was reviewed by Tomsovic in the Trento proceedings [141]. First eForts to apply this approach to the TRIPLE data were by Bowman et al. [22] and by Johnson and Bowman [83]. Johnson [84] reviews these eForts. Some aspects of this problem are also discussed in the review by Bowman et al. [24]. A recent application of this method to the TRIPLE data is by Tomsovic et al. [142]. 2. Experimental techniques With spallation neutron sources, neutron resonances can be studied over a large energy range, which is a prerequisite for using the statistical approach to determine the mean-squared weak matrix element. Spallation sources also make possible accurate determination of the neutron energy using time-of-:ight (TOF) techniques. In addition, the pulsed nature of the source has other advantages in the determination of detector backgrounds and in situ control of systematic errors. In this section we describe how the high intensity pulsed neutron :uxes available at LANSCE are used to study parity violation in neutron resonances. 2.1. PNC neutron transmission and capture experiments At LANSCE the TRIPLE Collaboration developed a sensitive apparatus for PNC studies in neutron resonances with longitudinally polarized neutrons. Two approaches were adopted to

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measure the longitudinal asymmetries of the resonance neutron cross sections. One method is based on measurement of the neutron transmission through a target, while in the other method one measures the total -ray yield from neutron capture in a target. In both methods, two neutron TOF spectra, N + and N − , are measured with neutron spins parallel or anti-parallel to their momenta. From these two spectra, a longitudinal asymmetry for a p-wave resonance cross section is obtained. The transmission method for the resonance neutron PNC measurements was pioneered by the Dubna team (see Section 1.3). A p-wave resonance appears as a small dip in the detector transmission yield N ± = N0 exp[ − np (1 ± fn p)], where N0 is the detector yield when the p-wave cross section p = 0, n the number of target nuclei=cm2 , fn the neutron beam polarization, and p the PNC longitudinal asymmetry. For an unbroadened resonance, the relative diFerence & of the neutron detector yields N + and N − is &≡

N+ − N− = −tanh(pfn np ) −pfn np ; N+ + N−

(10)

where the p-wave resonance cross section is p (E) =

gn  : 2 k (E − Ep )2 + (=2)2

(11)

Here n and  are the neutron width and the total width of the resonance, g is the statistical factor, k the neutron wave vector, and Ep the resonance energy. For an ideal unbroadened resonance one obtains the PNC asymmetry p directly from Eq. (10). In practice, Doppler broadening and instrumental resolution broadening must be included. For a sensitive measurement in a weak p-wave resonance, the transmission method requires a large quantity of sample material. The values of the observed longitudinal asymmetries lie in the range of 10−1 –10−3 , which for a typical p-wave resonance cross section p ∼ 10−24 cm2 , corresponds to a transmission asymmetry & = 10−2 –10−4 for n = 1023 =cm2 . Therefore one must use target thicknesses of order n ∼ 1023 =cm2 . Such thicknesses require samples with linear dimensions of ∼10 cm and masses of several kg. Due to the lack of the required quantity of target material, all nuclei of interest cannot be studied by the transmission method. The second method, measurement of the total -ray yield from neutron capture, was shown [100,124] to be more suitable for studies of parity violation using thin, isotopically enriched samples. In this method an ideal -ray detector surrounding a thin target intercepts all capture  rays emitted by the A + 1 compound system. The -ray yield is proportional to the total capture cross section p (E) p (E) =

gn  ; 2 k (E − Ep )2 + (=2)2

(12)

where  is the resonance radiative capture width. The p-wave capture resonance cross section p (E) has the same shape as the total cross section, but with  replaced by  . Since the neutron

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resonance widths are extremely small, the total width for such resonances in any non-Kssile heavy nucleus is given by  = n +   . Consequently, p (E) p (E), and therefore measuring PNC cross section asymmetries by capture and transmission are equivalent methods for the study of spatial parity violation in the compound nucleus. For a thin sample with ideal resolution, the detector count rate N is proportional to the capture cross section p and one obtains the longitudinal asymmetry p directly from the relative diFerence & of the -ray detector count rates N+ and N− & ≡

N+ − N− −pfn : N+ + N−

(13)

Complications due to Doppler and instrumental broadening are the same as in the transmission method. 2.2. LANSCE short-pulse spallation neutron source The short-pulse spallation neutron source of the Manuel Lujan Jr. Neutron Scattering Center (MLNSC) at LANSCE was designed to optimize the production of thermal and epithermal neutrons [96]. The 625-
s long, 797-MeV H− beam pulses from the LANSCE linear accelerator are injected into a Proton Storage Ring (PSR). As part of the injection process, the H− particles are stripped to H+ . In the PSR protons are accumulated and compressed into pulses with a roughly triangular-shaped longitudinal proKle, 250-ns wide at the base. The proton pulses are directed onto a target at the rate of 20 Hz and with an average current of 70
A. The neutron production target consists of two 10-cm diameter tungsten cylinders. The cylinders are located one above the other along the vertical proton beam axis. The upper cylinder is 7.5-cm long, while the lower cylinder is 27-cm long. The gap between the cylinders is 14 cm and is surrounded by neutron moderators and re:ector materials. The horizontal :ight paths are located at the level of the gap to minimize contamination of the neutron beam from  rays and high-energy neutrons. Our measurements were performed on :ight path 2, which has a gadolinium-poisoned water moderator and a cadmium=boron liner to reduce the number of low-energy neutrons emerging in the tail of the neutron pulse. At epithermal energies the neutron :ux from this ‘high-resolution’ moderator has a Maxwell–Boltzmann distribution with a maximum at 40 meV. In the higher energy region the :ux follows a 1=E 0:96 dependence. The neutron :ux, the number of neutrons with energies between E and E + XE per second on the detector, is approximated (assuming no material in the beam) by dN neutrons XE = N 0 0:96 · f · ) ; dt E eV · s · sr

(14)

where the constant N 0 = 2 × 1012 , XE is the energy width of a TOF channel, f ∼ 0:63 is the fraction of the 13-cm × 13-cm moderator surface viewed by the detector through the collimators, and ) ∼ 4 × 10−5 sr is the solid angle of the transmission detector at 56 m from the source.

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Fig. 1. Layout of the 62-m long polarized neutron beam line at the LANSCE spallation pulsed neutron source.

2.3. Polarized neutron beam line for PNC experiments 2.3.1. Beam line layout Roberson et al. [119] describe the experimental setup as utilized by the TRIPLE Collaboration in the initial experiment on 238 U. Although the experimental philosophy remained the same, for the later experiments many improvements were made to the apparatus. The latest layout of the polarized neutron beam line is shown in Fig. 1. After the water moderator the neutrons are collimated to a 10-cm diameter beam inside the 4-m thick biological shield which surrounds the target crypt containing the spallation target, and the water and hydrogen moderators. After the bulk shield the neutrons pass through a :ux monitor, a pair of 3 He and 4 He ion chambers. This ion chamber system is used for a sensitive (10−4 level) monitor of the beam stability. The chambers are Klled to a pressure of 760 Torr either with 3 He or 4 He gas. The 3 He chamber is sensitive to neutrons via the 3 He(n; p)3 H reaction, while both chambers are sensitive to

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 rays through the photo-electric eFect, the Compton eFect, and pair production. The diFerence between the counts in the two chambers yields the neutron :ux, which is measured for each beam burst. This beam monitor is described in detail by Szymanski et al. [139]. Next, the neutrons pass through a polarized-proton spin Klter where one of the two neutron helicity states preferentially scatters out of the beam, leaving a beam of longitudinally polarized neutrons. The primary neutron spin reversal, every 10 s, was accomplished by passing the polarized neutron beam through a spin :ipper located next to the proton spin Klter. The samples in the transmission measurements were installed in the polarized beam line at the exit of the spin :ipper. The neutron transmission detector, not shown in Fig. 1, is located at 56 m from the neutron source—about 3 m upstream from the -ray detector. In the neutron capture PNC measurements the samples are placed inside the -ray detector. Guide Kelds are provided to preserve the neutron spin direction as the neutrons travel inside the evacuated beam line downstream to the target at the end of the 59-m :ight path. Three additional collimator sets are installed between the spin :ipper and the -ray detector to form a 9-cm diameter beam spot at the target. Finally, a neutron polarimeter consisting of a 139 La target and 6 Li neutron detector, monitors the neutron polarization after the -ray detector. In the following sections we discuss essential features of the beam-line components. 2.3.2. Neutron spin
(15)

where fH is the proton polarization, n the number of protons=cm2 , and P the polarization cross section. In the energy region from 1 eV to several keV, P has a nearly constant value of 16:7 b. Neutrons with spin direction opposite to the proton polarization will be scattered, while neutrons with parallel spin direction will be attenuated. The protons in the target, in our case frozen ammonia, are polarized by the dynamic nuclear polarization (DNP) method at 1 K and in a 5-T magnetic Keld [112,113]. This neutron spin Klter is a cylindrical disk— 80-mm diameter and 13-mm long. The protons in the Klter were polarized more than 80%. In DNP microwave pumping is used to populate the nuclear state of interest. With diFerent microwave transition frequencies one can obtain proton polarization parallel or anti-parallel to the magnetic Keld direction without changing the magnetic Keld direction or strength. Reversal of the proton-polarization direction provides a means to check for possible systematic errors. Since the proton polarization reversal takes 1–2 h, this reversal was performed only a few times during the 1–2 week period of study for a typical target. The proton polarization is monitored by the nuclear magnetic resonance (NMR) method. Since the NMR measurement does not probe the entire target volume equally, and the distribution of ammonia in the target is not known, NMR may not provide a reliable absolute neutron polarization measurement. However, it does provide a rapid relative determination of the proton and thus the neutron beam polarization. The NMR measurement was calibrated either by comparing the neutron transmission through the proton target while it is polarized and unpolarized, or by adopting the large PNC eFect at 0:748 eV in 139 La as a standard and determining the neutron beam polarization from the

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measured asymmetry using Eq. (10). These methods to determine the neutron beam polarization are discussed in detail by Penttil,a et al. [112] and Yuan et al. [152]. The typical neutron beam polarization was about 70%. 2.3.3. Spin =ipper for resonance neutrons Time-dependent systematic eFects arise from drifts or :uctuations in experimental parameters such as detector gain, incident neutron :ux, and neutron polarization. The primary technique for reducing the false asymmetries generated by these changes is a rapid spin reversal by a spin :ipper described by Bowman et al. [27]. The spin :ipper consists of a series of longitudinal and transverse magnetic Kelds arranged along the neutron beam line. The longitudinal coils form a solenoidal Keld that points along the beam direction for the Krst half of the length of the spin :ipper and opposite to the beam direction for the second half. The transverse Keld is produced by Helmholtz coils on both sides of the spin :ipper and is perpendicular to the beam direction. As a function of distance along the beam direction, the longitudinal Keld follows a sine function, and the transverse Keld has a cosine dependence. The addition of these two ◦ components produces a Keld with constant magnitude of 100 G that rotates 180 over the length of the 2-m long spin :ipper. With the transverse coils oF, the neutrons pass through a magnetic Keld that reverses direction at the center of the spin :ipper and which has very small transverse components. The neutrons of interest travel too fast to have their spins reversed. With the transverse coils on, the magnetic ◦ Keld rotates 180 over the length of the spin :ipper. The neutrons adiabatically follow the magnetic Keld and emerge with their spins reversed. EFects of radial Keld components on oF-axis neutrons and the energy dependence of the spin-:ipping eMciency are discussed in detail by Bowman et al. [27]. During the experiments the neutron spin direction—parallel or antiparallel to the neutron beam momentum (positive or negative helicity state)—is rapidly reversed in an eight-step sequence controlled by the data acquisition computer. In the sequence each spin state lasts 10 s. The use of this sequence reduces the eFects of detector gain drifts and residual transverse magnetic Kelds on photomultiplier tubes to values smaller than other systematic errors. 2.3.4. Spin transport The magnetic Kelds from the polarizer and the spin :ipper guide the neutron spin to a distance of 9:7 m along the :ight path (the normal location of a transmission sample). To have suMcient neutron energy resolution in the TOF measurements, the target and the -ray detector are installed at the 59-m position relative to the water moderator. To prevent the neutrons from depolarizing in either the Earth’s magnetic Keld, or in stray magnetic Kelds during their ∼50-m long :ight path after the spin :ipper, magnetic guide Kelds were provided by wrapping the aluminum beam pipes with current carrying wires to produce a 10-G solenoidal Keld. To create a homogeneous Keld over the volume of the capture target, two thin-walled graphite cylinders of 5.1-cm radius and 130-cm length were wound and inserted into the up and downstream side of the -ray detector. The downstream part of the graphite tube guides longitudinal polarization to the 139 La target of the neutron polarimeter discussed in the following section. Monte Carlo calculations, where random neutron trajectories were transported through the spin transport Keld

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system, were performed by Crawford [44] to estimate the resulting depolarization of the neutron beam. The depolarization, D, is given by D=1−

"i |z |"i  ; "f |z |"f 

(16)

where z is the z-component Pauli matrix, and "i and "f are the initial and Knal spinor wave functions, respectively. The beam depolarization was an average over many neutron trajectories. At a neutron energy of 0:75 eV, the calculated depolarization value of 2.5% can be compared with the experimentally determined value of Dexp =(2 ± 4)%. The experimental value is obtained by comparing the beam polarizations measured at 9:7 m, fn (9:7 m), and at 61 m, fn (61 m), as Dexp = 1 −

fn (9:7 m) : fn (61 m)

(17)

2.3.5. Neutron polarimeter Our neutron polarimeter relies on the large and well known PNC asymmetry p = 0:095 [152] and the cross section p (E) at the 0.748-eV resonance in 139 La. With a transmission detector, the count rate asymmetry & is measured, and then the neutron beam polarization fn is determined using Eq. (10). In the transmission experiments a 139 La target is inserted for beam polarization measurements in the beam at 9:7 m. The thin capture targets allow the beam polarization measurement after the -ray detector and therefore a lanthanum target of n=6:53×1022 nuclei=cm2 is placed permanently at 61 m, followed by a 1-cm thick, 13-cm diameter, 6% by weight 6 Li-glass neutron transmission detector. For the beam depolarization measurements the lanthanum target was placed Krst at 9:7 m and then at 61 m, and the polarizations fn (9:7 m) and fn (61 m) were obtained in order to evaluate Dexp in Eq. (17). 2.4. The neutron transmission detector The neutron transmission detector for PNC measurements with spallation sources must have an energy independent detection eMciency over a large neutron energy range and must be capable of handling high instantaneous neutron rates. Our large-area neutron transmission detector consists of an array of 55 10 B-loaded liquid scintillator cells arranged in a honeycomb pattern as shown in Fig. 2. The eFective diameter of the detection area of the 55-module detector is 43 cm. The depth of the cells is 4 cm. The cells are separated by 1.6-mm thick aluminum walls with small holes allowing the scintillator liquid to :ow from one cell to another. The incident neutron passes through a 1.6-mm thick front aluminum window to enter the scintillator cell. The detector is discussed in detail by Yen et al. [151]. The boron-loaded liquid scintillator is trimethyl benzene solvent loaded with 10 B enriched trimethyl borate C3 H9 BO3 . We measured the 10 B concentration Nb by performing a neutron √ transmission experiment through a 5-mm thick scintillator sample and analyzing the 1= En component of the total cross section. We obtained Nb = (2:94 ± 0:10) × 1021 atoms=cm3 , which

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Fig. 2. The 55-module 10 B-loaded liquid scintillator detector. Top—the honeycomb arrangement for the 4-cm thick cells, with each cell viewed by a 5-cm diameter photomultiplier tube (PMT). Bottom—the cross sectional view.

corresponds to a 10 B content of about 5% by weight. The ratio of hydrogen and carbon to 10 B nuclei was taken as 18 : 1 and 11 : 1, respectively. The scintillation light from the capture reaction is detected by 55.5-cm diameter photomultiplier tubes (PMT). They are placed individually into 55 holes in the aluminum holder mounted against the scintillator container as shown in Fig. 2. A 1.6-mm thick glass window and a silicon optical coupling pad separate the PMT from the scintillator. A single photoelectron pulse at the anode of the PMT has a rise-time of ∼2 ns and a FWHM of ∼4 ns, while the FWHM of a neutron pulse is ∼8 ns. 2.4.1. Neutron mean capture time in the detector The energy resolution of our TOF spectrometer is discussed in Section 2.6. At high energies a substantial time broadening is introduced by the liquid scintillation detector [151]. For an inKnitely large scintillator one expects a delayed exponential detector time response exp(−t=+d ) for neutrons entering the detector at t = 0. In this case there is a single time constant (the

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Fig. 3. Neutron detection eMciency of the neutron detector. The dots represent the experimental results and the solid line is the Monte Carlo calculated eMciency.

neutron mean capture time) +d = (Nb v v)−1 , where v is the capture cross section for velocity v. Because of the 1=v dependence of the cross section, +d is independent of the neutron energy and can be calculated from (Nvth vth )−1 , where vth and vth are the cross section and velocity for thermal neutrons. Using the value of the boron atomic density Nb given in the previous section, one obtains an upper estimate of +d = 403 ns. In a real detector, neutron leakage due to edge eFects or to an in:ux of neutrons moderated in surrounding materials may contribute. Experiments were performed to measure +d [42]. The average experimental value for the neutron mean capture time in the detector is +d = (416 ± 5) ns. 2.4.2. Neutron detection e>ciency and background The mean free path for n–p scattering is ∼1 cm in this scintillator. The 4-cm thick liquid 10 B-loaded scintillator is expected to have a high neutron detection eMciency because it conKnes neutrons scattered by protons until the capture by 10 B occurs or the neutron escapes. The energy dependence of the eMciency &d versus E was calculated by a Monte Carlo simulation and also determined experimentally. The detection eMciency is the ratio of the number of detector counts minus the background counts, to the number of incident neutrons. We performed transmission measurements in the energy range from 25 to 900 eV using thin and thick Pr 2 O3 targets. In this energy region praseodymium has several strong resonances with energies Ei . Measurement with a thick sample determines the beam background at the resonance energies Ei of these ‘black’ resonances. For all other energies E the background was interpolated. Measurement with the thin sample served to determine the energy dependence of the eMciency by comparison with the well known energy dependence of the neutron :ux. The absolute value of the eMciency was normalized to the calculated value of 93% at E = 25 eV. The experimental data on &d versus E are shown in Fig. 3; within errors they agree with the Monte Carlo simulation. The neutron detection eMciency decreases slowly from a value of 95% at E = 10 eV to a value of 71% at E = 1000 eV. The largest sources of background in the transmission measurement are fast neutrons scattered and moderated in the beam pipe components and neutrons produced in secondary reactions.

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These neutrons can reach the detector at times when the neutrons of interest are measured and thus contribute as background. In addition to detecting neutrons, the 10 B-loaded scintillator is sensitive to  rays that originate from several processes during and following neutron production. The total background in the neutron energy range from 1 to 400 eV was measured by the technique of ‘black’ resonances described in detail by Yen et al. [150]. These saturated resonances remove all neutrons of a given energy from the beam while leaving the background essentially unchanged. 2.4.3. Data acquisition The instantaneous counting rate in each PMT can be 10 MHz, giving a total rate for the whole detector of greater than 500 MHz. The data acquisition system that processes the signals from the detector is described by Knudson et al. [89]. It is a hybrid system operating in a digital-analog mode. The signals from each PMT are standardized by a discriminator set above the single photo-electron noise and sent to the main electronics setup located about 150 m away. There the signals are reshaped in discriminators and combined in an analog summing module to yield the total ‘current’. This analog signal is processed by a transient digitizer which samples the data with a selectable dwell time (TOF channel width) and accumulates the data in an 8192-channel memory. The full width of the shaped signals is the same as the dwell time; each neutron event is registered in one and only one time channel. The memory module is read out after each 10-s spin reversal interval and accumulated by our data acquisition computer for storage and later analysis. The transient digitizer features a subtract as well as an add mode; we exploit this by retriggering it in the subtract mode a multiple of 1=60 s after the main trigger to eliminate noise generated by 60-Hz pickup. This data acquisition system has the advantages of the hybrid technique—one can standardize the signal pulses before recording them. This is particularly important in situations where diFerent reaction paths lead to widely varying detector responses. This system is also insensitive to pickup, as information is transmitted in the form of digital signals, and has low dead time, about 20 ns. This system also has the advantages of low cost, as the linear summation of the 55 signals results in the need for only one digitizer and memory. The information accumulated during 200 neutron bursts (nominally during 10 s—the running time for one spin-state of the neutron beam) form a ‘pass’. A data ‘run’ consists of 160 passes and takes about 30 min. The data acquisition system uses the XSYS-language [144] and operates on CAMAC modules and a microVAX computer. Fig. 4 shows a sample TOF spectrum with a natural indium sample in the beam which was obtained with the acquisition system described above. The background is subtracted, so that counts at the ‘black’ resonance at 39:62 eV approach zero level. 2.5. The -ray detector The  rays from neutron capture in the target nuclei are detected with an array of 24 CsI(pure) crystals. The crystals are 15-cm long wedges that form two rings around the beam with 20-cm inner diameter and 40-cm outer diameter. The total length L of the two rings is 30 cm. The detector subtends a 3 eFective solid angle with respect to the center of the target. A hollow cylinder, 5-cm thick, made of 6 Li-loaded polyethylene (10% by weight) shields the detector

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Fig. 4. Sample of the natural indium time-of-:ight transmission spectrum with the background subtracted. The points are the experimental data and the solid line represents the FITXS-code Kt to the data.

against neutrons scattered from the beam. There is also an outside shield consisting of 10 cm of lead and a 15-cm thick outer layer of 5% boron-loaded polyethylene. The two halves of the detector and shielding are placed on movable tables. The capture target is located in the middle of the two detector rings and can be accessed by sliding the two tables apart. Hamamatsu R5004 photomultiplier tubes are attached to the upstream (downstream) face of the upstream (downstream) crystals and lie parallel to the beam direction. 3.8-mm thick Corning glass 9863 Klters are placed between the CsI and phototubes and reduce the light from the slow 3300 ns (480–600 nm) decay component by a factor of Kve; this light would otherwise contribute about 20% to the light output of the 6- and 23-ns components. The phototubes have a stated rise time of 3 ns. The full detector assembly is shown in Fig. 5. The -ray detector is described in detail by Seestrom et al. [122]. The data acquisition system for the PV measurements with this detector is essentially the same as for the transmission measurements. Examples of TOF spectra taken with this detector at diFerent operating conditions are shown in Fig. 6. Determining the background in the TOF spectra from the -ray detector is simpler than in the transmission measurements. For the resonance measurements, the background is Kxed by the detector counts in channels outside the resonance, and interpolated to the resonance channels. Another simpliKcation in the neutron capture method is due to the fact that the -ray detector does not introduce an additional time uncertainty to the total TOF response function of the resonance spectrometer. 2.5.1. The -ray detector e>ciency The detector is designed to measure neutron capture events by registering  rays produced in cascades from excited states of the compound system. The typical excitation energy is E ∗ ∼ 6 MeV, and the average multiplicity of the cascade is M 3. The optimal detector regime

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Fig. 5. Photograph of the 24-module -ray detector for parity violation study via the neutron capture method.

Fig. 6. Sample of the 106 Pd time-of-:ight (TOF) neutron capture spectrum taken with the 24-module -ray detector. The TOF scale with a 100-ns channel width is converted to neutron energy. The strong peaks are s-wave resonances and the weak peaks are p-wave resonances.

for our PNC measurements was two-fold coincidence operation with a 0.3-MeV threshold for registering  rays in each of 12 detector sections. The calculated detector eMciency for a neutron capture event under these conditions is 47%, according to analytical and Monte Carlo calculations performed in [122]. The measured eMciency of 51% for the 15.5-eV resonance in 121 Sb agrees well with the calculations. Since 133 Cs has a large neutron capture cross section, the detector was designed with a 5-cm thick, 6 Li-loaded polyethylene cylinder between the target and the detector. According to Monte Carlo calculations [71], this cylinder stops more than 99.85% of neutrons with energies below 1000 eV, while generating only 3  rays per 1000 incident neutrons.

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2.6. Shape analysis of time-of-=ight data The TOF spectra were analyzed with the Ktting code FITXS [30], which was developed for the analysis of resonance neutron transmission and radiative capture data. The code includes all major instrumental resolution eFects that are observed in the neutron TOF spectra: pulse shape produced by the neutron moderator, time response of the detector, channel bin length, target temperature, and Doppler (D) broadening. With the FITXS code, the Breit–Wigner resonance parameters (E0 , gn , and total radiative width  ) of the Doppler-broadened cross section D (E) are determined by Ktting directly to the data—detector count rate versus the TOF channel t. The following Ktting functions for the transmission (T ) and the capture (C) experiments were used:   FT (t) = NT (t)&T [RT (t  )e−nD (t−t ) ] dt  + BT ; (18)   FC (t) = NC (t)&C

 D (t − t  ) −nD (t−t  ) RC (t ) ) dt  + BC ; (1 − e D (t − t  ) 

(19)

where NT (t), NC (t) and &T , &C are the neutron :uxes and detector eMciencies in the transmission and neutron capture experiments, and BT and BC are the corresponding background count rates. The response functions RT (t  ) and RC (t  ) were determined by studying resonances with known intrinsic widths and are described in detail by Crawford et al. [42]. 2.6.1. Beam response function and Doppler broadening The TOF response function of the TRIPLE spectrometer depends upon the :ight path length, the shape of the neutron pulse after the moderator, the signal combiner electronics, and the detector characteristics. Aside from the detector part, the function was found to consist of two terms, with a relative contribution of 80% for the Krst and 20% for the second, and each represented by a convolution of a Gaussian characterized by a standard deviation  (the same for both terms) with an exponential characterized by a decay constant +. These response parameters are functions of the neutron energy En as shown in Fig. 7 [151]. The Doppler broadened cross sections D and D contain intrinsic convolutions which are Krst performed numerically. FITXS converts to velocity space for a given region of TOF channels and uses a fast Fourier transform to convolute the cross sections p (v) or p (v) with the Doppler response function m 2 D(v) = e−(mv =2kB TeF ) ; (20) 2 kB TeF where m is the target mass, kB is the Boltzmann constant, and TeF is the eFective temperature. FITXS takes account of parity violation by adding additional terms (pp ) or (pp ) to the corresponding p-wave resonance cross sections of Eqs. (11) and (12). After inserting the result of these convolutions in the appropriate place in Eqs. (18) and (19), FITXS then converts back to TOF and performs numerically a convolution with the instrumental response function. At this point FITXS compares the F array with the data spectrum in the given channel region in order

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Fig. 7. Parameters for the response function of the TOF spectrometer. The standard deviation  for the Gaussian part and the decay constants +1 , +2 for the asymmetric tail are parameters of the neutron water moderator. The constant +d is the neutron mean capture time in the neutron detector. The factor D is the TOF response for the Doppler width of resonances with  = 100 meV in targets with mass A ∼ 100.

to determine 22 . FITXS then chooses a new set of parameters, recalculates F, and repeats this process until 22 is minimized. 2.7. Determination of resonance parameters and cross section asymmetries The resonance energies and neutron widths were determined by Ktting the TOF spectra summed for both of the helicity states. Details of the FITXS code application to the data analysis are discussed by Crawford et al. [41]. The accuracy of the neutron widths was governed mainly by the uncertainty in the determination of the :ux-eMciency product N (t)&, and was typically about 5%. In TOF measurements, due to the basic relationship XE=E = 2Xt=t, the relative accuracy of the resonance energy is better if a longer :ight path l (a larger TOF t) is used. The relationship between the nonrelativistic neutron kinetic energy and the TOF parameters can be written as  2 1 l En = m ; (21) 2 (Cn − Co )tdwell where m is the neutron mass, Cn is the nth TOF channel, tdwell is the time interval allocated for each TOF channel, and Co is the oFset channel number associated with the electronic start signal. Typical TOF parameters (obtained by calibrating to well known resonance energies of 238 U and 232 Th) were l=56:736 ± 0:003 m, and C =2:71 ± 0:14 channels for t o dwell =200 ns. With this calibration, the neutron resonance energies were obtained for other nuclei with a relative uncertainty of 0.01%. The resonance parameters were held Kxed while the longitudinal asymmetries p+ and p− (which are obtained from p+ = p + p+ p and p− = p + p− p ) were Kt separately for the + and − helicity data. Finally, the longitudinal asymmetry p was determined from

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Fig. 8. PNC asymmetries histograms obtained from 152 runs for silver. Left—histogram for the 36-eV resonance in 107 Ag; right—histogram for the 32-eV resonance in 109 Ag.

p = (p+ − p− )=(2 + p+ + p− ). Of course, p+ and p− are expected to have the same value but opposite sign, so that p+ + p− 0. The PNC longitudinal asymmetries were determined separately for each measurement run. A small correction for spin-:ipping eMciency was made. The neutron polarization was also determined for each run and the corrected asymmetry obtained. For each p-wave resonance studied the asymmetries pk from separate runs with k = 1 to N were histogrammed to obtain a mean value and its uncertainty Xp = =(N )1=2 , where  is given by the variance 2 = (N − 1)−1

N


(pk − p) Y 2:

(22)

k=1

In the absence of systematic errors, the variance is determined by the statistics of count rates. Since Xp is determined directly from the histogram, it should include all sources of possible errors and be the most robust way to determine the overall uncertainty. An example of the histograms obtained for resonances in 107 Ag and 109 Ag is shown in Fig. 8. 3. Statistical analysis of parity violation in neutron resonances 3.1. General approach: MJ determined by Bayesian analysis In this section we describe the Bayesian likelihood analysis used to extract the values and uncertainties for the rms PNC matrix element MJ from the experimental data. Since the matrix elements depend on the level density, a more useful quantity for comparing results from diFerent nuclei is the weak spreading width w deKned by Eq. (7). The use of the spreading width approximately removes the level density dependence. One can formulate the problem completely in terms of this spreading width and obtain w directly from the longitudinal asymmetries p. In fact one is forced to take this approach in certain cases due to lack of spectroscopic information. We spell this out explicitly below. However, for pedagogic purposes we initially formulate the discussion in terms of the rms matrix element MJ .

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First we outline the procedure followed to obtain MJ . We use Bayesian likelihood analysis. The corresponding likelihood function L(m) is deKned by the Bayes theorem for conditional probabilities [53] L(m) = P(y|m; )P(m) ;

(23)

where the a priori probability density P(m) describes our knowledge about the parameter m before the new experimental information y (obtained with error ) was available. L(m) can be considered the (un-normalized) probability density that describes our knowledge of the parameters m after the measurement. For most nuclei that we have studied, nothing is known a priori about MJ . We might make a theoretical estimate of MJ , say Mth , and argue that it is very unlikely that the true value of MJ is greater than Mmax = 10Mth . We would then take as the prior a function that is uniform between 0 and Mmax . Formally, Eq. (23) should contain in the denominator the normalization constant P(y|m; )P(m) dm. We omit this normalization constant in the discussion below. The above choice of the prior will guarantee normalizability. In practice, the precision with which the rms weak matrix element can be determined is governed by the PNC data and the amount of spectroscopic information available. Since the parity violation in (weak) p-wave resonances is caused by mixing with (strong) s-wave resonances, clearly one needs the spectroscopic parameters for both the s- and p-wave states. With all of the spectroscopic information known, the fractional error in MJ is determined by the number of resonances, n, for which asymmetries are measured with small statistical errors [26]  XMJ =MJ = 2=n : (24) However, in most cases there is incomplete information available for some or all of the relevant spectroscopic quantities, and the error in MJ is larger than the sampling error given by Eq. (24). Below we consider the methods of analysis appropriate under various circumstances. We derive the probability density functions for the longitudinal asymmetry and the appropriate likelihood expressions used to determine MJ . The importance of the spectroscopic information in determining the level densities and strength functions is emphasized. It is convenient to consider target spin I = 0 and I = 0 separately. The I = 0 case is much simpler conceptually, while the I = 0 case needs more consideration. This is due both to the additional resonance spins possible and to the two projectile-spin amplitudes in the entrance channel, for which there is always insuMcient experimental information. 3.2. Extraction of rms matrix element for I = 0 targets 3.2.1. PNC asymmetry for mixing with several s-levels For I = 0 all s-wave resonances have J = 1=2+ , the p-wave resonances have J = 1=2− or 3=2− , and the corresponding p-wave neutron amplitudes are pure j = 1=2 or 3=2 (where j is the neutron total angular momentum, which we denote as projectile spin). Usually the s- and p-wave neutron widths and resonance energies are known, but the spins (particularly of the much weaker p-wave resonances) often are not known. This complicates the analysis because p-wave resonances that do not have a measurable PNC eFect may be either J = 1=2 or 3=2 states. The 3=2− levels cannot mix with the 1=2+ s-wave levels through the parity violating

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interaction and therefore cannot show parity violation. However, some of the 1=2− levels do not show a PNC eFect because their parity-violating asymmetry is smaller than the nonzero experimental error. The Krst order perturbation theory expression for the PNC asymmetry was obtained by a number of authors [138,32,4,145]. The observed asymmetry for a given p-wave level 5 has contributions from many s-wave levels 6, and the PNC asymmetry is


p5 = 2

6

V65 61=2 n ; 1=2 E6 − E5 5n

which can be rewritten as
p5 = A65 V65

(25)

(26)

6

with A65 = 2(6n =5n )1=2 =(E6 − E5 ), where (5n )1=2 ≡ g5 and (6n )1=2 ≡ g6 are the neutron decay amplitudes of levels 5 and 6; E5 and E6 are the corresponding resonance energies, and V65 is the matrix element of the PNC interaction between levels 5 and 6. The A65 are known since they are functions of the known neutron widths and the resonance energies. There are many more unknown V65 than there are equations and therefore the individual mixing matrix elements V65 cannot be determined. Consistent with the statistical model of the compound nucleus discussed above, Bowman et al. [21] assumed that the V65 were independent Gaussian random variables with mean zero and variance MJ2 . The variance MJ2 is the weak interaction mean-squared matrix element. Since each p5 is the sum of the variables V65 with  constant coeMcients, each p5 is a Gaussian random variable with variance MJ2 A25 , where A25 = 6 A265 . In what follows, to stress the importance of the J value, we will use the notation AJ as well as A5 . 3.2.2. Probability density function for PNC asymmetry The probability density function (PDF) of the longitudinal asymmetry p is  1 p2 √ ≡ G(p; (MJ AJ )2 ) : exp − P(p|MJ AJ ) = 2 2 2MJ AJ 2 MJ AJ

(27)

In the following we use the symbol G(x; 92 ) for a mean-zero Gaussian distribution of the variable x with variance 92 . To include the experimental error p in the measurement of p, the convolution theorem for Gaussian probability density functions is used. The PDF for the asymmetry is still Gaussian, but with variance (MJ AJ )2 + (p )2 : P 1=2 (p|MJ AJ ; ) = G(p; (MJ AJ )2 + (p )2 ) :

(28)

For the I =0 case this is the PDF for resonances with spin J =1=2. Resonances with spin J =3=2 cannot exhibit parity violation, but they may have nonzero asymmetries due to experimental error. For the J = 3=2 resonances the PDF is a mean-zero Gaussian with variance p2 : P 3=2 (p|p ) = G(p; p2 ) :

(29)

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For a p-wave resonance with J = 3=2, the PDF for the asymmetry does not involve the weak rms matrix element. Since the PNC interaction can only mix states of the same J , the matrix element between J =1=2 s-wave states and J =3=2 p-wave states vanishes identically. Therefore a measurement of the PNC asymmetry for J =3=2 p-wave resonances cannot yield any information about the matrix element MJ =1=2 . 3.2.3. Bayesian likelihood analysis for I = 0 target p-wave spins known. First we consider the likelihood function when I = 0 and the spins of the p-wave resonances are known. We are therefore analyzing only the data for spin J = 1=2 resonances. Here and in the following we assume that the values of the asymmetries measured for diFerent p-wave resonances have mean zero and are statistically independent. It follows that the likelihood function for several resonances is the product of their likelihood functions deKned by Eq. (23). If the experimental asymmetry is p5 and the a priori distribution of the rms matrix element is P(M1=2 ), then L(M1=2 ) = P(M1=2 )

N

P(p5 |M1=2 A5 ; 5 )

(30)

5=1

and using Eq. (28) we obtain the Knal expression L(M1=2 ) = P(M1=2 )

N

G(p5 ; (M1=2 A5 )2 + (5 )2 ) :

(31)

5=1

A sample likelihood function for the case with all spins known is shown in Section 5. p-wave spins not known. Next, consider the situation when the p-wave resonance spin is unknown. Clearly the p-wave resonance has spin J = 1=2 or 3=2. If the p-wave resonance has spin J =1=2, it can display parity violation and the PDF for the asymmetry p given by Eq. (28). For p-wave resonances with J = 3=2, the PDF is given by Eq. (29). Therefore the likelihood function for each level is the sum of two terms: L(M1=2 ) = P(M1=2 )

N

[p(1=2)G(p5 ; (M1=2 A5 )2 + 52 ) + p(3=2)G(p5 ; 52 )] ;

(32)

5=1

where p(1=2) and p(3=2) are the probabilities that J =1=2 and 3=2, respectively. The evaluation of the relative probabilities p(J ) is discussed in Section 3.4. We note that the likelihood function in Eq. (32) is not normalizable unless P(M1=2 ) tends to zero for large M1=2 . This diFerence is due to the J = 3=2 terms, which are independent of M1=2 and lead to a divergent normalization integral. To put this situation in context consider the 64.57-eV resonance in 232 Th that shows a parity-violating asymmetry of 14% with a statistical signiKcance of 35 standard deviations. The probability of an eFect of this signiKcance occurring by chance is extremely small, but the normalization integral of the likelihood function is formally divergent because there is a small chance that the spin of the 64.57-eV resonance is 3=2 and the 35 standard-deviation PV asymmetry occurred by chance. In fact, the observation of a nonzero

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parity-violating asymmetry for a level usually establishes the spin of the level with greater conKdence than using other methods such as the ratio of -ray intensities. To obtain a formally normalizable function, we can assume that P(M1=2 ) is constant from M1=2 = 0 to Mmax , and zero elsewhere. Although purists may object to this procedure, the choice of Mmax is of little practical consequence. We shall demonstrate this in Section 5 with several examples. Note that the maximum likelihood estimate, mL , is obtained by Knding the value of m that maximizes L(m) deKned by Eq. (23). The maximum likelihood estimate mL is a random variable in the sense that if the experiment is repeated for another set of resonances, a diFerent value of mL will be obtained. There is an issue of the conKdence intervals in a Bayesian approach. The deKnition of conKdence intervals for mL is discussed by Eadie et al. [53]. A conKdence interval for mL can be estimated by solving the equation   L(m± ) 1 =− : ln (33) L(mL ) 2 Note that in this approach the normalizability of L(m) is not an issue. For a Gaussian distribution of m this error estimate corresponds to the standard deviation. However, it should be noted that the likelihood distributions obtained for rms matrix elements from a few PNC eFects are nonnormal and in some cases strongly nonnormal. 3.3. Extraction of rms matrix element for I = 0 targets For a target with spin and parity I (I = 0) the s-wave levels can have (I ± 1=2) , while the p-wave levels can have (I ± 1=2)− and (I ± 3=2)− . The p-wave states with J = I ± 1=2 can be formed with both p1=2 and p3=2 neutrons, and thus there are two entrance channel neutron amplitudes. We use the following coupling scheme: the neutron orbital angular momentum ˜‘ and the neutron spin ˜i are Krst coupled to form the projectile spin ˜j =˜‘+˜i. The angular momentum ˜j is then coupled to the target spin ˜I to form the total spin ˜J =˜I +˜j of the target-projectile system. For s-wave resonances the projectile spin is j = 1=2, while for p-wave resonances j = 1=2 or 3=2. Very few projectile-spin amplitudes have been measured. In addition, the resonance spins are often unknown. For these cases we derive expressions for the PDF of the longitudinal asymmetry and the likelihood functions by averaging over unknown spectroscopic parameters. In the I = 0 case only the j1=2 spin channel contributes to parity violation. This is accounted for by replacing Eq. (25) with
2V65 g51=2 g 6 p5 = R with R =  ; (34) E6 − E5 5n g52 1=2 + g52 3=2 6 where g51=2 is the j = 1=2 entrance channel neutron amplitude and g52 1=2 + g52 3=2 ≡ 5n . 3.3.1. Probability density function If all level spins and projectile-spin amplitudes are known and there is complete knowledge of the spectroscopic parameters of all levels, then the factor R has a Kxed value, resulting in

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a PDF similar to that for the I = 0 case. The asymmetry p has a Gaussian distribution with variance (MJ AJ R)2 P I (p|MJ AJ R) = G(p; (MJ AJ R)2 ) :

(35)

The projectile-spin amplitudes are essentially always unknown for low energy p-wave resonances. Therefore we must consider the situation with unknown projectile-spin amplitudes. According to Eq. (34), the quantity p is the product of R and Q, where R is a random variable and Q is the Gaussian random variable given by
2V56 g 6 : Q= (36) E − E5 5n 6:J6 =J5 6 To obtain the PDF of p, which is no longer Gaussian, one needs the PDF of R, which is a function of the projectile-spin amplitudes. According to the extreme statistical model [19] of the compound nucleus, the projectile-spin amplitudes g1=2 and g3=2 are statistically independent Gaussian random variables. We call their variances X 2 and Y 2 for g1=2 and g3=2 , respectively, and introduce the ratio a2 ≡

Y2 : X2

(37)

It can be shown that a2 is the ratio of the p3=2 and p1=2 neutron strength functions. Strength functions (and their experimental determination) are discussed in Section 3.4. The PDF’s for the projectile-spin amplitudes entering the quantity R are P(g1=2 | X ) = G(g1=2 ; X 2 )

and

P(g3=2 | Y ) = G(g3=2 ; Y 2 ) :

(38)

We convert to polar coordinates: g1=2 = r sin @ and g3=2 = r cos @. Then R = sin @ and we obtain the probability density function for the variable @ P(@ | a) =

1 a : 2 2 2 (a sin @ + cos2 @)

The PDF of the product of the two independent random variables R and Q is  a 2 =2 G(p; (MJ AJ sin @)2 + (p )2 ) d@ ; P I (p|MJ AJ ; a; p ) = 0 a2 sin2 @ + cos2 @

(39)

(40)

where p is the experimental error in the asymmetry p. The PDF of Eq. (40) for small values of a is approximately Gaussian and is essentially the same as the PDF for I = 0 case. With increasing a (increasing magnitude of the p3=2 amplitude versus the p1=2 amplitude) the distribution changes. For values of a about 0.3 and higher the distribution gradually develops a spike at p = 0 at the expense of large values of p. In practice, for masses near A = 110, the experimental values of a range from about 0.5 to 0.8 and the distribution P I is still similar, in the range of p = 10−3 –10−2 , to the distribution for I = 0. Plots of P I for diFerent values of a are shown in Bowman et al. [28].

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The extreme statistical model does not always hold—amplitudes (and widths) in diFerent channels may be correlated. Channel correlations are predicted for doorway states [93] and for direct reactions. These predictions were conKrmed by Mitchell et al. [105], who also observed large correlations in circumstances where the statistical model worked well for other observables. Predictions for the size or frequency of these correlations cannot be made reliably. However, formally the problem is straightforward—on the basis of the central limit theorem one expects the joint probability density function of g51=2 and g53=2 to be a bivariate Gaussian form with some linear correlation coeMcient A. The result is given in Bowman et al. [28]. Although the eFect of the correlation is to distort the shape of the PDF, MJ is insensitive even to large correlations. The additional uncertainty due to lack of information about channel correlations seems small compared to the uncertainty arising from lack of information about the ratio of the projectile-spin amplitudes. Therefore we assume in the following that the projectile-spin amplitudes are uncorrelated. 3.3.2. Bayesian likelihood analysis for I = 0 target More parameters are involved in the expressions for the likelihood functions for target spin I = 0, and there are more cases to consider. In practice for I = 0, one never knows all of the parameters. We consider several possibilities. All level spins known, projectile-spin amplitudes not known. Suppose that the projectile-spin mixing amplitudes are not known, but that the spins of the p-wave resonance and of all s-wave resonances are known. The factor A5 in Eq. (34) is then known, but R is not and one must use the probability density function given by Eq. (40). The likelihood function is given by L(MJ ) = P(MJ )

N

P I (p5 |MJ A5 ; a; 5 ) :

(41)

5=1

Examples of the likelihood functions for this case are given in Section 5. s-wave spins known, p-wave spins and projectile-spin amplitudes not known. Next, suppose that neither the spin of the p-wave level nor its projectile-spin amplitudes are known, but that the spins of all s-wave resonances are known. If the spin of the p-wave level is assumed, then the factor A5 can be evaluated, but A5 = A5 (J ) depends on the spin sequence assumed because only s-wave levels with the same spin as the p-wave level mix to produce parity violation. The likelihood function is then obtained by summing over p-wave level spins as in the corresponding situation when I = 0. Due to the level density eFect, the rms PNC matrix element may be diFerent for J = I ± 1=2 states. Since it is unlikely that there is any other dependence of the parity violation on J , we assume that w is independent of J . We also assume that the level spacing DJ has the J dependence given in Section 3.4. The likelihood function can be expressed as a function of the weak spreading width   N



L(w ) = P(w )  p(J )PpI (p5 |MJ A5 (J ); a; 5 ) + p(J )G(p5 ; 52 ) ; 5=1

J =I ±1=2

J =I ±3=2

(42)

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where MJ should be written as a function of w , deKned in Eq. (7). Note that the level densities for diFerent values of J are diFerent. The expression of Eq. (42) is inconsistent with Eqs. (31) and (41), where the likelihood is written as a function of MJ . In order to be consistent, one should use the weak spreading width as the variable throughout the equation and transform the prior according to P(w ) = P(MJ (w ))

dMJ (w ) : d(w )

(43)

The change of the argument and the prior does not change the Knal (most likely) value of the matrix element, but changes the corresponding errors because of the nonlinear relationship of the variables in Eq. (7). Although in this case one must formulate the problem in terms of the spreading width, in most cases one can determine the most likely value of the rms matrix element and obtain w trivially from the known matrix element and the level density. s-wave spins, p-wave spins, and projectile-spin amplitudes not known. It is very diMcult to evaluate the likelihood function if only the level energies and neutron widths (and their sor p-wave character) are known. The situation is discussed at length in Bowman et al. [28]. Assume that the resonance parameters are known for the p-wave levels, and that the resonance parameters of the s-wave levels are known except for the spins. One must deal explicitly with the uncertain level spins in formulating the likelihood function. For large N , this gives many terms in the sum in the likelihood expression. Fortunately, in our experiments there is always partial information on the spins of the s-wave resonances, and the total number of resonances with uncertain spin is not large. In practice we add terms in the likelihood expressions to account for these unknown spins. In the Bayesian spirit, one could adopt the view that all resonances that display a parity violation with greater than some given statistical signiKcance, say 3, must have the same spin J as the spin of the strongest neighboring s-wave resonance. One could then analyze this set of resonances. The resulting likelihood curve could then be used as the a priori distribution P(w ). This new function is normalizable. The experimental results provide information about the resonance spin. This is simplest for I = 0. Clearly a resonance with a large PNC eFect must with very high probability have J = 1=2. A resonance with zero (within error) PNC eFect is more likely to have spin J = 3=2. The argument is similar for I = 0, except there are now two allowed spins and two spins (probably) disallowed. For example, a resonance with a strong parity violation must have J = I ± 1=2, and not J = I ± 3=2. 3.4. Level densities and neutron strength functions The spin-dependent level density is A(E; J ) = f(J )A(E), where A(E) is the nuclear level density and E is the excitation energy. The spin distribution can be approximated by [74] f(J ) = e−J

2

=2c2

2 2 ∼ 2J + 1 e−( J +1=2)2 =2c2 : − e−( J +1) =2c = 2

2c

(44)

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The spin cut-oF parameters c2 were taken from von Egidy et al. [54]. The expression for f(J ) is used to determine the relative probability p(J ) that enters the likelihood expression when the spins are unknown. The exponential term is important only for higher J values. The standard deKnition for the neutron strength function is [111] Sl =

g(J )nl 

(2‘ +

l 1)Dobs

;

g(J ) =

2J + 1 ; 2(2I + 1)

(45)

where the average is over all spins J . Here g is the spin statistical weight factor, nl is the l reduced neutron width, and Dobs is the observed level spacing for all levels. This deKnition makes use of the experimental fact that the neutron strength function does not depend on spin J . However, it does not include the possible dependence of the strength function on the projectile-spin j. For p-wave neutrons the spin–orbit coupling clearly leads to a j dependence of S 1 . Therefore a more suitable strength function deKnition [98] for our purposes is 3=2 1
S = 3 1

I
+3=2

g(J )Sj1 (J )

with Sj1 (J ) =

j=1=2 |J =I −3=2|

nj (J )

D(J )

;

(46)

where the neutron width is averaged over the resonances with a given spin J . Assuming that Sj1 (J ) does not depend on J , one obtains 1 1 + 23 Sj=3=2 : S 1 = 13 Sj=1=2

(47)

1 1 and Sj=3=2 have been determined in the mass region A ≈ 100 The strength functions Sj=1=2 from measurements of the angular dependence of the average diFerential elastic scattering cross section [115]. These measurements were performed at the Dubna pulsed reactor; results for many samples have been reported [114,109]. For some nuclides of interest the value of the 1 1 parameter a2 = (Sj=3=2 =Sj=1=2 ) can be taken from these data. Values of the parameter a (either obtained from the direct measurements or estimated from the empirical behavior in this mass region) were then used to characterize the projectile-spin amplitudes in the likelihood analysis.

3.5. Bayesian assignment of resonance parity With the known resonance parameters the parity assignment often can be made probabilistically with the use of the average statistical properties of the neutron widths. Again, a Bayesian analysis can be performed to obtain the estimate of the appropriate probability. Such an approach was developed by Bollinger and Thomas [18], and makes use of the average resonance parameters Dl and S l and of the Porter–Thomas distribution for neutron widths. At low neutron energies, because of the large diFerence in penetrabilities for s-wave and p-wave resonances, most of the stronger resonances are s-wave and most of the weaker resonances are p-wave. The Bayesian conditional probability of a resonance being p-wave is BP(l = 1|gn ) =

P1 P(gn |l = 1) ; P1 P(gn |l = 1) + P0 P(gn |l = 0)

(48)

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191

where P0 and P1 are a priori probabilities for the resonance to be s- or p-wave and P(gn |l=0) and P(gn |l = 1) are the Porter–Thomas probabilities for a given gn value and l = 0 or 1. Since we assume a (2J + 1) dependence for the level densities, we expect twice as many p-wave resonances as s-wave resonances for all targets with I larger than 1=2. For even–even (I = 0) targets one expects three times as many p-wave resonances as s-wave resonances. The value of BP that results when the Porter–Thomas probabilities for s- and p-wave choices are equal is taken as the a priori probability value that divides the s- and p-wave resonances. For the present case this a priori value is 66.7% for I ¿ 3=2, 69.2% for I = 1=2, and 75.0% for even–even targets. Of course the assignment is less reliable when the probability is close to the a priori value. The distribution of the neutron reduced widths is the Porter–Thomas distribution [116,111] gnl e−x=2 P(x) = √ where x = : (49) gnl  2 x The Knal Bayesian probability, in the notation adopted by the TRIPLE Collaboration, is     −1 p c1 (E) s 3 s S1 c0 (E) gn c0 (E) 1 − ; (50) BP = 1 + exp − p p S0 c1 (E) 2D0 S0 3 s S1 c0 (E) where s = p is the ratio of s- and p-wave level densities, S0 and S1 are the s- and p-wave strength functions, D0 is the average s-wave level spacing, and gn is the neutron width of the resonance in question. The functions cl (E) are cl (E) =

[1 + (kR)2l ]  ; (kR)2l E(eV)

(51)

where the nuclear radius is assumed to be R = 1:35A1=3 fm. The probabilities depend on the sand p-wave strength functions, and—with the above (2J + 1) assumption—only on the average s-wave spacing. The strength functions are determined according to Eq. (45) and the reduced widths were calculated in the usual way [111]: gnl = cl (E)gn :

(52)

The process of assigning resonances with this probabilistic argument, and then determining the strength functions and level densities, is usually iterated until the probabilities are stable. Examples can be found in the TRIPLE Collaboration spectroscopic papers. The IRMM group also used this method [154]. 4. PNC asymmetries and spectroscopic results 4.1. Overview of the TRIPLE data The TRIPLE Collaboration measured PNC longitudinal asymmetries for nuclei near mass A 110 and 230. A summary of our results for the asymmetries p for each nuclide measured

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Table 1 Parity violations observed by TRIPLE Target

Reference

All

p+

p−

81

[67] [125] [132] [97] [97] [134] [134] [43,134] [43,134] [121] [136] [133] [101] [101] [101] [140] [126] [152] [135] [127] [41]

1 0 4 8 4 1 3 2 0 2 9 4 5 1 7 1 1 1 10 6 5 75 59

1 0 3 5 2 0 3 0 0 2 5 2 3 0 5 0 1 1 10 2 3 48 36

0 0 1 3 2 1 0 2 0 0 4 2 2 1 2 1 0 0 0 4 2 27 23

Br Nb 103 Rh 107 Ag 109 Ag 104 Pd 105 Pd 106 Pd 108 Pd 113 Cd 115 In 117 Sn 121 Sb 123 Sb 127 I 131 Xe 133 Cs 139 La 232 Th below 250 eV 232 Th above 250 eV 238 U Total Total excluding Th 93

is listed in Table 1. The total number of statistically signiKcant values is listed along with the number of eFects with positive and negative signs. By deKnition, the sign of p is positive when the cross section for positive helicity is larger than the cross section for negative helicity. Only eFects with statistical signiKcance greater than three standard deviations are included. Altogether we observed 75 statistically signiKcant PNC eFects. In the subsections below we present detailed PNC results and the relevant spectroscopic data for individual targets. The neutron resonance parameters, the enhancement factors A, and the observed asymmetries are listed in the tables given for each nuclide studied. For some nuclei a signiKcant number of new resonances were observed, and many spin and orbital angular momentum values determined. In some cases there was appreciable uncertainty about the J values—these are noted. The spirit of the tables is to provide suMcient information (detailed resonance parameters and the measured longitudinal asymmetries) to permit independent analysis of the results. For each of the targets studied, we report the measurement method and the sample properties, and note any additional measurements performed to provide spectroscopic information. It should be noted that for targets with spin I = 0, resonances with spin J = I ± 3=2 constitute about

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

193

half of the p-wave resonances, but cannot parity mix with s-wave resonances. Therefore one expects that at most about one half of p-wave resonances can have a PNC eFect. The fraction that can show PNC eFects is even smaller for I = 0 targets. Most of the PNC measurements were performed in transmission, with the system and procedures described in Section 2 and with rather thick targets. The majority of these targets were either monoisotopic (or eFectively so). Three targets (bromine, silver, and antimony) consisted of approximately 50% of each of two isotopes, while the natural palladium target had six isotopes. Many studies of isotopically enriched targets were performed in order to aid in the isotopic identiKcation of the resonances. For targets that required samples of enriched isotopes, insuMcient material was available to perform transmission measurements. Therefore measurements were performed for a number of samples with the -ray detector, using the system described in Section 2. As discussed in Section 3, spectroscopic information is crucial to extract the weak matrix elements and spreading widths. The J values of the neutron resonances are rarely determined in conventional neutron measurements. This is especially true for the weak p-wave resonances, but often is true even for the much stronger s-wave resonances. Measurements to determine resonance spins were performed at the GELINA pulsed neutron source facility at IRMM using the time-of-:ight technique [78,154]. The spin determinations were obtained using the low-level population method. The relative population of low-lying states depends signiKcantly on the initial resonance spin. This method had been widely used in the past for s-wave resonances and was successfully extended to the much weaker p-wave resonances by the IRMM group [153,40]. Except for single resonances in bromine and xenon where the analysis was performed with the single level code PVIO [157], and for the cadmium data, which were analyzed with the code NEWFIT [110], the neutron resonance parameters and asymmetries in the TRIPLE data were Kt with the code FITXS as described in Sections 2.6 and 2.7. The initial code PVIO included only a Gaussian approximation to the eFective Doppler and instrumental broadening of the resonance shapes. Although it gave correct results for the PNC asymmetries of isolated resonances, the code PVIO was not suitable to determine resonance parameters nor to obtain asymmetries in a general case with interfering resonances. Therefore the data were reanalyzed with the code FITXS, and the results for resonance parameters and asymmetries are listed in the tables. The enhancement factors AJ are also listed in the tables for resonances with a measured PNC asymmetry. Frequently the J values of the s-wave resonances were known, but the J value of the p-wave resonance was not. In this case, the AJ values are listed for both possible spin assignments. 4.2. Bromine The TRIPLE transmission measurement on the 0.88-eV p-wave resonance [67] conKrmed the Krst observation of the PNC eFect (p = 2:4 ± 0:4%) in 81 Br made by the Dubna team [4], who also measured the resonance parameters. Later the PNC eFect in the 0.88-eV resonance was also conKrmed at KEK [128] with the result p = 2:1 ± 0:1%. The areal density of the natural bromine liquid sample in the TRIPLE experiment was 1:8 × 1023 atoms=cm2 . The analysis of the parity-violating eFect for the 0.88-eV resonance was performed with the PVIO code [157]. Since the resonance spins are unknown, Table 2 presents tentative values of AJ using an arbitrary assumption of J =1 for the E =101-eV s-wave resonance and J =2 for the E =135:5-eV s-wave

194

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 2 Resonance parameters and PNC asymmetries p for E (eV)

‘

0.88b 101.0c 135:5c

1 0 0

J

81

Br. Parameters AJ are in units eV−1

gn (meV)

A1 a

A2 a

p (%)

|p|=Xp

(5:8 ± 0:3) × 10−5 97:5 ± 7:0 165 ± 18

7.9

7.1

1:77 ± 0:33

5.4

a

Tentative values in the two-level approximation; see text for discussion. Resonance parameters from AlKmenkov [4]. c Resonance parameters from Mughabghab [111]. b

resonance. For bromine the TRIPLE measurements were performed with the initial (preliminary) experimental system. 4.3. Niobium 93 Nb

was measured in transmission [125]. The niobium target was 99.999% chemically pure in the form of a cylinder with an areal density 5:10 × 1023 atoms=cm2 . The resonance parameters, enhancement factors, and asymmetries for 93 Nb are listed in Table 3. When the J value of the p-wave resonance is unknown, the AJ factors are calculated for both J values that allow parity mixing. These factors are very small for all p-wave resonances in niobium. None of the 18 p-wave resonances studied exhibited a statistically signiKcant parity-violating longitudinal asymmetry. Earlier, the Dubna [6] and KEK [128] teams made measurements on the lowest two p-wave resonances of niobium, and also did not observe any PNC eFect. Niobium is one of only two targets studied by the TRIPLE Collaboration that showed no PNC eFect. 4.4. Rhodium 103 Rh

was studied with the -ray detector [131,132]. The target was natural rhodium metal (99.9% chemically pure). The eFective target area was a circle of diameter approximately 10 cm deKned by the collimation system. The areal density was 1:75 × 1022 atoms=cm2 . The resonance parameters, enhancement factors, and longitudinal asymmetries are listed in Table 4. A total of 32 p-wave resonances were studied below 500 eV and four statistically signiKcant PNC eFects were observed. 4.5. Palladium Natural palladium consists of six isotopes with mass numbers 102, 104, 105, 106, 108, and 110. We performed transmission PNC measurements on a natural target [133], capture PNC measurements on enriched 106 Pd and 108 Pd targets [43], and auxiliary spectroscopic total capture measurements on targets of 104 Pd; 105 Pd, and 110 Pd [134].

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 3 Resonance parameters and longitudinal asymmetries p for E (eV) −105:4

35.9 42.3 55.0b 94.4 105.9 119.1 193.8 243.9 318.9 335.5 362.7 364.8 378.4 392.4 460.3 500.5 598.8 603.7 617.2 640.9 671.9 678.2 720.9 741.0 757.0 808:6b 910.1 933.3 952.9 1011 1127 a b

‘a 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1

Ja 4 5 4 3 4 5 5 4 5 4 5 5 5 4 6 4 6 4 4 4 5 6 4

gn (meV) √

16:6 E 0:055 ± 0:005 0:044 ± 0:004 0.0016 0:16 ± 0:02 0:22 ± 0:02 2:30 ± 0:18 23:0 ± 2:5 1:02 ± 0:08 0:87 ± 0:08 7:04 ± 0:56 0:15 ± 0:01 0:30 ± 0:03 53:0 ± 4:0 1:05 ± 0:08 3:91 ± 0:31 2:54 ± 0:20 0:57 ± 0:05 1:57 ± 0:13 0:68 ± 0:05 2:65 ± 0:22 4:22 ± 0:34 1:07 ± 0:09 6:08 ± 0:49 81:0 ± 6:5 1:11 ± 0:09 0:29 ± 0:03 2:50 ± 0:02 210 ± 17 6:50 ± 0:50 290 ± 24:0 8:00 ± 0:64

93

195

Nb. Parameters AJ are in units eV−1

A4

A5

p (%)

|p|=Xp

0.21 1.52 0.0

−0:01 ± 0:02 0:01 ± 0:02 0:04 ± 0:16 −0:01 ± 0:03

0.5 0.5 0.3 0.3

0.27

−0:02 ± 0:04 −0:07 ± 0:07

0.5 1.0

2.3 0.39

0.56 1.95

0:07 ± 0:10 0:02 ± 0:07

0.7 0.3

0.14

1.03

0:10 ± 0:09

1.1

0.09

0:22 ± 0:11 −0:03 ± 0:12 0:01 ± 0:10 0:18 ± 0:11

2.0 0.3 0.1 0.9

0.68 3.5 0.0

0.12

0.22 0.0 0.22

0.0 0.14

0.0 0.30 0.36

0.0 0.12

−0:05 ± 0:10 0:12 ± 0:13 0:001 ± 0:09

0.5 0.9 0.01

1.08 0.69

0.16 0.49

−0:13 ± 0:18 0:07 ± 0:23

0.7 0.3

Values from Mughabghab [111]. New resonances.

The transmission target was a cylinder of palladium metal with an areal density of 5:40 × To reduce the Doppler resonance broadening, the target was cooled to liquid nitrogen temperature. The 106 Pd target had a mass of 23:328 g and was enriched to 98.51%. The 108 Pd target had a mass of 21:669 g and was enriched to 98.59%. Their areal densities were n = 2:11 × 1021 atoms=cm2 of 106 Pd and n = 1:92 × 1021 atoms=cm2 of 108 Pd. The neutron resonance parameters, enhancement factors AJ , and observed asymmetries are listed in Table 5 for 104 Pd, in Table 6 for 105 Pd, in Table 7 for 106 Pd, and in Table 8 for 108 Pd. As demonstrated in the tables, many new p-wave resonances were observed, and their resonance parameters 1023 atoms=cm2 .

196

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Table 4 Resonance parameters and PNC asymmetries p for

103 Rh.

E (eV)

‘

Ja

gn (meV)

1.257 34.46 44.47 46.84 51.92 68.33 83.51 95.71 98.77 108.8 110.8 112.6b 114.0 125.6 154.6 179.3 187.2 199.7 205.0 251.1 253.9 263.1 264.2 272.3 289.9 312.5 319.8 321.6 327.7 353.9 362.5 366.3 373.9 376.3 388.6 406.2 427.6 432.9 435.7 443.9 447.1 450.0 472.8 479:1b 486.4 489.2 492.0 504.7 526.0 546.9 555.5

0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0

1

0:39 ± 0:01 0:0118 ± 0:0006 0:0028 ± 0:0001 0:39 ± 0:02 0:00088 ± 0:00004 0:154 ± 0:008 0:0076 ± 0:0004 1:60 ± 0:08 0:059 ± 0:003 0:0092 ± 0:0005 0:126 ± 0:006 0:0083 ± 0:0004 0:087 ± 0:004 4:7 ± 0:2 50 ± 5 0:125 ± 0:006 31:2 ± 1:6 0:042 ± 0:002 0:076 ± 0:004 0:077 ± 0:004 31:0 ± 1:5 0:91 ± 0:05 0:39 ± 0:02 51:0 ± 2:5 10:1 ± 0:5 0:114 ± 0:006 67:5 ± 7:5 0:77 ± 0:04 0:35 ± 0:02 0:070 ± 0:003 0:28 ± 0:01 1:48 ± 0:07 0:42 ± 0:02 0:113 ± 0:006 0:212 ± 0:011 9:5 ± 0:5 0:086 ± 0:004 0:88 ± 0:04 133 ± 20 0:20 ± 0:01 0:136 ± 0:007 3:01 ± 0:15 0:92 ± 0:05 0:051 ± 0:003 0:96 ± 0:06 0:135 ± 0:008 2:3 ± 0:1 0:46 ± 0:03 0:60 ± 0:04 0:065 ± 0:005 65 ± 15

a Values b New

1 1 1

1 0 1

1 1 1 1

1 1 1

1

from Mughabghab [111]. resonances.

Parameters AJ are in units eV−1 A0

A1

p (%)

0.76 1.79

1.51 10.11

3.59

9.89

−1:11 ± 0:63

1.8

1.96

3.16

−0:08 ± 0:18

0.4

0.94 2.96 0.84 3.42 1.10

3.57 3.89 1.09 4.52 1.50

0:120 ± 0:074 −0:23 ± 0:25 0:17 ± 0:05 0:46 ± 0:31 0:05 ± 0:06

1.6 0.9 3.7 1.5 0.8

1.68

4.05

0:07 ± 0:083

0.8

1.68 1.10 0.60

4.05 2.66 14.50

0:07 ± 0:083 0:03 ± 0:14 −0:45 ± 0:32

0.8 0.2 1.4

0.16 0.24

2.10 3.40

−0:06 ± 0:05 −0:002 ± 0:09

1.1 0.0

0.33

6.82

0:26 ± 0:19

1.3

0.12 0.18 0.36 0.36 0.07 0.14 0.26 0.18

10.10 3.61 2.44 2.44 0.47 0.88 1.73 1.49

0:36 ± 0:12 −0:27 ± 0:12 −0:46 ± 0:31 −0:46 ± 0:31 −0:03 ± 0:05 −0:02 ± 0:10 0:03 ± 0:27 −0:11 ± 0:15

3.1 2.3 1.5 1.5 0.6 0.2 0.1 0.7

0.27 0.08

9.78 8.78

−0:43 ± 0:51 −0:45 ± 0:15

0.8 3.0

0.17 0.21

6.44 6.46

0:29 ± 0:32 −1:10 ± 0:47

0.9 2.3

0.08 0.33 0.07 0.20

0.76 2.86 0.60 1.54

−0:10 ± 0:08 1:16 ± 0:77 0:01 ± 0:08 0:06 ± 0:46

1.3 1.5 0.1 0.1

0:007 ± 0:05 2:33 ± 0:19

|p|=Xp

0.1 12.3

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 5 Resonance parameters and PNC asymmetries p for E (eV)

‘

109.7a 156.7a 182.4 266.6a 294.5a 347.3a 522.0a 524.4a 607.5a 638.7a 678.9a 738.2a 769.2a 888.1a 935.0a 944.5a 994.9a 1178a

1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1

a

J

0.5 0.5

0.5 0.5

104

197

Pd. Parameter AJ is in units eV−1

gn (meV)

AJ

p (%)

0:039 ± 0:001 0:015 ± 0:002 303 ± 9 0:67 ± 0:03 0:81 ± 0:04 9:5 ± 0:7 2:7 ± 0:2 1:2 ± 0:1 2:8 ± 0:2 4:9 ± 0:4 1:5 ± 0:1 1:7 ± 0:1 0:13 ± 0:02 4:5 ± 0:4 8:8 ± 0:7 671 ± 36 24:0 ± 2:0 0:5 ± 0:2

2.1

0:08 ± 0:10

0.6 0.4

−0:12 ± 0:03 0:01 ± 0:18

|p|=Xp

0.8 4.0 0.06

New resonances.

measured. For 105 Pd there are three statistically signiKcant PNC eFects, for 106 Pd there are two PNC eFects, and for 106 Pd there is one PNC eFect, while for 108 Pd there is no statistically signiKcant eFect. 4.6. Silver Natural silver is 51.8% 107 Ag and 48.2% 109 Ag. We took advantage of this approximately equal isotopic mixture to study parity violation in both isotopes with one target. A natural silver target was studied in transmission [97]. Studies of the separated isotopes were performed in order to assist in the isotopic identiKcation of the resonances and to determine the resonance spins. A sample enriched to 98.3% 107 Ag was studied at Los Alamos with the capture -ray detector for purposes of isotopic identiKcation. This same sample was studied at IRMM along with another sample enriched to 97.1% 109 Ag. These measurements provided additional identiKcation information and also provided spin assignments for many resonances [154]. The target was a cylinder of natural silver (99.999% chemical purity) with an areal density of 1:92 × 1023 atoms=cm2 . The neutron resonance parameters, enhancement factors AJ , and observed asymmetries are listed in Table 9 for 107 Ag and in Table 10 for 109 Ag. As demonstrated in the tables, a signiKcant number of new resonances were observed, and many spin and orbital angular momentum values were determined. For 107 Ag there are eight statistically signiKcant PNC eFects and for 109 Ag there are four statistically signiKcant PNC eFects.

198

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Table 6 Resonance parameters and PNC asymmetries p for E (eV) −6:07a

3.91b 11.78 13.22 24.49b 25.10 27.59b 30.05 38.43 41.19b 42.56 44.39b 49.93b 55.23 68.3 72.5b 77.7 79.5b 80.5b 82.9b 83.3b 86.7 94.3b 101.2 104.0 113.5b 116.9b 126.2 130.5b 132.5b 134.1b 136.5b 141.1 144.4b 147.8b 150.0 154.6 158.70 161.0b 165.9b 168.2 170.7b 183.9 202.5 208.3b 215.4b

‘ 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1

Ja 3 3 2 3 2 3

3 3 2

3 3 3

2 2 3 2 3 2 2

105

gn (meV) √

0:95 E 0:00046 ± 0:00003 0:117 ± 0:004 1:33 ± 0:05 0:080 ± 0:05 1:79 ± 0:05 0:0032 ± 0:0003 0:159 ± 0:008 0:189 ± 0:009 0:0053 ± 0:0002 0:033 ± 0:001 0:0079 ± 0:0003 0:0021 ± 0:0001 3:9 ± 0:1 0:92 ± 0:03 0:0139 ± 0:0006 7:8 ± 0:2 0:014 ± 0:001 0:033 ± 0:001 0:032 ± 0:001 0:039 ± 0:002 10:2 ± 0:3 0:008 ± 0:001 0:028 ± 0:001 0:72 ± 0:03 0:007 ± 0:001 0:036 ± 0:002 1:88 ± 0:06 0:044 ± 0:002 0:025 ± 0:001 0:122 ± 0:005 0:026 ± 0:001 5:5 ± 0:2 0:019 ± 0:001 0:158 ± 0:007 32:6 ± 1:0 2:07 ± 0:08 3:5 ± 0:1 0:026 ± 0:001 0:040 ± 0:002 0:87 ± 0:04 0:082 ± 0:004 7:7 ± 0:4 5:6 ± 0:2 0:057 ± 0:002 0:103 ± 0:004

Pd. Parameters AJ are in units eV−1 A2

A3

p (%)

|p|=Xp

2.9

7.5

−0:06 ± 0:24

0.3

2.4

5.5

0:25 ± 0:16

1.6

9.1

5.8

0:59 ± 0:066

9.8

27.2 11.1 6.2 5.1

7.7 5.8 9.4 9.4

−0:072 ± 0:043 −0:02 ± 0:078 0:21 ± 0:05 0:18 ± 0:047

1.7 0.3 4.2 4.5

2.2

4.7

−0:154 ± 0:093

1.7

2.3

2.2

−0:14 ± 0:11

1.3

3.6 5.4 2.8 8.2

3.3 3.2 1.2 2.3

0:21 ± 0:12 0:27 ± 0:31 −0:07 ± 0:70 0:40 ± 0:30

1.8 0.9 0.1 1.3

18.1 13.2

2.7 1.2

0:17 ± 0:50 0:30 ± 0:25

0.3 1.2

12.3 4.9

3.4 4.3

0:061 ± 0:60 −0:11 ± 0:35

1.6 0.3

2.8

2.7

0:08 ± 0:20

0.4

3.8 1.6

1.3 1.4

−0:24 ± 0:27 −0:20 ± 0:21

0.9 1.0 (Continued on next page)

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

199

Table 6 Continued E (eV)

‘

222.6b 226.8 230.4b 251.4 252.4 260.0 268.3b 286.8 305.1 311.0b 313.3 322.1b

1 0 1 0 0 0 1 0 0 1 0 1

a b

Ja 3 2 3 2 3 2 2

gn (meV) 0:049 ± 0:002 4:0 ± 0:1 0:050 ± 0:002 3:0 ± 0:1 19:9 ± 0:8 22:4 ± 0:7 0:116 ± 0:005 3:15 ± 0:10 53:3 ± 1:7 0:057 ± 0:003 2:05 ± 0:09 0:072 ± 0:003

A2

A3

p (%)

|p|=Xp

2.0

4.5

0:90 ± 0:52

1.7

2.0

5.3

0:06 ± 0:50

0.1

3.4

1.8

−0:30 ± 0:29

1.0

Values from Mughabghab [111]. New resonances.

4.7. Cadmium 113 Cd

was studied with the prototype -ray detector [121]. The J values were determined for a number of resonances at IRMM [78]. The 91.2-g target was enriched to 93.35% 113 Cd. The areal density was 7:13 × 1021 atoms=cm2 of 113 Cd. The data analysis was performed with the code NEWFIT [110] which implements a skewed-Gaussian Kt (convoluted with a Lorentzian) to an asymmetric line shape. The resonance parameters, enhancement factors, and asymmetries are listed in Table 11. The 3 eFect for the 7.0-eV resonance, p = (−0:98 ± 0:30)%, was observed in an earlier Dubna measurement [7]. Two new statistically signiKcant PNC eFects were observed. It should be noted that the size of the 4 eFect for the 289.6-eV resonance depends strongly on the high resolution ORELA data by Frankle et al. [70]. In that experiment this weak resonance was observed on the shoulder of the strong 291.6-eV resonance, while in the TRIPLE measurements the resonances were not resolved. Since PNC eFects are measurable only in p-wave resonances, the directly measured asymmetry of (0:069±0:015)% for the large composite peak at an energy about 291 eV was renormalized to obtain the p value for the 289.6-eV resonance. This assumes the neutron widths listed in Table 11. The neutron width for the very weak 289.6-eV resonance may have a large error, which would have a direct eFect on the asymmetry value. The large size of the PNC asymmetry obtained for the 289.9-eV resonance with this procedure led to an extremely large weak spreading width reported in Ref. [121]. We reconsider this result in Section 5.3. 4.8. Indium Natural indium is 95.72% 115 In and 4.28% 113 In. The total cross section was measured with a natural indium sample and a large number of new (weak) resonances were observed. We then studied the capture reaction with a small sample enriched to 99.99% 115 In. This latter measurement provided isotopic identiKcation of the new resonances [69]. The parity violation

200

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 7 Resonance parameters and PNC asymmetries p for E (eV)

‘

63.47a 146.4a 156.9a 281.5 299.8a 406.4a 461.9a 521.9a 562.5a 593.4a; b 644.9a 870.6a 922.0a 967.5 1005a 1148a 1206a 1306a 1323a 1377a 1398a 1511a 1557a 1585a 1597a 1624a 1764a 1839a

1 1 1 0 1 1 1 1 1 (1) 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0

a b

J

0.5

0.5 0.5 0.5

0.5 0.5

0.5

106

Pd. Parameter AJ is in units eV−1

gn (meV)

AJ

p (%)

|p|=Xp

0:013 ± 0:001 0:60 ± 0:03 0:27 ± 0:01 515 ± 14 0:24 ± 0:01 0:83 ± 0:03 1:16 ± 0:04 6:0 ± 0:3 5:5 ± 0:2 12:5 ± 0:6 0:52 ± 0:05 877 ± 30 705 ± 26 16 ± 1 58 ± 4 4:0 ± 0:4 10:0 ± 0:7 3:4 ± 0:3 7:8 ± 0:8 2:2 ± 0:2 231 ± 17 28 ± 2 1:7 ± 0:2 158 ± 16 12 ± 1 10 ± 1 18 ± 2 914 ± 67

1.6 0.4 0.7

0:07 ± 0:07 0:02 ± 0:08 −0:16 ± 0:046

1.0 0.3 3.5

5.8 0.5 0.3 0.1 0.1 0.1 0.5

0:09 ± 0:15 −0:07 ± 0:12 −0:04 ± 0:12 −0:06 ± 0:06 −0:04 ± 0:07 −0:17 ± 0:04 0:60 ± 0:38

0.6 0.6 0.3 1.0 0.6 4.2 1.6

0.4

0:12 ± 0:07

1.7

0.2 0.1 0.2 0.2 1.0

0:58 ± 0:24 −0:11 ± 0:15 0:36 ± 0:40 −0:17 ± 0:21 −0:53 ± 0:66

2.4 0.7 0.9 0.8 0.8

0.1 0.7

0:09 ± 0:12 −1:2 ± 1:2

0.8 1.0

0.6 0.2 0.2

−0:17 ± 0:22 −0:12 ± 0:28 −0:15 ± 0:21

0.8 0.4 0.7

New resonances. Possible doublet.

experiment was performed at a later date using a natural indium target in transmission [136]. In addition the same enriched sample was studied at IRMM in order to determine resonance spins [154]. The targets for the PNC experiment were natural indium with an areal density of 2:88 × 1023 and 5:86 × 1023 atoms=cm2 . The neutron resonance parameters, enhancement factors, and asymmetries are listed in Table 12. Nine statistically signiKcant PNC eFects were observed in 115 In. 4.9. Tin 117 Sn

was studied with the -ray detector [133]. The target was 362 g of tin enriched to 87.6% The areal density was 3:37 × 1022 atoms=cm2 of 117 Sn. The resonance parameters, enhancement factors, and asymmetries are listed in Table 13. For 117 Sn the J values of the s-wave resonances are unknown above about 200 eV. We assume that the J = 1 states should 117 Sn.

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 8 Resonance parameters and PNC asymmetries p for

108

Pd. Parameter AJ is in units eV−1

E (eV)

‘

J

gn (meV)

2:96a 32:98 90:98 112:7 149:8 302:7 410:6 426:6 480:3 544:4 635 642 797 843 905 955 962a 1082 1121b 1140b 1215 1359 1433 1456 1505b 1523 1652 1710 1743b 1815b 2010 2118 2165b 2287

1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1

1:5 0:5 0:5

0:00504 ± 0:00005 123 ± 4 214 ± 6 1:03 ± 0:05 0:060 ± 0:006 3:70 ± 0:15 0:69 ± 0:02 371 ± 11 0:62 ± 0:02 5:6 ± 0:3 396 ± 12 1:3 ± 0:1 6:3 ± 0:4 1:3 ± 0:1 585 ± 29 877 ± 37 47:1 ± 0:4 17 ± 1 0:51 ± 0:05 0:08 ± 0:02 418 ± 42 28 ± 2 148 ± 15 4:5 ± 0:5 0:33 ± 0:05 2:8 ± 0:3 1269 ± 127 77 ± 8 0:47 ± 0:07 2:4 ± 0:2 696 ± 70 7:5 ± 0:8 2:6 ± 0:3 37 ± 4

a b

0:5 0:5

0:5 0:5 0:5

0:5 0:5

0:5 0:5 0:5

201

AJ

p (%)

|p|=Xp

1:4 2:6 0:22 2:9

0:04 ± 0:04 0:06 ± 0:30 0:03 ± 0:06 −0:22 ± 0:25

1:0 0:2 0:5 0:9

1:0 0:25

0:03 ± 0:30 −0:04 ± 0:09

0:1 0:4

5:1 0:21 0:69

0:37 ± 0:34 0:12 ± 0:14 −0:45 ± 0:65

1:1 0:8 0:7

0:15 0:86 2:4

0:09 ± 0:12 0:7 ± 2:3 −5:0 ± 5:7

0:7 0:3 0:9

0:10

0:03 ± 0:14

0:2

0:54 1:1 0:39

0:45 ± 0:54 −1:2 ± 5:2 −0:11 ± 0:93

0:8 0:2 0:1

1:5 0:37

−8:7 ± 4:9 1:2 ± 1:8

1:8 0:7

0:19 0:24 0:04

0:23 ± 0:81 0:4 ± 2:5 −0:31 ± 0:29

0:3 0:2 1:1

Resonance parameters from Mughabghab [111]. New resonances.

predominate by a factor of approximately three, and therefore above 200 eV the AJ factors were calculated assuming that all of the s-wave resonances with unknown spin have J = 1. Four statistically signiKcant PNC eFects were observed. 4.10. Antimony Natural antimony (57.3% 121 Sb and 42.7% 123 Sb) was studied in transmission [101]. We took advantage of the approximately equal isotopic abundance to study parity violation in both

202

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 9 Resonance parameters and PNC asymmetries p for E (eV)

‘

−11:1a 16:3 ± 0:02 18:9 ± 0:02b 20:3 ± 0:02b 35:84 ± 0:03b 41:57 ± 0:05 42:81 ± 0:03b 44:90 ± 0:03 51:56 ± 0:05 64:24 ± 0:05b 64:74 ± 0:05b 73:21 ± 0:06b 83:55 ± 0:07 101:2 ± 0:1b 107:6 ± 0:1b 110:8 ± 0:1b 125:1 ± 0:1b 126:1 ± 0:1b 128:5 ± 0:1 136:7 ± 0:1b 141:5 ± 0:1b 144:2 ± 0:1 154:8 ± 0:1 162:0 ± 0:2 166:9 ± 0:2 173:7 ± 0:2 183:5 ± 0:2b 201:0 ± 0:2b 202:6 ± 0:2 218:9 ± 0:2 228:3 ± 0:2b 231:0 ± 0:2b 235:5 ± 0:2b 251:3 ± 0:3 259:9 ± 0:3 264:5 ± 0:3 269:9 ± 0:4 310:8 ± 0:4 328:2 ± 0:4 346:8 ± 0:4 359:7 ± 0:4b 361:2 ± 0:4 372:5 ± 0:5 381:8 ± 0:5 384:9 ± 0:5b 403:9 ± 0:5 409:2 ± 0:5 422:5 ± 0:6b 444:0 ± 0:6 460:9 ± 0:6 a Values b New

0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0

J 1 0

1 1 1 1 2 1 2 1 2 0 1 2 0 1 1 0 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1 2 0 0 1

from Mughabghab [111]. resonances.

107 Ag.

Parameters AJ are in units eV−1

gn (meV) √

7:4 E 2:9 ± 0:2 (1:1 ± 1:5)10−4 (1:2 ± 0:6)10−4 (3:4 ± 0:5)10−4 2:8 ± 0:4 (4:9 ± 1:1)10−3 0:62 ± 0:1 17:9 ± 1:8 0:018 ± 0:002 0:013 ± 0:001 0:027 ± 0:006 0:015 ± 0:002 0:004 ± 0:003 0:014 ± 0:002 0:081 ± 0:009 0:010 ± 0:001 0:018 ± 0:002 0:092 ± 0:009 0:028 ± 0:003 0:010 ± 0:001 4:0 ± 0:8 0:025 ± 0:003 0:28 ± 0:02 0:19 ± 0:01 5:50 ± 0:5 0:13 ± 0:01 0:27 ± 0:02 12:90 ± 0:5 0:084 ± 0:008 0:040 ± 0:004 0:052 ± 0:004 0:029 ± 0:004 16:0 ± 4 0:25 ± 0:03 2:5 ± 0:2 0:20 ± 0:02 65 ± 15 0:60 ± 0:10 0:40 ± 0:04 0:26 ± 0:1 15:5 ± 1:0 0:19 ± 0:02 0:29 ± 0:03 0:10 ± 0:04 0:30 ± 0:08 0:36 ± 0:05 0:18 ± 0:02 21:3 ± 2:0 18:0 ± 2:0

A0

A1

p (%)

|p|=Xp

12:4

30:0

−4:05 ± 0:38

10:7

5:2

0:13 ± 0:06

2:2

0:0

0:135 ± 0:060

2:3

2:2 0:0 1:7 0:0

0:390 ± 0:060 −0:004 ± 0:016 0:87 ± 0:11 0:050 ± 0:058 0:022 ± 0:017

6:5 0:1 7:9 0:9 1:3

2:3

−0:40 ± 0:10

4:2

1:8 9:8

−0:003 ± 0:049 −0:107 ± 0:022

0:1 4:9

1:9

0:037 ± 0:067

0:6

2:5

0:308 ± 0:038

8:1

1:8

0:120 ± 0:036

3:3

0:550 ± 0:083

6:6

0:0 0:0 2:7 0:0

0:18

1:1

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 10 Resonance parameters and PNC asymmetries p for E (eV)

‘

J

5:19 30:6 32:7a 40:3 55:8 71:0 78:5a 79:8a 82:5 87:7 91:5 106:3 113:5 133:9 139:6 160:3a 164:3a 169:8 173:1 199:0a 209:2 219:2a 251:2 259:0 264:7 272:4 275:8a 284:0a 290:6 293:3 300:9 316:2 322:1 327:8 340:2 351:4a

0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1

1 1 1 1 0 1

9:5 ± 0:3 5:4 ± 0:5 0:013 ± 0:002 4:4 ± 0:4 5:4 ± 0:5 18:9 ± 1:8

2 1 2 0 2 1 1 1 2 0 1 1 1 2 1 0 2 1

0:016 ± 0:002 4:10 ± 0:3 0:029 ± 0:003 0:14 ± 0:015 0:017 ± 0:004 69:1 ± 6:0 1:50 ± 0:5 0:04 ± 0:01 0:014 ± 0:005 0:36 ± 0:06 33:7 ± 3:0 0:11 ± 0:02 18:6 ± 2:0 0:06 ± 0:01 4:4 ± 0:4 3:4 ± 0:3

a

2 1 1 0 1 1 2 2

gn (meV)

1:5 ± 0:2 0:054 ± 0:006 0:28 ± 0:03 8:3 ± 0:8 0:30 ± 0:04 1:5 ± 0:2 150:0 ± 15:0 0:11 ± 0:015 0:65 ± 0:07 0:33 ± 0:03 0:055 ± 0:006

109

203

Ag. Parameters AJ are in units eV−1 A0

A1

20:5

p (%)

|p|=Xp

1:22 ± 0:02

60:0

0:0

0:0

−0:03 ± 0:05

0:5

0:0

0:0

−0:12 ± 0:07

1:7

0:0

0:0

−0:09 ± 0:07

1:3

0:0

5:7 0:0

−0:09 ± 0:07 0:02 ± 0:13

1:3 0:2

3:1

0:19 ± 0:04

4:8

0:0

−0:16 ± 0:05

3:0

5:2

−0:35 ± 0:04

8:8

0:0

New resonances.

nuclides with one target. The target was natural metallic antimony with 3:67 × 1023 atoms=cm2 of 121 Sb and 2:74 × 1023 atoms=cm2 of 123 Sb. A sample enriched to 99.48% 121 Sb was studied with the -ray detector in order to aid in the isotopic identiKcation of the resonances. The resonance parameters, enhancement factors, and longitudinal asymmetries are listed for 121 Sb in Table 14 and for 123 Sb in Table 15. A values above 170 eV are not quoted because of J

204

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 11 Resonance parameters and PNC asymmetries p for E (eV)

‘

Ja

0.178c 7.00 18.36 21.83 43.38 49.77 56.23 63.70 81.52 84.91 98.52 102.3 108.3 143.0 158.7 166.6 192.8 196.1 203.5 215.2 232.4 237.8 252.7 261.1 269.4 281.8 289.6d 291.6 312.3 343.8 351.6 359.3 376.8 385.0 414.1 432.0 447.1 457.8 489.9 501.0

0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0

1 1 1 2 0 1 2 1

a

1 2 1 1 0 1 0 1 1 1 2 2 1 0 1 (1) 1 2 0 2 1 1 1 1 0 1 1 1

Cd. Parameters AJ are in units eV−1

gn b (meV) 0:49 ± 0:02 0:00031 ± 0:00003 0:141 ± 0:001 0:0071 ± 0:0002 0:0047 ± 0:0004 0:0150 ± 0:0005 0:0403 ± 0:0006 2:60 ± 0:03 0:0052 ± 0:0006 22:4 ± 0:1 0:042 ± 0:001 0:037 ± 0:001 8:52 ± 0:06 2:34 ± 0:03 6:47 ± 0:06 0:020 ± 0:002 45:8 ± 0:1 0:100 ± 0:005 0:067 ± 0:003 20:2 ± 0:1 1:06 ± 0:01 0:125 ± 0:004 0:140 ± 0:004 26:3 ± 0:2 17:5 ± 0:1 0:48 ± 0:01 0:06 ± 0:006 4:40 ± 0:07 0:491 ± 0:007 0:17 ± 0:01 0:036 ± 0:003 0:28 ± 0:01 0:83 ± 0:01 0:089 ± 0:006 94:5 ± 0:4 18:3 ± 0:2 2:10 ± 0:02 1:62 ± 0:02 0:72 ± 0:02 36:9 ± 0:3

J values from Gunsing [78]. gn values from Frankle [70]. c Values from Mughabghab [111]. d Doublet not resolved in TRIPLE experiment. e Deduced value for one component of doublet. b

113

A0

0.0 1.03

A1

p (%)

|p|=Xp

29.7

−0:80 ± 0:36

2.2

0.0

0.2 0.6 0.2 2.3

0.0

2.9 0.0

−0:04 ± 0:22 −0:32 ± 0:55 −0:05 ± 0:22 0:23 ± 0:10

1.6

38.5

0:56 ± 1:15

0.5

0.0

0.0 58.4

−0:33 ± 0:21 1:04 ± 0:22

1.6 4.7

3.7

4.4

2:00 ± 1:10

1.8

13.0

1.7 3.1

−1:65 ± 0:76 −0:50 ± 0:40

2.2 1.2

0.0 0.0

0.0 0.0

0:24 ± 0:21 0:25 ± 0:25

1.1 1.0

1.0 8.9

−0:20 ± 0:14 5:1 ± 1:1e

1.4 4.6

0.0 0.0 0.8 0.6 2.3

0:16 ± 0:15 −0:41 ± 0:51 −0:46 ± 1:24 −0:22 ± 0:34 −0:33 ± 0:13 −0:18 ± 0:61

1.1 0.8 0.4 0.6 2.5 0.3

0.5 1.3

−0:05 ± 0:10 0:04 ± 0:23

0.5 0.2

0.0 0.4 0.0 0.42

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 12 Resonance parameters and PNC asymmetries p for

115

E (eV)

‘

J

gn (meV)

1.457a 3.850 6.853 9.12 12.10 13.46 22.73 29.68 39.62 40.68 46.40 48.17 58.76 62.97 66.40 69.53 73.06 77.81 80.87 83.31 85.46 86.32 88.44 94.37 100.81 103.70 110.86 114.41 120.64 125.97 132.94 144.07 145.64 146.78 150.24 156.42 158.53 162.23 164.65 168.11 174.15 177.90 186.79 190.91 192.29 194.47 198.6

0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1

5 4 5 5 4 5 5 5 5

1.670 0.170b (2:3 ± 0:2) × 10−4 0:80 ± 0:08 0:049 ± 0:005 (9:2 ± 0:9) × 10−4 0:449 ± 0:045 (11:2 ± 1:1) × 10−4 2:02 ± 0:10 0:0037 ± 0:0009 0:128 ± 0:011 0:264 ± 0:032 (3:3 ± 0:2) × 10−4 0:358 ± 0:026 (4:0 ± 0:2) × 10−5 0:158 ± 0:008 0:012 ± 0:001 0:0016 ± 0:0001 0:65 ± 0:05 3:33 ± 0:19 0:0031 ± 0:0008 0:002 ± 0:001 (8:5 ± 1:6) × 10−4 1:40 ± 0:07 0:031 ± 0:002 0:0004 ± 0:0002 0:021 ± 0:002 0:067 ± 0:004 0:027 ± 0:002 1:59 ± 0:08 1:91 ± 0:27 0:084 ± 0:009 0:028 ± 0:003 0:023 ± 0:005 1:74 ± 0:14 0:0051 ± 0:001 0:046 ± 0:004 0:072 ± 0:007 7:50 ± 0:47 0:90 ± 0:12 0:084 ± 0:009 1:2 ± 0:2 9:85 ± 0:50 0:021 ± 0:002 0:19 ± 0:03 0:035 ± 0:008 0:031 ± 0:004

4 5 4 5 5 4 5

5 4 5 3 4 5 4 5 5 3 4 5 4 4 5 5 4 4 5 3 4

205

In. Parameters AJ are in units eV−1 A4

A5

p (%)

|p|=Xp

67.4

−1:45 ± 0:11

13.0

20.3

0:61 ± 0:07

8.7

12.4

0:44 ± 0:04

11.0

2.7

44.6

−0:55 ± 0:04

13.8

17.0

16.5

−0:52 ± 0:38

1.4

13.7

4.3 17.6

0:046 ± 0:023 −0:63 ± 0:16

2.0 3.9

6.8 2.3 8.8

31.0 8.9 2.9

0:13 ± 0:23 −0:025 ± 0:024 −0:22 ± 0:65

0.6 1.0 0.34

1.1 0

0 2.2 9.9 4.4 8.5

10.8 0 3.5

0:007 ± 0:019

0.4

0

0:04 ± 0:03

1.3

1.9

0:115 ± 0:031

3.7

1.8 0

−0:045 ± 0:019 0:022 ± 0:037 0:084 ± 0:044

2.4 0.6 1.9

7.3 1.7

−0:10 ± 0:17 0:54 ± 0:03 −0:014 ± 0:025

0.6 18.0 0.6

1.6

−0:034 ± 0:028

1.2

4.0 1.4 0

0:05 ± 0:13 0.4 0:03 ± 0:03 1.0 −0:03 ± 0:06 0.5 0:04 ± 0:07 0.6 (Continued on next page)

206

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 12 Continued E (eV)

‘

J

gn (meV)

205.6 211.9 214.0 219.9 224.0 226.9 246.7 249.0b 250.8b 264.5 266.8 275.6 276.6 282.2 285.1 288.9 294.1b 294.7b 302.6 304.1 308.1 313.4 316.2 319.4

0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0

5 5 4

14:2 ± 1:7 0:24 ± 0:03 0:076 ± 0:010 0:0077 ± 0:0004 10:1 ± 2:0 2:1 ± 1:3 0:057 ± 0:012 0:40 ± 0:02 17:26 ± 0:86 0:04 ± 0:02 2:21 ± 0:11 0:007 ± 0:003 0:048 ± 0:011 0:050 ± 0:003 0:027 ± 0:014 8:05 ± 0:88 15:06 ± 0:75 4:21 ± 0:21 0:177 ± 0:019 0:42 ± 0:24 0:073 ± 0:006 0:11 ± 0:09 0:05 ± 0:03 5:8 ± 1:4

a b

5 4 4,5 4,5 5

4 4,5 4,5 4 5 5 4

A4

A5 2.7

2.2 3.8 1.6

3.0

−0:11 ± 0:13

0.8

9.5 3.6 4.8 8.2

1:07 ± 0:60 −0:06 ± 0:10 0:032 ± 0:098 −0:23 ± 0:35

1.8 0.6 0.3 0.7

2.2 3.7

−0:46 ± 0:06 −0:061 ± 0:045 0:06 ± 0:13

7.7 1.3 0.5

3.1

−0:11 ± 0:25

0.4

19.0

8.6

8.6 3.3 5.0 10.5

7.2

|p|=Xp

−0:058 ± 0:026 0:15 ± 0:04 1:00 ± 0:62

1.6 6.4

2.6

p (%)

From Mughabghab [111]. Components of doublet.

the absence of spin assignments for many s-wave resonances. Five statistically signiKcant PNC eFects were observed in 121 Sb and one statistically signiKcant PNC eFect in 123 Sb. 4.11. Iodine 127 I

was studied in transmission [101]. The target consisted of natural crystalline iodine of areal density 7:24 × 1023 atoms=cm2 . The resonance parameters, enhancement factors, and longitudinal asymmetries are listed in Table 16. Above 220 eV the spins of the s-wave resonances are unknown; therefore no AJ factors are quoted. Several new p-wave resonances in iodine were observed. Statistically signiKcant PNC eFects were observed for seven of the twenty p-wave resonances. 4.12. Xenon Natural xenon was studied in transmission [140]. A PNC eFect in the 3.2-eV resonance was observed, but the resonance was not identiKed with any speciKc isotope. The target at

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 13 Resonance parameters and PNC asymmetries p for E (eV) −29:2a

1.33 15.39c 21.39c 26.21c 34.04 38.80a 74.39 120.5 123.9 158.3c 166.3 196.2 200.8 221.2 275.2 297.4 341.6 357.6 400.0 420.7a 423.3c 459.0a 488.5c 526.3 532.6 554.6 573.2c 580.8a 628.6c 646.7 658.5 685.7 694.4c 698.3c 705.7 789.4 812.9a 852.6c 864.5 882.3 939.2a 983.3a 989.4a 996.1a 1045c 1078c 1116c 1150c 1164 a Values

‘ 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0

Ja 1 1

1 1 0 1

0

0

1

117 Sn.

Parameters AJ are in units eV−1

gn (meV) √

5:55 E 0:000138 ± 0:000007 0:000092 ± 0:000005 0:000206 ± 0:000011 0:00207 ± 0:00010 0:0187 ± 0:0009 3:10 ± 0:15 0:034 ± 0:002 4:95 ± 0:25 2:1 ± 0:1 0:0025 ± 0:0001 0:160 ± 0:008 12:2 ± 0:6 0:48 ± 0:02 0:22 ± 0:01 0:17 ± 0:01 0:43 ± 0:02 15:9 ± 0:8 12:0 ± 3:5 3:7 ± 0:2 62:5 ± 7:5 1:55 ± 0:08 12:5 ± 1:5 0:036 ± 0:002 0:96 ± 0:07 1:46 ± 0:10 0:74 ± 0:06 0:78 ± 0:06 30 ± 3 0:141 ± 0:013 1:20 ± 0:12 2:2 ± 0:2 1:15 ± 0:12 0:19 ± 0:02 0:72 ± 0:08 2:6 ± 0:3 11:0 ± 1:3 65 ± 6 0:79 ± 0:10 10:5 ± 2:1 3:6 ± 0:5 20 ± 2 0:92 ± 0:13 200 ± 30 90 ± 15 0:42 ± 0:06 0:66 ± 0:10 0:37 ± 0:06 1:14 ± 0:18 15:6 ± 2:5

from Mughabghab [111]. above 200 eV are not unique; see text for explanation. c New resonances. b Values

207

A0 b

A1 b

p (%)

|p|=Xp

2.0 1.5 0.52 0.20

11.1 20.8 16.3 6.50 5.34

0:79 ± 0:04 −0:38 ± 0:82 −0:04 ± 0:66 0:28 ± 0:15 −0:08 ± 0:02

19.8 0.5 0.1 1.8 4.0

0.29

1.0

−0:00 ± 0:03

0.1

1.84 0.19

4.80 0.68

0:02 ± 0:03 0:68 ± 0:66

0.5 1.0

0.08 0.11 0.13 0.08

2.23 0.67 0.52 0.40

−0:01 ± 0:03 0:00 ± 0:04 0:01 ± 0:06 −0:03 ± 0:04

0.3 0.0 0.2 0.7

0.16

4.97

−0:31 ± 0:05

6.0

1.42 0.23 0.20 0.49 1.63

1.46 0.21 0.16 0.21 0.19

−1:32 ± 0:58 −0:04 ± 0:05 −0:01 ± 0:04 0:01 ± 0:06 −0:06 ± 0:07

2.3 0.8 0.2 0.2 0.9

0.64 0.12 0.11 0.18 0.69 0.53

0.45 0.17 0.12 0.19 0.48 0.25

−0:05 ± 0:30 0:03 ± 0:06 0:06 ± 0:05 0:04 ± 0:076 −0:05 ± 0:30 −0:07 ± 0:10

0.2 0.5 1.2

0.06

0.83

0:06 ± 0:13

0.4

0.03

0.30

−0:01 ± 0:05

0.2

0.04

5.1

−0:04 ± 0:18

0.2

0.05 0.04

1.04 0.54

1:07 ± 0:34 0:12 ± 0:24

3.1 0.5

0.2 0.7

208

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 14 Resonance parameters and PNC asymmetries p for E (eV) −12:0

a

6.24a 15.50a 29.65a 37.9 53.5a 55.21 64.5a 73.8a 89.6a 90.3a 92.10c 110.7c 111.4a 126.8a 131.9a 141.2c 144.3a 149.9a 157.1a 160.6a 167.1a 174.5c 176.9 184.7 192.3a 200.3c 214.0a 222.6a 228.6 230.6a 235.9 245.9 249.0 261.6 265.8 270.0 274.8 286.4a

‘

Ja

0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0

2 3 2 3 2 3 2 3 3 2 3 3 2 3 2 2

3

3

gn (meV) 1:05 ± 0:05 3:45 ± 0:20 2:55 ± 0:20 0:0085 ± 0:0009 1:0 ± 0:1 0:014 ± 0:002 0:335 ± 0:025 3:75 ± 0:25 5:25 ± 1:25 2:75 ± 0:20 0:017 ± 0:002 0:037 ± 0:005 1:40 ± 0:15 13:5 ± 1:5 5:25 ± 0:50 0:0081 ± 0:0008 6:5 ± 0:5 14:0 ± 0:5 0:067 ± 0:015 0:75 ± 0:15 7:5 ± 1:0 0:0054 ± 0:0005 0:043 ± 0:004 0:126 ± 0:012 0:75 ± 0:10 0:0054 ± 0:0005 0:675 ± 0:050 2:60 ± 0:26 0:044 ± 0:004 0:4 ± 0:1 0:019 ± 0:002 0:235 ± 0:022 0:128 ± 0:012 0:181 ± 0:018 0:167 ± 0:017 0:208 ± 0:021 0:153 ± 0:015 7:0 ± 0:35

121

Sb. Parameters AJ are in units eV−1 A2 b

A3 b

p (%)

|p|=Xp

2.8

4.8

0:018 ± 0:016

1.1

10.2

2.3

−0:133 ± 0:018

7.3

2.2 17.6

20.2 3.1

−0:51 ± 0:05 2:15 ± 0:06

10.2 35.8

18.4

12.5

1:26 ± 0:12

10.5

10.7

5.3

0:045 ± 0:033 0:03 ± 0:07 −0:051 ± 0:033

1.4 0.4 1.5

−0:029 ± 0:076

0.4

−0:072 ± 0:075

1.0

−0:05 ± 0:16 0:017 ± 0:045 0:138 ± 0:052 −0:029 ± 0:036 0:080 ± 0:048 0:179 ± 0:046 0:128 ± 0:050

0.3 0.4 2.7 0.8 1.7 3.9 2.6

a

Values from Mughabghab [111]. Values above 170 eV are not listed; see text for explanation. c New resonances. b

Los Alamos was natural liqueKed xenon of 524 l-atm. in a copper container. The areal density was 1:75 × 1023 atoms=cm2 . To obtain information about the isotopic origin of the PNC eFect, a 1 l-atm. target of xenon enriched to 80.6% 129 Xe was studied. The areal density was

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 15 Resonance parameters and PNC asymmetries p for E (eV)

‘

Ja

−17:0a

0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0

3 4 3

21.4a 50.5a 67.0a 76.7a 105.0a 131.0a 176.4 186.1 191.8a 197.7 202.0b 218.6a 225.2 240.8a 295.9a 299.3a a b

4 3

3

4 4

gn (meV) 15:0 ± 1:5 1:5 ± 0:15 0:013 ± 0:0013 2:85 ± 0:20 26:5 ± 2:5 0:60 ± 0:06 0:176 ± 0:017 0:154 ± 0:015 22:5 ± 1:5 0:243 ± 0:024 0:160 ± 0:016 2:05 ± 0:20 0:160 ± 0:016 9:0 ± 1:5 0:8 ± 0:10 12:9 ± 1:2

123

209

Sb. Parameters AJ are in units eV−1 A3

A4

p (%)

|p|=Xp

1.5 4.2

0.9 0.8

−0:076 ± 0:042 −0:012 ± 0:035

1.8 0.3

3.3 2.4

0.6 0.7

−0:02 ± 0:035 −0:46 ± 0:12

0.6 3.8

1.3

1.1

−0:014 ± 0:045

0.3

Values from Mughabghab [111]. New resonances.

4:28 × 1021 atoms=cm2 of 129 Xe. These measurements eliminated 129 Xe and all xenon isotopes with mass number less than A = 130 from consideration. The most likely remaining isotope was 131 Xe. A subsequent -ray decay study at JINR, Dubna, of the 3.2-eV resonance identiKed that resonance as belonging to 131 Xe [129]. The Dubna target was natural pressurized xenon of 120 l-atm. in a stainless steel container. The corresponding areal density was 0:38 × 1023 atoms=cm2 . The analysis was performed with the code PVIO [157] and the longitudinal asymmetry determined. The resonance parameters for the resonance showing the PNC eFect and for the nearest two resonances are listed in Table 17, along with the enhancement factors and the longitudinal asymmetry. The spin of the p-wave resonance is unknown. There are two nearby resonances in 131 Xe with diFerent J values. Therefore we have used the two-level approximation and calculated the enhancement factor AJ for the two J values. 4.13. Cesium 133 Cs

was measured in transmission [126]. The 99.999% chemically pure target of CsF was contained in an aluminum cylinder and had an areal density of 2:42 × 1023 cesium atoms=cm2 . The resonance parameters, enhancement factors, and asymmetries are listed in Table 18. About 20 p-wave resonances in cesium were observed for the Krst time. Since their spins are unknown, there are two entries for the coeMcients AJ for each p-wave resonance. The values of these coeMcients are exceptionally large, and thus favor observation of PNC eFects. Nevertheless only the 9.5-eV resonance showed a statistically signiKcant eFect. Together with the absence of

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Table 16 Resonance parameters and PNC asymmetries p for E (eV)

‘

Ja

−57:7a −52:3a

0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0

2 3

7.51c 10.34c 13.93c 20.43a 24.63c 31.24a 37.74a 45.39a 52.20c 53.82 64.04 65.93a 78.53a 85.84 90.38a 101.1c 126.0c 134.1 136.9c 139.7a 145.7 153.6 168.5a 173.9a 178.1a 195.3a 206.2a 223.4c 237.1a 244.7a 256.8 265.1a 271.1a 274.7c 282.1c 292.1a 299.3a 310.6a 324.3a 328.7a 346.5a 352.0 353.3 362.2a 374.5a 385.6a 392.7a 420.0a a Values

3 2 2 2

2 3

3

3 3 2 3 3

127 I.

Parameters AJ are in units eV−1

gn (meV)

A2 b

A3 b

p (%)

0:00012 ± 0:0001 0:0028 ± 0:0003 0:0014 ± 0:0001 0:68 ± 0:05 0:00064 ± 0:0006 13:0 ± 1:5 26:0 ± 2:5 11:5 ± 2:0 0:00085 ± 0:0008 0:019 ± 0:002 0:008 ± 0:001 0:80 ± 0:15 15:5 ± 2:0 0:0174 ± 0:002 10:4 ± 1:5 0:014 ± 0:002 0:0021 ± 0:0002 0:025 ± 0:003 0:040 ± 0:004 23:0 ± 2:3 0:033 ± 0:003 0:096 ± 0:003 487:0 ± 6:5 1:38 ± 0:13 0:467 ± 0:065 56:0 ± 3:5 18:0 ± 1:5 0:011 ± 0:001 24:65 ± 1:55 5:65 ± 0:50 0:052 ± 0:005 20:35 ± 1:65 3:70 ± 0:35 0:022 ± 0:002 0:0045 ± 0:0005 0:27 ± 0:05 13:8 ± 1:7 17:8 ± 1:7 0:50 ± 0:09 2:72 ± 0:18 0:45 ± 0:07 0:088 ± 0:009 0:089 ± 0:009 3:61 ± 0:19 62:5 ± 2:0 108:0 ± 5:0 0:33 ± 0:20 12:3 ± 1:0

37.6 9.0 15.3

22.5 5.2 9.0

0:13 ± 0:14 −0:005 ± 0:03 0:01 ± 0:04

0.9 0.2 0.3

51.7

19.3

1:65 ± 0:16

10.3

47.8 8.8 13.5

13.1 2.9 6.8

0:10 ± 0:18 0:24 ± 0:02 0:06 ± 0:02

0.5 12.0 3.0

4.7

13.6

0:24 ± 0:02

11.0

5.8 22.3 7.9 6.8

6.6 16.5 10.9 17.1

0:10 ± 0:03 −0:48 ± 0:16 0:02 ± 0:02 0:731 ± 0:016

3.2 3.0 1.0 45.7

10.5 9.4

9.0 2.4

0:00 ± 0:03 0:01 ± 0:02

0.0 0.5

−0:01 ± 0:13

0.1

0:04 ± 0:04

1.0

−0:32 ± 0:15 −0:47 ± 0:53

2.1 0.9

−0:539 ± 0:064 0:05 ± 0:064

8.4 0.8

from Mughabghb [111]. above 220 eV are not quoted; see text for explanation. c New resonances. b Values

|p|=Xp

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 17 Resonance parameters and PNC asymmetries p for E (eV) −84:0a

3:2 14.4a a b

‘ 0 1 0

Ja 1 2

131

Xe. Parameters AJ are in units eV−1

gn (meV) √

211

235.0 E 0:00016 ± 0:00002 7:0 ± 0:5

A1 b

A2 b

p (%)

|p|=Xp

37.2

25.6

4:3 ± 0:2

21.5

Values from Mughabghb [111]. Values in the two-level approximation.

any PNC eFects in other resonances and considering the large size of the AJ coeMcients, this results in a small rms matrix element MJ in cesium. This is discussed in Section 5.3. 4.14. Lanthanum The nuclide 139 La is the most studied of all those in which parity violation has been observed. Since the Krst observation of the PNC eFect in the 0.748-eV resonance by the Dubna team [4], measurements have been performed at KIAE [15], KEK [100], and LANL [152]. The value of (9:56 ± 0:35) × 10−2 [20] was Knally established. The initial Dubna result was about 25% less but was later revised [7]. In subsequent TRIPLE PNC experiments lanthanum was routinely measured in transmission for normalizing the absolute value of the neutron beam polarization with the use of the well-known PNC eFect. Two metal targets of 6:53 × 1022 atoms=cm2 each were used in these measurements. Resonance parameters of the 0.748-eV resonance were obtained with FITXS code. These parameters are listed in Table 19 along with the enhancement factors and the longitudinal asymmetry. The spin of the p-wave resonance is assumed to be the same as for the s-wave bound level responsible for parity mixing. The total width of the p-wave resonance at 0:748 eV is 42.5±2.5 meV. 4.15. Thorium The TRIPLE PNC transmission measurements on thorium were performed twice: Krst with our initial equipment [65,66] and then later with the improved experimental system [135]. The target was a cylinder of natural thorium (232 Th) with an areal density of 3:40 × 1023 atoms=cm2 . The neutron resonance parameters, enhancement factors, and PNC asymmetries are listed in Table 20. Initially we had no information about the J values of the p-wave resonances. Therefore the analysis was performed treating the spin values as unknown. Based on the large PNC eFects observed for a number of the p-wave resonances, we assigned J = 1=2 to these resonances. Such assignments are denoted by parentheses surrounding the J assignment in Table 20, which presents results for the resonances below 285 eV. All of the statistically signiKcant asymmetries have the same relative sign. This unexpected result led to a great deal of theoretical interest; we discuss this ‘sign correlation’ in Section 6. It was considered important to extend the analysis in 232 Th to higher energies, and to examine whether the nonstatistical behavior observed at low energy persisted to higher energies. Unfortunately the resolution limitations made an application of our standard analysis impossible

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G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 18 Resonance parameters and PNC asymmetries p for E (eV) −40:8a

5.91 9.50 16.77 18.86 19.98 22.52 30.00b 33.00b 42.75b 44.63b 47.52 58.09b 59.61 60.24b 78.52b 80.00b 82.71 88.96b 94.21 110.45b 115.00b 117.51b 119.92b 126.1 140.0 146.0 155.3b 167.0b 181.5 201.1 207.5 217.1b 220.5 234.1 238.4 267.5b 271.0b 273.6b 284.9b 288.4b 295.5 312.0b 324.0b 328.0b 330.2b 359.1 362.8b 377.1 386.3b 400.5 aJ

‘ 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0

Ja 4 3

3

3

4

4 3 4 3 4 4 4 4 4 4

4

4 3

values from Mughabghab [111]. resonances.

b New

133 Cs.

Parameters AJ are in units eV−1

gn (meV) √

43:8 E 3:23 ± 0:15 (0:95 ± 0:10) × 10−3 (0:77 ± 0:08) × 10−4 (0:68 ± 0:09) × 10−4 (0:38 ± 0:04) × 10−3 3:38 ± 0:20 (0:55 ± 0:07) × 10−4 (2:90 ± 0:40) × 10−4 (0:65 ± 0:08) × 10−3 (3:40 ± 0:40) × 10−3 8:72 ± 0:71 (0:4 ± 0:10) × 10−3 (0:36 ± 0:10) × 10−1 (1:95 ± 0:23) × 10−3 (0:50 ± 0:07) × 10−3 (1:54 ± 0:25) × 10−3 3:18 ± 0:47 (1:60 ± 0:13) × 10−2 11:6 ± 1:00 (0:16 ± 0:02) × 10−2 (0:41 ± 0:05) × 10−2 (0:40 ± 0:06) × 10−2 (5:40 ± 0:45) × 10−2 58:6 ± 0:5 3:72 ± 0:35 13:6 ± 1:20 (0:88 ± 0:09) × 10−1 (0:20 ± 0:02) × 10−1 1:04 ± 0:11 10:6 ± 1:00 2:08 ± 0:21 0:27 ± 0:03 11:1 ± 1:3 193:3 ± 15:0 7:0 ± 0:8 (8:20 ± 1:0) × 10−2 (3:6 ± 0:5) × 10−2 (1:40 ± 0:13) × 10−2 (12:6 ± 1:1) × 10−2 (28:6 ± 3:1) × 10−2 61:2 ± 6:0 (4:0 ± 0:4) × 10−2 (3:0 ± 0:4) × 10−2 (3:0 ± 0:4) × 10−1 (1:6 ± 0:2) × 10−1 18:6 ± 1:6 (1:6 ± 0:2) × 10−1 8:9 ± 0:9 (0:30 ± 0:03) × 10−1 132:0 ± 18:0

A3

A4

p (%)

|p|=Xp

38.0 88.8 133 79.4

9.6 34.2 36.7 15.8

0:24 ± 0:02 −0:35 ± 0:47 −0:28 ± 0:62 −0:01 ± 0:14

10.4 0.8 0.5 0.1

35.7 49.0 34.9

18.2 12.4 54.6

0:05 ± 0:30 −0:17 ± 0:18 0:06 ± 0:15

0.1 0.9 0.4

51.4

17.3

1:21 ± 1:74

0.7

44.4 22.4 13.6

7.90 24.6 15.6

−0:08 ± 0:14 −1:20 ± 1:35 −0:17 ± 0:29

0.5 0.9 0.6

10.3

23.0

−0:05 ± 0:03

1.7

8.8 5.7 7.5 1.6

18.9 20.4 37.3 86.7

0:62 ± 0:44 0:02 ± 0:27 0:12 ± 0:23 0:05 ± 0:30

0.7 0.1 0.5 1.7

1.2 1.9

7.2 5.2

−0:07 ± 0:03 −0:08 ± 0:10

−0:8

0.7 1.2 2.1 2.2

3.8 5.7 9.0 4.3

−0:07 ± 0:08 0:05 ± 0:20 −0:45 ± 0:50 0:02 ± 0:06

0.9 0.2 0.9 0.3

2.5

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 19 Resonance parameters and PNC asymmetries p for E (eV) −48:6a

0:748 72:20a a b

‘ 0 1 0

Ja 4 4 3

139

213

La. Parameters AJ are in units eV−1

gn (meV) √

80:0 E (3:75 ± 0:18) × 10−5 16:6 ± 0:5

A3 b

A4 b

p (%)

|p|=Xp

55.1

9:56 ± 0:35

27.3

Resonance parameters from Mughabghb [111]. Values in the two-level approximation.

for resonances at higher energies. However, we were able to perform a more limited analysis in the region 250 –2000 eV [127]. These results are discussed in Section 6.3. 4.16. Uranium The Krst TRIPLE PNC measurement was a transmission measurement on 238 U [21,157]. The transmission measurement was later repeated with the improved experimental system [41]. The 238 U target was a cylinder with an areal density of 3:025 × 1023 atoms=cm2 . The target was depleted of 235 U; from Ktting known resonances of 235 U, the amount of 235 U in the target was (0:21 ± 0:01)%. The neutron resonance parameters, enhancement factors, and observed asymmetries are listed in Table 21. The spins of most of the p-wave resonances were determined at IRMM [78]. The AJ factor listed in the table is for the spin value J = 1=2. When the spin J = 3=2 is measured, the AJ values for such resonances are identically zero and these resonances are omitted from the analysis. Five resonances showed statistically signiKcant PNC eFects. The results listed in Table 21 demonstrate that only p-wave resonances with the proper angular momentum value show parity violation. 5. Experimental average resonance parameters 5.1. Level densities The neutron spectroscopic results for the individual resonance parameters E0 ; gn , and J , which are presented in Section 4, determine the ampliKcation factors AJ needed to obtain the PNC asymmetries p. As discussed in Section 3, the subsequent determination of the weak spreading widths requires the level spacings DJ . Determination of the resonance parity requires the values of the s- and p-wave neutron strength functions, in addition to the level spacing DJ . We begin description of the TRIPLE information on average resonance properties with the level density. For nearly all of the nuclides studied, the neutron cross section compilation of Mughabghab et al. [111] provided initial values of the ‘observed’ s-wave level spacing 0 . However, the ‘observed’ p-wave level spacing D1 Dobs obs was known for very few nuclides. Our results are presented in Table 22. These level densities were obtained by direct counting, considering only the linear region of the plot of the cumulative number of levels versus

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G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 20 Resonance parameters and PNC asymmetries p for E (eV) −9:38

8.36 13.14 21.82 23.45 36.98 38.23 41.07 47.07 49.94 58.77 59.52 64.57 69.23 90.14 98.06 103.63 113.00 120.83 128.17 129.16 145.83 148.06 154.29 167.11 170.30 178.86 192.60 196.20 199.25 202.58 210.91 221.11 231.95 234.07 242.25 251.47 263.04 276.45 285.68 a

‘ 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0

Ja 0.5 (0.5) 0.5 0.5 (0.5) (0.5) 0.5 (0.5) 0.5 (0.5) 0.5 0.5 (0.5) 0.5 0.5 (0.5) 0.5 0.5 (0.5) 0.5 (0.5) 0.5 (0.5) 0.5 0.5 0.5

232

Th: Parameter AJ =0:5 is in units eV−1

gn (meV)

AJ

p (%)

|p|=Xp

√

6:18 E (2:67 ± 0:04) × 10−4 (1:93 ± 0:04) × 10−4 2:18 ± 0:044 4:10 ± 0:082 (8:8 ± 0:2) × 10−4 (4:8 ± 0:1) × 10−4 (5:1 ± 0:1) × 10−4 (1:7 ± 0:4) × 10−4 (4:3 ± 0:1) × 10−4 0:0090 ± 0:0002 3:88 ± 0:083 (7:9 ± 0:4) × 10−4 44:52 ± 0:91 0:0056 ± 0:0001 0:0043 ± 0:0001 0:00650 ± 0:00013 13:07 ± 0:27 22:67 ± 0:47 0:0801 ± 0:0044 3:59 ± 0:79 0:088 ± 0:003 0:0063 ± 0:0001 0:193 ± 0:015 0:0235 ± 0:0006 62:23 ± 1:35 0:0246 ± 0:0007 16:36 ± 0:36 0:070 ± 0:002 9:58 ± 0:19 0:0422 ± 0:002 0:0181 ± 0:0004 29:25 ± 0:60 0:0102 ± 0:0005 0:0161 ± 0:0004 0:0434 ± 0:0009 31:05 ± 0:65 21:16 ± 0:50 0:0086 ± 0:0002 30:56 ± 0:76

25.0 38.5

1:78 ± 0:09 0:16 ± 0:14

19.8 1.1

20.5 27.1 27.0 17.3 40.0 58.3

− 0:01 ± 0:17 6:41 ± 0:32 − 0:09 ± 0:27 2:52 ± 0:13 − 0:24 ± 0:39 0:02 ± 0:03

0.1 20.0 0.3 19.4 0.6 0.7

103

14:2 ± 0:4

34.5

11.6 12.9 13.4

0:21 ± 0:19 − 0:70 ± 0:22 0:22 ± 0:16

1.1 3.2 1.4

13.6

2:31 ± 0:12

19.2

0:00 ± 0:10 − 0:11 ± 0:34

0.0 0.3

33.8

3:21 ± 0:10

32.1

15.5

0:19 ± 0:28

0.7

11.4

0:90 ± 0:18

5.0

11.2 10.5

1:10 ± 0:25 − 0:23 ± 0:32

4.4 0.7

12.6 10.1 7.04

4:77 ± 0:68 − 0:16 ± 0:45 0:18 ± 0:17

7.0 0.4 1.0

0:46 ± 0:76

0.6

2.89 12.4

17.1

Values in parentheses are assigned to resonances with asymmetries p ¿ 3.

neutron energy. The error bars are calculated following the prescription by Lynn [98]—XD=D =  1 0:27=N , where N is the number of spacings. Most of the Dobs values are obtained from our measurements.

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241 Table 21 Resonance parameters and PNC asymmetries p for E (eV) −137:0

10.235 11.309 19.521 20.866 36.67 45.158 49.613 63.496 66.02 72.373 80.741 83.672 89.218 93.081 97.975 102.60 111.18 116.89 124.94 133.18 145.64 152.39 158.94 165.26 173.18 189.70 208.47 214.85 218.33 237.34 242.67 253.84 257.17 263.89 273.61 282.41 290.96 a

‘ 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0

Ja 0.5 1.5 0.5 1.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.5 1.5 0.5 0.5 1.5 0.5 1.5 1.5 0.5 0.5 0.5 0.5 0.5 0.5 1.5 1.5 0.5 1.5 0.5

238

215

U. Parameter AJ is in units eV−1

gn (meV)

AJ

p (%)

|p|=Xp

0.0 46.9 0.0

0:034 ± 0:016 0:728 ± 0:038 −0:016 ± 0:018

2.1 19.3 0.9

35.7 37.7 41.1

−3:15 ± 0:18 −0:066 ± 0:26 4:41 ± 0:10

17.1 0.3 44.9

42.3

0:09 ± 0:38

0.2

15.6 5.03 0.0 0.0

−0:090 ± 0:079 −0:351 ± 0:078 0:108 ± 0:080 −0:024 ± 0:081

1.1 4.5 1.4 0.3

33.1

0:22 ± 0:27

0.8

0.0 12.0

0:28 ± 0:18 0:10 ± 0:31

1.5 0.3

0.0 0.0

−0:085 ± 0:080 −0:04 ± 0:22

1.1 0.2

0:398 ± 0:064

6.3

√

61:5 E 0:00168 ± 0:00005 0:00041 ± 0:00001 0:00150 ± 0:00005 10:6 ± 0:3 34:8 ± 1:1 0:00205 ± 0:00007 0:00108 ± 0:00002 0:0094 ± 0:0003 24:7 ± 0:9 0:0018 ± 0:0002 1:7 ± 0:2 0:0090 ± 0:0003 0:085 ± 0:003 0:0062 ± 0:0002 0:0044 ± 0:0002 71:7 ± 2:2 0:0067 ± 0:0005 25:3 ± 1:0 0:0196 ± 0:0007 0:0078 ± 0:0003 0:74 ± 0:02 0:052 ± 0:002 0:0164 ± 0:0005 3:2 ± 0:2 0:048 ± 0:002 174:2 ± 5:2 51:0 ± 1:7 0:055 ± 0:002 0:036 ± 0:004 25:8 ± 0:9 0:203 ± 0:009 0:116 ± 0:004 0:025 ± 0:002 0:259 ± 0:008 24:3 ± 0:7 0:112 ± 0:004 16:1 ± 0:5

7.96 10.9 9.85

−0:85 ± 0:67 −0:18 ± 0:43

1.3 0.4

4.63 0.0 6.58 0.0

0:12 ± 0:26 −0:07 ± 0:18 −1:22 ± 0:42 0:12 ± 0:17

0.4 0.4 2.9 0.7

0:11 ± 0:19

0.6

0.0

Values for p-wave resonances from Gunsing [78].

With the assumption of parity independence of the level density for a given spin J , and 1 D0 =3 for I = 0 with the (2J + 1) approximation for the spin dependence, one expects Dobs obs 1 D0 =2 for I ¿ 3=2 targets. We use this estimate in our analysis even though targets and Dobs obs 1 1 many spacings Dobs were obtained after identifying p-wave resonances. These measured Dobs 0 are often larger than the spacing predicted by scaling from Dobs . This is because of the limited

216

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

Table 22 Level densities A

I

0 Dobs (eV)

81

3=2 9=2 1=2 0 5=2 0 0 1=2 1=2 1=2 9=2 1=2 5=2 7=2 5=2 3=2 7=2 7=2 0 0

94 ± 15 95 ± 8 44:9 ± 3:1 220 ± 65 12 ± 1 217 ± 61 182 ± 33 25 ± 3 21 ± 2 24:8 ± 2:6 11:0 ± 0:6 30 ± 2 13 ± 2 30 ± 4 23 ± 3 70 ± 20 20:5 ± 1:9 210 ± 10 19 ± 3 21 ± 3

Br Nb 103 Rh 104 Pd 105 Pd 106 Pd 108 Pd 107 Ag 109 Ag 113 Cd 115 In 117 Sn 121 Sb 123 Sb 127 I 131 Xe 133 Cs 139 La 232 Th 238 U 93

a b

1 Dobs (eV)

Comments a

50 ± 6 14:3 ± 3:1 74 ± 15

10 85 ± 19 95 ± 24 11:0 ± 1:3

20 11:0 ± 1:2

10

39

25

50

12 8:0 ± 1:0

b b b b b b b

a a

8:3 ± 1:2 9:1 ± 1:6

Values from Mughabghab [111]. 0 Dobs revised.

experimental sensitivity to weak p-wave resonances at low neutron energies. In such cases no attempt was made to calculate the missing level fraction and the spacings are listed in Table 22 0 values are diFerent without errors. In several cases, as noted in the comments, the TRIPLE Dobs from those in Ref. [111]. These diFerences arise because of diFerent parity assignments—our 0 parity assignments were made using the Bayesian approach described in Section 3.5. The Dobs values that are listed without comments agree with those given by [111]. 5.2. Neutron strength functions The deKnition of the neutron strength function S l for various partial waves l is given in Section 3.4. Neutron strength functions have been a topic of major emphasis in neutron physics for many years. Extensive data were compiled by Mughabghab et al. [111]. It should be noted that for the mass region near A = 110, p-wave strength functions were obtained indirectly by Camarda [37] from analysis of the energy averaged neutron transmission—the s- and p-wave contributions were separated by their diFerent energy dependence over the neutron energy range up to 600 keV. The LANSCE spallation pulsed neutron source provided the Krst opportunity to measure many weak p-wave resonances for neutron energies up to several hundred eV. The neutron strength functions obtained by TRIPLE in the PNC measurements are presented

G.E. Mitchell et al. / Physics Reports 354 (2001) 157–241

217

Table 23 Neutron strength functions and mixing parameter a aa

A 81

Br Nb 103 Rh 104 Pd 105 Pd 106 Pd 108 Pd 107 Ag 109 Ag 113 Cd 115 In 117 Sn 121 Sb 123 Sb 127 I 131 Xe 133 Cs 139 La 232 Th 238 U 93

a b

0.67 0.61 0 1.0 0.8 0.8 0.74 0.58 0.60 0.65 0.65 0.66 0.70

S 0 (10−4 )

S 1 (10−4 )

Refs.

0:8 ± 0:1 0:6 ± 8 0:43 ± 0:08 0:47 ± 0:24 0:55 ± 0:15 2170:6 ± 0:3 0:9 ± 0:4 0:50 ± 0:15 0:84 ± 0:23 0:32 ± 0:02 0:30 ± 0:06 0:17 ± 0:05 0:30 ± 0:05 0:25 ± 0:7 0:8 ± 0:1 1:2 ± 0:4 0:80 ± 0:17 0:78 ± 0:11 0:9 ± 0:3 1:6 ± 0:6

1:5 ± 0:5b 5:1 ± 1:6 8:8 ± 1:2 3:2 ± 1:1 4:4 ± 1:0 4:0 ± 1:0 4:0 ± 1:0 3:5 ± 0:8 2:8 ± 0:8 3:0 ± 0:5 3:2 ± 0:6 3:4 ± 1:0 2:5 ± 0:8b

[111] [125] [131] [134] [134] [42] [42] [97] [97] [70] [69] [130] [111] [111] [111] [111] [126] [111] [135] [41]

1:6 ± 0:5b 1:1 ± 0:3 0:4 ± 0:1 0:8 ± 0:2 1:2 ± 0:4

Estimated from data [114,115]. Estimated in this work.

in Table 23 and in Fig. 9. The strength functions are obtained directly from the deKnition, Eq. (45), using the measured reduced neutron widths calculated after the resonance parity was  l l assigned. The error bars are XS =S = 2=N , where N is the number of resonances [98]. The neutron strength function data from diFerent neutron energy regions (ours and those of [37]) agree within the limits of the uncertainties. The spin–orbit interaction causes a J dependence of the p-wave neutron strength function. For 1 and S 1 components of the 3-p maximum some time, the size of the splitting between the S1=2 3=2 was a matter of debate. The issue was settled by Popov and Samosvat [114,115] with neutron 1 1 scattering angular distribution measurements. We use their data on the S1=2 and S3=2 strength functions to estimate the entrance channel j-spin mixing of the neutron amplitudes, as described in Section 3. The corresponding parameter a (see Eq. (37)), which is the square root of the 1 =S 1 ratio, is also listed in Table 23. S3=2 1=2 5.3. Rms weak matrix elements 5.3.1. Overview of data In extracting the rms matrix element MJ from the PNC asymmetry data, the TRIPLE Collaboration followed the statistical procedure described in Section 3. Due to the entrance channel

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Fig. 9. P-wave neutron strength function S 1 versus mass number A in the region of the 3p maximum. The TRIPLE data are represented by solid circles.

projectile-spin amplitude problem, the analysis procedure diFerentiates between the target spin zero (even–even targets) and spin nonzero cases. The precision with which the rms weak matrix element MJ can be determined is governed by the PNC data and the amount of available spectroscopic information. The status of these quantities for each nuclide studied is given in the tables of Section 4. Usually the s- and p-wave neutron widths and resonance energies are measured, and the spins are known for most of the s-wave resonances, but the spins of the p-wave resonances are not known. For this case one proceeds with Eqs. (32) and (41) of the Bayesian likelihood analysis to extract the values and uncertainties for the rms PNC matrix element MJ from the experimental asymmetries p. Measurements by the IRMM group for silver, cadmium, indium, and uranium provided spin information; this permitted application of the ‘all spins known’ analysis option where one applies Eqs. (31) and (42). In a few cases there were indications of overlapping resonances that were not resolved in these experiments, but which showed a statistically signiKcant PNC asymmetry. In these cases we omit this information unless a plausible assumption on the doublet components is available. 5.3.2. Speci
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219

Fig. 10. Likelihood functions for 238 U: left—with complete spin information (only the seven known spin J = 1=2 resonances), right—without spin information (all 24 p-wave resonances taken as having unknown spin).

Applying the likelihood analysis with the option ‘p-wave spins known’, Eq. (31), to these seven J = 1=2 resonances, one obtains the likelihood function shown in the left of Fig. 10 with the result M1=2 =0:64+0:22 −0:14 meV. Assuming, for the moment, that no p-wave spins are known and applying the option of ‘p-wave spins not known’, Eq. (32), to all 24 resonances one obtains the likelihood function shown in right of Fig. 10, with M1=2 =0:69+0:26 −0:17 meV. If all available (but incomplete) spin information for the 24 resonances is used, one obtains M1=2 = 0:67+0:24 −0:16 meV. −7 eV is obtained The corresponding value of the spreading width w =2 M 2 =D=(1:35+0:97 ) × 10 −0:64 with the level spacing listed in Table 22, Section 5.1. For an even–even target with a suMcient number of measured asymmetries there is very little diFerence when the spins are known, or when the purely statistical approach is adopted without any spin information. The physical reason for this is that resonances that show no statistically signiKcant parity violation (whether p3=2 states that cannot display parity violation or p1=2 states that accidentally have only a small parity violation), have very little eFect on the Knal value of MJ . Thorium. The longitudinal PNC asymmetries p for 232 Th [135] are plotted versus energy E in Fig. 11. There are 10 statistically signiKcant positive asymmetries and none with negative sign. Since these data are not centered around zero, we represent the thorium data, following Bowman et al. [21], as the sum of two terms: a :uctuating term and a constant term. The expression used is p5 = 2B6 [U65 =(E6 − E5 )](n6 =n5 )1=2 + B[(1 eV)=E6 ]1=2 ;

(53)

where E is in eV. The quantities U65 , E6 , and E5 are independent random variables, and the Krst term has average value zero. The energy dependence of the ratio of widths is E −1=2 . Expressing the constant term relative to the value at En =1 eV by the oFset parameter B gives the convenient result that the ratio of the :uctuating and constant terms does not depend on energy. Next, we proceed with the maximum likelihood method, except there are now two parameters—the rms PNC matrix element M and the empirical oFset B (expressed in %),

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Fig. 11. Longitudinal PNC neutron cross section asymmetries p versus neutron energy E for thorium. The plot demonstrates the ‘sign eFect’, which consists of ten asymmetries in a row with the same sign.

Fig. 12. Two-parameter likelihood plot for thorium. The curves are contours of constant likelihood with values 80%, 60%, 40%, and 20% of the maximum likelihood.

Eq. (53). A two-parameter maximum likelihood plot for the 232 Th data is shown in Fig. 12. The +5:0 values for MJ and B are MJ = 1:12+0:32 −0:22 meV and B = 14:9−5:0 %. For comparison, we also treat the 238 U data [41] in the same manner. A two-parameter maximum likelihood plot for 238 U is +2:34 shown in Fig. 13. The values for MJ and B are MJ = 0:65+0:23 −0:15 meV and B = −1:96−2:31 %. These Kgures demonstrate very clearly that the sign eFect exists in thorium and is absent in uranium. With the thorium level spacing D0 = 17:0 eV from Table 22, this matrix element corresponds −7 eV. If one ignores the oFset B and Kts the data to a weak spreading width of w = 4:7+2:7 −1:8 × 10

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Fig. 13. Two-parameter likelihood plot for 238 U. The curves are contours of constant likelihood with values 80%, 60%, 40%, and 20% of the maximum likelihood.

+5:3 −7 eV. with only the one parameter MJ , the result is MJ = 1:58+0:44 −0:31 meV and w = 9:4−3:5 × 10 An extensive discussion of the sign eFect in the thorium PNC asymmetries is given in the next section. 1 Palladium. As seen from Table 22, even–even palladium isotopes have level spacings Dobs about 200 eV, which is 10 times larger than the level spacings in uranium or thorium. One expects the size of PNC eFects to be correspondingly reduced. 108 Pd showed no statistically signiKcant PNC asymmetry. 104 Pd and 106 Pd yielded one and two statistically signiKcant PNC asymmetries, respectively, which led to rather uncertain matrix elements of 1:9+2:5 −0:9 meV for 104 Pd and 1:9+1:8 meV for 106 Pd. −0:9 106 Pd has a 3:5 asymmetry in a weak p-wave resonance at 156:9 eV and a 4 asymmetry in a strong resonance at 593:4 eV. The latter resonance can only marginally be assigned as the p-wave resonance because it has nearly equal probability to occur in Porter–Thomas distributions of neutron widths for s- and p-wave resonances. The PNC asymmetry with the p-wave assignment for this resonance alone yields an extremely large matrix element of 10:9 meV [43]. On the other hand, the PNC asymmetry in the 156.9-eV resonance alone gives a reasonable value of MJ . A plausible interpretation is the existence of a doublet of p- and s-wave resonances at 593 eV. In the absence of any information on the energy separation and strengths of the doublet components, the PNC information obtained from the 593-eV resonance is not reliable and therefore was omitted from the analysis.

5.3.3. Speci
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known. The likelihood function [125] with no maximum has a long tail. The upper limits for w are 0.1 and 1.0 (in units of 10−7 eV) for 68 and 95% conKdence levels, respectively. The upper limits for the rms matrix elements are 0.6 and 1:8 meV for the same conKdence levels. When comparing small niobium asymmetries with PNC asymmetries in uranium, one should take into account the relationships for the ampliKcation factors AJ (93 Nb) (0:03–0:1)AJ (238 U) and for level spacings DJ (93 Nb) 10DJ (238 U). Based on uranium percent size asymmetry p and assuming a constant spreading width one expects the size of PNC asymmetries in niobium at the level of (0.1– 0.3)%. For most of the resonances measured, the threshold of observability for a PNC asymmetry was about 0.15%, and for the Krst niobium p-wave resonances at 35.9 and 42:3 eV, the threshold was 0.02%. Rhodium. The longitudinal cross section asymmetries were measured for 32 p-wave resonances in 103 Rh in the neutron energy range from 30 to 490 eV. Statistically signiKcant longitudinal asymmetries were observed for resonances at En = 44:5; 110:8; 321:6; and 432:9 eV. The spins of s-wave resonances below 500 eV are known, while the spins of p-wave resonances are not known. We veriKed that the eFect of the unknown s-wave resonance J values at higher energies was negligible by performing the likelihood analysis with the unknown spins Krst all set to J = 0 and then all set to J = 1. The results were essentially identical. The value of the −7 eV, which results from the likelihood analysis [132], weak spreading width w = (1:4+1:2 −0:6 ) × 10 leads to the matrix element MJ =1=2 = 1:2+0:5 −0:4 meV. Palladium-105. PNC measurements on 105 Pd were made with a target of natural palladium (22.3% abundance of 105 Pd). Due to the high density in 105 Pd and the relatively low densities in the even–even palladium isotopes, most of the observed p-wave resonances were in 105 Pd. They were measured for the Krst time. The longitudinal asymmetries were measured for 23 p-wave resonances in the neutron energy range from 40 to 300 eV. Statistically signiKcant longitudinal asymmetries were observed at two energies: 72.5 and about 83 eV. While a 9 PNC asymmetry in the 72.5-eV p-wave resonance presents no complications, there is an indication that near 83 eV there are two p-wave resonances. They are not resolved, and the values listed in Section 4, Table 6, are obtained assuming resonance peaks at 82.9 and 83:3 eV. The spins of the s-wave resonances in 105 Pd are known, while the p-wave spins are not. The likelihood analysis −7 eV, which results in of Smith et al. [134] yields a weak spreading width w = (0:8+1:3 −0:5 ) × 10 +0:3 a matrix element MJ = 0:6−0:2 meV. Silver. For silver, measurements were performed for both the PNC asymmetries [97] and the p-wave resonance spins [154]. A total of 15 p-wave neutron resonances were studied in 107 Ag and nine p-wave resonances in 109 Ag. Statistically signiKcant asymmetries were observed for eight resonances in 107 Ag and for four resonances in 109 Ag. A likelihood analysis with the option −7 eV for 107 Ag and of all spins known, yielded a weak spreading width of w = (2:67+2:65 −1:21 ) × 10 +2:49 −7 109 w = (1:30−0:74 ) × 10 eV for Ag. Knowing the spins of the p-wave resonances in silver permits this I = 0 target to be treated directly in terms of the weak rms matrix element. Fig. 14 shows the 109 Ag likelihood function calculated from PNC data for resonances with spin J = 1. Since there are only four asymmetries, the curve is broader then in the corresponding case of uranium (which has seven asymmetries, see the top of Fig. 10), producing a larger uncertainty +0:5 107 Ag is M in the matrix element MJ =1 = 0:76+0:54 J =1 = 1:2−0:3 meV. It was −0:26 meV. The result for 107 possible to estimate the MJ =0 matrix element in Ag from the PNC data for three resonances

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Fig. 14. Likelihood function for the J = 1 resonances in element M .

109

223

Ag versus the root-mean-square weak interaction matrix

with spin J = 0. The result MJ =0 = 5:6+5:0 −2:1 meV is in qualitative agreement with the expected J dependence of the matrix element. Cadmium. The PNC study of cadmium resonances [7,121] and the spin measurements [78] were of particular interest because the Krst enhancement of parity violation in the compound nucleus [1] was observed in the asymmetry of the -ray yield following capture of polarized thermal neutrons by cadmium. The spins of the s- and p-wave resonances were known. The asymmetries p of the neutron capture cross sections were measured for nine J = 1 resonances with three statistically signiKcant eFects observed at energies 7.0, 102.3, and 289:6 eV. Analysis of all of the data [121] led to a very large value of the matrix element. The last PNC eFect, however, represents a case of insuMcient spectroscopic information for the energy unresolved pair of s- and p-wave resonances. Therefore we excluded the 289.6-eV result from the analysis. −7 eV and an rms matrix The remaining data provide a weak spreading width w = (3:2+3:4 −1:6 ) × 10 element MJ =1 = 1:3+0:6 −0:4 meV. Indium. A total of 36 p-wave neutron resonances were studied in 115 In [136] up to neutron energy 316 eV, and statistically signiKcant asymmetries were observed for nine resonances. The results of spin measurements, as reported in [136], are less complete than for the other targets measured by the IRMM group. Therefore the statistical likelihood analysis for obtaining MJ was performed in terms of the spreading width with maximum available but incomplete information on spins. The resulting likelihood function is shown at the left of Fig. 15 and yields a value −7 eV. Assuming equal spacings D for spins J = 4 and 5, we obtain of w = (1:30+0:76 J −0:43 ) × 10

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Fig. 15. Likelihood functions for 115 In versus the weak spreading width w : left—with all available but incomplete spin information; right—without spin information.

a matrix element of 0:67+0:16 −0:12 meV. As an example of the importance of the resonance spin assignments, the right side of Fig. 15 shows the likelihood functions for 115 In with all p-wave spin information omitted. There is a small diFerence in MJ , and the curve is broader due to the many terms participating in the likelihood function for I = 0 when the spins are unknown. Tin. The longitudinal asymmetries in 117 Sn were measured for 29 p-wave resonances in the neutron energy range 0.8–1100 eV, with three statistically signiKcant eFects below 423 eV. Since information on the spins of the s-wave resonances is absent above ∼490 eV, we report the results of the likelihood analysis for data below 490 eV, where 14 p-wave resonances were studied. In this energy region, the J values are known for most of the s-wave resonances that are near the p-wave resonances which display signiKcant asymmetries. Since the PNC eFect is inversely proportional to the energy diFerence between the s- and p-wave resonances, the nearest s-wave resonances are the most important. In order to estimate the magnitude of the eFect on the weak spreading width due to the remaining s-wave resonances, we made two extreme assumptions: the unknown spins of s-wave resonances were assumed to be all J = 0 or all J = 1. These two options had very little eFect on the weak spreading width, as seen from plots presented by −7 eV and the Smith et al. [133]. The average result for the two options is w = (0:28+0:56 −0:15 ) × 10 matrix element MJ =1 = 0:6+0:4 −0:2 meV. Antimony and iodine. For the isotopes of antimony and iodine we report preliminary results based on the Ph.D. dissertation of Matsuda [101] and additional analysis that is in progress [102]. A total of 17 p-wave resonances were studied in 121 Sb below 275 eV with Kve statistically signiKcant asymmetries, while Kve p-wave resonances in 123 Sb were measured with only one resonance with a nonzero asymmetry. The spins of the s-wave resonances are known, while the spins of the p-wave resonances are not known. The results of the likelihood analysis for −7 eV for 121 Sb and  = (1:9+15 ) × 10−7 eV the weak spreading width are w = (4:8+8:6 w −2:9 ) × 10 −1:4 for 123 Sb. The matrix elements obtained from these results are MJ = 1:4+0:9 meV for 121 Sb and −0:5 123 Sb. MJ = 1:3+2:7 −0:7 meV for

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Fig. 16. Likelihood functions for p-wave resonances in on a logarithmic scale.

133

225

Cs: left—versus w on a linear scale; right—versus w

In iodine, the measurements were performed on 20 p-wave resonances below 353 eV, with statistically signiKcant nonzero asymmetry results for seven resonances. Again, the spins of the s-wave resonances are known and the spins of the p-wave resonances are not known. The analysis was performed in terms of the weak spreading width with the results w = (0:6+0:9 −0:4 ) × 10−7 eV and MJ = 0:5+0:3 meV. −0:2 Cesium. In cesium a total of 28 new extremely weak p-wave resonances were found, their neutron widths determined, and the PNC longitudinal asymmetries of the resonance cross sections measured below 400 eV. In many cases, the neutron spectroscopic analysis of the observed p-wave resonances gave large ampliKcation parameters AJ which are favorable for PNC eFects. However, only one small asymmetry was observed and the experimental limits for the other resonances were rather small. From this result, the quantitative conclusion is that cesium has an exceptionally small value of the weak rms matrix element MJ and the weak spreading width w . The spins of the s-wave resonances in 133 Cs are known, while the spins of the p-wave resonances are not. The statistical analysis was performed in terms of w . The likelihood function L(w ) has a long tail, as shown at the left of Fig. 16, however, the likelihood function versus ln w is less asymmetric (right side of the Kgure). The maximum likelihood estimate with the 68% conKdence interval calculated from the area under the likelihood function is −7 eV, while a standard deKnition of errors according to Eq. (33) leads to w = (0:006+0:154 −0:003 ) × 10 −7 eV. Neglecting any possible diFerences in M and D between the result w =(0:006+0:018 J J −0:004 ) × 10 states with J = 3 and 4, we obtain a value of the rms matrix element MJ = (0:06+0:25 −0:02 ) meV. These values are the smallest of all targets studied by the TRIPLE Collaboration. 6. Sign e%ect and o%-resonance PNC asymmetry in thorium As discussed in Sections 4 and 5, the initial experiment on 232 Th yielded the unexpected result that all of the PNC eFects had the same sign. The improved experiment on 232 Th [135]

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found 10 statistically signiKcant PNC asymmetries below En = 250 eV, all of which have the same sign. This conKrms the nonstatistical eFect (sign correlation). Below we review the large number of attempts to explain this correlation. Both chronologically and in the general physics approach, the explanations divide into two categories. The Krst set of explanations can be loosely designated as ‘distant’ doorway state models. 6.1. Distant doorway state models By deKnition, the compound nucleus is very complicated and is expected to display random phases. Single particle or doorway state eFects were considered Krst as the origin of the sign correlation. One can express the oFset parameter B, see Eq. (53) in Section 5, in terms of doorway states |d as   d 1+ −
 (n)  d|U PNC | 12 5 B=2  p 2 : (54) (E5 − Ed ) (n) d

The Krst explanation was due to Bowman et al. [23]. Their approach uses single particle s- and p-wave states that are located some Kve MeV away from the p-wave resonances that display parity violation. The in:uence of the single-particle state leads to a sign correlation. However, in order to explain the size of the observed eFect, the matrix element d|U PNC |5 must be 100 times larger than all other evidence suggests. This failing—that an unphysically large weak matrix element is required in order to reproduce the size of the nonstatistical eFect—proved to be a recurring theme. Auerbach [9] writes the spreading width due to parity violation as w =


d

d (n)

+

−

| 12 d|U PNC | 12 5|2 : (E5 − Ed )2 + (d =2)2

(55)

He suggested using the J = 0− spin dipoles as the relevant doorway states. Auerbach and Bowman [10] then combined the spirit of these two ideas. The doorway states are the spin dipole giant resonances, and are distant in the sense that they are located several MeV from the p-wave resonances under consideration. Auerbach and Bowman start from the parity violating asymmetry
Vnm n pm = 2 ; (56) Em − En m n which is the standard result expressed in their notation, where |n are s-wave resonances, |m is the p-wave resonance of interest, and their energies are En and Em . The reduced neutron widths n and m can be written in terms of single particle amplitudes as n = s 0+ s1=2 |n ;

(57)

m = p 0+ p1=2 |m :

(58)

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The matrix element can then be written as Vnm = n|Dm Dm |U PNC |m ;

(59)

which illustrates the role of the doorway state |Dm . Taking into account the spin-dipole nature of the parity violating potential and using closure, one obtains
|Dm |n|2 2s + pm = 0 s1=2 |U PNC |0+ p1=2  : (60) p Em − En n The distribution |Dm |n|2 has its maximum near the doorway state, has a smooth shape, and is MeV away from the p-wave resonances that are measured. This implies that the sign of the parity violating asymmetry is Kxed for the p-wave resonances |m. However, to explain the size of the observed value of B requires a parity violating matrix element at least two orders of magnitude greater than considered reasonable. Flambaum [59] used a valence model approach in which the neutron interacts near the nuclear surface. He transformed the weak Hamiltonian into its surface form and calculated the valence component. In this description inelastic excitations in the target enhance the PNC matrix element. However, again the magnitude of the matrix element must be unreasonably large in order to explain the size of the observed eFect. The optical model was employed by Koonin et al. [91] and by Carlson and Hussein [38] and Carlson et al. [39] in eForts to explain the sign eFect. The optical model was used for the strong parity conserving part and the weak parity nonconserving term obtained from perturbation theory. The two groups use diFerent choices of the optical potential. Both results require a PNC matrix element at least 100 times too large. Lewenkopf and Weidenm,uller [95] utilized a single-particle approach with an enhancement of the weak parity violating matrix element due to an eFect called barrier penetration enhancement that results when the neutron (via the strong interaction) is in a virtual p-wave resonance channel. This highly excited p-wave state is MeV above threshold. They use single-particle states as doorways. The combination of the doorways and the barrier enhancement eFect leads to a sign correlation. However, to explain the size of the eFect requires a matrix element that is two orders of magnitude larger than considered reasonable. Auerbach and Spevak [11] adopted a projection operator approach and used a one-body form for both the parity violating part of the potential and the strong interaction part. The doorway states are spin dipole resonances. They numerically evaluated the barrier enhancement term proposed by Lewenkopf and Weidenm,uller. Again a matrix element that is two orders of magnitude too large was required to explain the eFect. At this stage it was clear that the distant state approach did not work. This had important implications: if the sign correlation is a general eFect and not some speciKc nuclear structure eFect, then a serious problem results. Therefore attention turned to diFerent models which were speciKc rather than general. 6.2. Local doorway state models The diMculty with the distant doorway state models was simply that the energy separation between the p-wave resonances and the doorway was so great that an unphysically large matrix

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element was required in order to provide an eFect of the magnitude observed experimentally. This problem can be removed by assuming a local or nearby doorway. However, now the solution to the problem generates a new problem. Single-particle states and spin dipole states are known to exist, and there are reasonable estimates for their locations and widths. Such guidance is lacking in establishing the physical origin of the local doorways. Some eForts have focussed on the special properties of the nuclide 232 Th, while others simply postulate the existence of a doorway with convenient features without addressing its origin. The general spirit is illustrated by the approach of Auerbach et al. [12]. Assume a p-wave resonance labeled |r  with escape amplitude r and a doorway d. The longitudinal asymmetry is
(Er − Ed )d|U PNC |r d p ∼ −2 : (61) 2 ] [(Er − Ed )2 + d=4 r d Assume the doorway is 50 eV from the p-wave resonance of interest and has a width d of 100 eV. Then for a typical ratio of penetrabilities for d /r of 103 , one obtains a matrix element of a few meV. Thus the inconsistency is removed and the problem is shifted to the origin and characteristics of the doorway state. The doorway states in this approach are intermediate structure resonances that are assumed not to overlap, and that have spacings intermediate between single particle and compound nuclear states. Since the striking nuclear structure feature of 233 Th is its octupole deformation, it was natural to consider this property. Intermediate structure resonances [16,17] have been observed in the neutron Kssion cross section for 233 Th, and have widths and spacings of the same order of magnitude as required in the local doorway approach. Auerbach and Bowman postulate the doorway as occurring in the third well, where the so-called parity doublets nearly coincide. Flambaum and Zelevinsky [61] and Auerbach et al. [14] discuss the eFects of the octupole doublets. They conclude that the idea is attractive but physically unlikely. Desplanques and Noguera [49] explicitly consider the octupole doublet or third well approach to be very unlikely. As a speculation they suggest that if the nucleus had a nonzero value of ˜ · p ˜ , then suppression factors that enter in the usual case do not appear. Desplanques and Noguera also provide a detailed general description of various possible outcomes given diFerent widths and locations of the doorways. All of these considerations emphasize the need for additional parity violation data on 232 Th, in order to constrain the characteristics of the local doorway, what ever its origin. In another local doorway approach—by Hussein et al. [82]—the doorway is a standard 2 particle–1 hole (2p–1h) state which happens by chance to be located near the p-wave resonances in question. This doorway couples at random to the compound nuclear states and has nothing directly to do with the shape of the thorium nucleus. The general role of doorways in such symmetry breaking studies is discussed at length by Feshbach et al. [55]. They say that this measurement of the sign correlation in thorium may be the Krst direct evidence for 2p–1h doorways. Unfortunately their approach provides no speciKc guidelines for the circumstances under which such nonstatistical eFects should occur—the eFect is almost random. To summarize, the present status of the sign correlation is that there is no generally accepted explanation for the physical origin of the eFect. The simplest explanation involves a local doorway state, but no convincing speciKc physical argument for the doorway has been presented. There is evidence that the sign correlation does not occur elsewhere. The results for the

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229

neighboring nuclide 238 U are consistent with a random sign for the PNC longitudinal asymmetries. Evidence from all of our other measurements on many nuclei in A = 90–130 region indicate that the signs of the PNC asymmetries are random. Thus, the sign correlation appears to be a real eFect that is at conKned to 232 Th. None of the numerous proposed explanations for this nonstatistical eFect provide a compelling explanation. 6.3. Thorium data above 250 eV Many of the theoretical discussions emphasize the need for PNC data at higher energies in thorium, in order to constrain the properties of the hypothetical doorways. With the improved sensitivity of the TRIPLE experimental system, and extension of the measurement to higher energies, one might expect to observe PNC eFects at higher energies in 232 Th. The diMculty is that the analysis procedure used to obtain the PNC asymmetry p relies on knowledge of the resonance shape. However, since the limited experimental resolution obscures many p-wave resonances, this analysis is unreliable at higher energies. Therefore the analysis of the 232 Th data above 250 eV was performed in terms of the PNC cross section diFerences X(Ep ) = + (Ep ) − − (Ep ), where the energies Ep are the peak energies of p-wave resonances. These peak cross section diFerences are measured directly and can show a PNC eFect even when the resonance peaks are not observed in the sum of the two helicity spectra. One must distinguish between the ideal Breit–Wigner cross section diFerence X(Ep ) and the resolution-broadened cross section diFerence XR (Ep ). The last quantity is related directly to the PNC transmission experiment, while the quantity X(Ep ), which is convenient for some theoretical formulations [91,39], must be deconvoluted from XR (Ep ). The PNC transmission asymmetry, &R , deKned as the relative diFerence in the detector yield due to the neutron spin :ip, is related to XR (Ep ) by n &R (Ep ) ≈ fn XR (Ep ) : 2

(62)

where n is the number of nuclei=cm2 in the target, and fn is the neutron beam polarization. The key point is that one can perform the analysis without knowledge of the resonance parameters. The details of the deconvolution procedure are spelled out by Sharapov et al. [127]. The results are presented in Table 24. The most favorable locations for observation of a PNC eFect is at s-wave interference minima. Above 250 eV we observed four negative and two positive statistically signiKcant longitudinal transmission asymmetries, all at interference minima. Three of these correspond to known resonances and three others to new p-wave resonances in 232 Th. The same procedure was applied to the data below 250 eV and gave results in agreement with the standard shape analysis. Other checks were performed—for example we assumed that the PNC eFect was due only to the nearest s-wave resonance, and calculated the weak matrix element using the two-level approximation. The resulting matrix elements are qualitatively consistent with those obtained at lower energies. It should be emphasized that this approach is extremely selective and that the six PNC eFects observed represent only a very small fraction of the eFects that would be observed with an ideal experimental system.

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Table 24 Longitudinal transmission asymmetries &R and PNC cross section diFerences XR for

232

Th resonances

Ep (eV)

&R (10−3 )

XR (mb)

38.23 47.07 64.57 98.0 128.17 167.11 196.20 202.58 231.95 250.0 302.4 687.2 1517 1898 1967

3:50 ± 0:25 3:30 ± 0:20 4:41 ± 0:18 0:54 ± 0:16 6:32 ± 0:35 2:37 ± 0:09 0:90 ± 0:27 0:95 ± 0:15 1:30 ± 0:13 −0:27 ± 0:05 −0:58 ± 0:06 3:00 ± 0:10 0:70 ± 0:04 −0:50 ± 0:13 −0:80 ± 0:08

156 ± 11 180 ± 11 332 ± 13 67 ± 20 1210 ± 68 581 ± 22 265 ± 80 310 ± 50 470 ± 50 −110 ± 20 −320 ± 33 5250 ± 180 3650 ± 210 −3600 ± 900 −6310 ± 630

The new results show that negative PNC eFects in 232 Th appear at neutron energies above 250 eV. This supports the local doorway state explanation of the sign correlation and provides some constraints on the properties of these doorway states. 6.4. OC-resonance PNC asymmetry in thorium In discussing the physical origin of the nonzero average asymmetry p, Y Weidenm,uller [147] suggested that the large single-particle matrix element which arises in the distant state explanation must have other observable consequences. In particular, Weidenm,uller noted an enhanced PNC asymmetry for neutrons scattered oF-resonance PoF = (+ − − )=(+ + − ) (+ − − )=2pot ;

(63)

where pot is the potential scattering cross section. On the other hand, the statistical model of the resonance enhancement (with a standard single-particle matrix element) must imply a small parity violation between resonances because the neutron potential scattering is not subject to PNC enhancement. Moreover, theoretical studies by Michel [104], Flambaum [59], and others reviewed by Mitchell [107], suggested a ‘kinematical suppression’ of the PNC asymmetry PoF in neutron potential scattering at low energies. At an energy of 100 eV, the theoretical limit PoF 0:3 × 10−7 follows from a standard choice for the strength of the neutron–nucleus weak interaction. In principle, some contribution to the asymmetry PoF should arise from parity violation in compound-nuclear states through the extended resonance tails. For a given p-wave resonance, the corresponding cross section diFerence Xp; res = (+ − − )p; res is expected to decrease as [2(E − E0 )=]2 , where  is the resonance total width. Neutron resonances in 232 Th are extremely narrow:  0:025 eV as compared with the average spacing D 17 eV. With a typical value

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231

of Xp; res 0:3 b [127], the estimate of a p-resonance contribution to PoF for the ‘symmetric’ energy position (E − E0 ) = D=2 between two parity-mixed resonances separated by D is PoF ∼ 0:3 × 10−7 —which is the same size as the ‘standard’ theoretical prediction for the nonresonant PNC violation. This allows room for a search for an enhanced ‘nonstandard’ single-particle matrix element. The Krst experimental search for parity violation in nonresonant neutron scattering on thorium was performed by Bowman et al. [25] with the result PoF = (0:98 ± 2:17) × 10−5 for the oF-resonance longitudinal asymmetry. The latest thorium data [135], with much better statistics and improved data quality, permitted Mitchell et al. [107] to reduce the above experimental limit by a factor of ten. The new analysis was performed for neutron energies between 30 and 300 eV. The available energy region was limited at low energy by the Knite number of TOF channels and at high energy by resolution resonance broadening. Energy intervals around all p- and s-wave resonances were excluded and statistical analysis of the transmission asymmetry & was performed in 20 intervals, each with an integrated count rate of 109 . The measured values were consistent with a zero oF-resonance transmission asymmetry within the limits of the statistical accuracy of ∼2:5 × 10−5 for an individual data region. At this level of accuracy, there is no energy dependence in the 20 energy regions analyzed. The weighted average is &=(0:16 ± 0:52) × 10−5 , with a corresponding chi-squared value per degree of freedom 22 =0:79. This result is normal from a statistical viewpoint, since the probability of observing such a value of 22 for a 6 = 19 distribution is about 70%. From this result and Eq. (10) with n = 0:34 atom=b and p replaced by pot = 13 b, we obtain the asymmetry value PoF = (0:5 ± 1:6) × 10−6 . This accuracy is not suMcient to distinguish between diFerent theoretical models. Nevertheless, the experiment establishes an upper limit for the oF-resonance PNC eFect which is four orders of magnitude smaller than the typical percent size of the PNC-enhanced resonance eFect. The eFective energy for which the present result was determined is about 100 eV. Because of the kinematical reduction of the PNC eFect in potential scattering, determination of the nonresonant PNC eFect has better prospects if performed at higher energies, e.g., up to 20 keV. The ideal test would be on targets, such as 208 Pb or 209 Bi, that have no dominant s-wave resonances in the energy region of interest. 7. Summary and discussion 7.1. Weak spreading widths One key question is whether the eFective nucleon–nucleus weak interaction is mass dependent. If there is a global mass dependence of the weak spreading width, it should be a slow function of the atomic number. The TRIPLE Collaboration studied PNC longitudinal asymmetries of cross sections in p-wave resonances of nuclei in mass regions A 110 and 230. The results for the weak spreading width are shown in Fig. 17 and listed in Table 25. Most of the data are obtained by the likelihood analysis procedure for measurements on ensembles of p-wave resonances in each nuclide. However, in order to have at least a rough estimate of w for nuclei in the region A = 30–60, and for 81 Br, 131 Xe, and 139 La, where only one p-wave resonance (and parity violation) was observed, we obtained the spreading width from its deKnition assuming

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Fig. 17. TRIPLE results for weak spreading widths w versus mass number in the region A = 90 − 238. See text for explanation of the data points at A = 35 and 56.

MJ Vsp and using the appropriate level spacing DJ . For the 35 Cl and 56 Fe data points in Fig. 16 we used the MJ -values deduced by Bunakov et al. [34] from thermal neutron PNC data. First we observe that the likelihood functions for the measured spreading widths are quite nonsymmetric. They tend to have tails to large values of w . The likelihood functions for the logarithm of the weak spreading widths are more symmetric as seen in Fig. 17. We therefore performed the least-squared analysis in terms of x = ln w . Our analysis is approximate because it assumes Gaussian distributions for x. Values of x and the one-standard-deviation upper, X+ x, and lower, X− x, limits are listed in Table 26 for all of the nuclei that we studied experimentally and which have a number of p-wave resonances. The central limit theorem implies that the distribution of the average x should have a probability density that tends towards a Gaussian as more data are included in the average, even if the individual data have nonGaussian probability density functions. We therefore give a formal symmetric error for x, Xx, obtained as the average of the upper and lower limits. When x is transformed back to the spreading width, the upper and lower errors are again nonsymmetric, but not to the same extent as for the individual data. We tested the hypothesis that all values of x are described by a common value. First we calculated the average value x and the value of 22 omitting 93 Nb and 108 Pd from the analysis, since these nuclei showed no statistically signiKcant parity violation and their likelihood functions versus ln w are not Gaussians. Note that 93 Nb has a very low upper limit for w .

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233

Table 25 Spreading widths A

I

w (10−7 eV)

Refs.

81

3=2 9=2 1=2 0 5=2 0 0 1=2 1=2 1=2 9=2 1=2 5=2 7=2 5=2 3=2 7=2 7=2 0 0

2 60:1

[108] [125] [132] [134] [134] [134] [134] [97] [97] [121] [136] [133] [102] [102] [102] [108] [126] [108] [135] [41]

Br Nb 103 Rh 104 Pd 105 Pd a 106 Pd a 108 Pd 107 Ag 109 Ag 113 Cd a 115 In 117 Sn 121 Sb 123 Sb 127 I 131 Xe 133 Cs 139 La 232 Th 238 U 93

a

1:4+1:2 −0:6 1:0+4:4 −0:7 0:8+1:3 −0:5 1:0+2:8 −0:7 612 2:7+2:6 −1:2 1:3+2:5 −0:7 3:2+3:4 −1:6 1:3+0:8 −0:4 0:3+0:6 −0:2 4:8+8:6 −2:9 1:9+15 −1:4 0:6+0:9 −0:4

0:6 0:006+0:018 −0:004

1 4:7+2:7 −1:8 1:3+1:0 −0:6

See Section 5 regarding doublet cases.

We call this data set choice I. The results of the least-squared analysis are listed in Table 26. The reduced (per degree of freedom) 22 shows that our hypothesis is not valid for this data set. The nuclei that give the largest contributions to 22 are 133 Cs and 232 Th. Next, we removed 133 Cs from the data set and call this set of values choice II. We repeated the least-squared analysis and found that this hypothesis is acceptable. This suggests that there is no reason to exclude thorium based on its higher 22 contribution. However, one should note that the value of the spreading width for 232 Th was obtained in a diFerent way than for all other nuclei. The lowest ten resonances in 232 Th all showed positive asymmetries and an average asymmetry was Kt to the data before calculating w from the :uctuations about the average asymmetry. We conclude that the measured spreading widths are not consistent with the hypothesis that there is a single value of the spreading width that describes all nuclei. However, the data set −7 eV. The without 93 Nb and 133 Cs can be described with a single value of w = 1:8+0:4 −0:3 × 10 TRIPLE data suggest that there are local :uctuations in the weak spreading widths. 7.2. Weak matrix elements Many PNC eFects were observed for p-wave resonances and the rms weak mixing matrix elements were determined for the nuclei studied. The TRIPLE values of the weak matrix

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Table 26 22 analysis of spreading widths with x = ln w Nuclei 103

Rh Pd 105 Pd 106 Pd 107 Ag 109 Ag 113 Cd 115 In 117 Sn 121 Sb 123 Sb 127 I 133 Cs 232 Th 238 U 104



22

2 2red

x

w (10−7 eV)

x

X+ x

X− x

Xx

22 − I

22 − II

+0:33

0.62 1.69 0.94 1.70 0.67 1.07 0.72 0.48 1.10 1.03 2.18 0.92 1.39 0.45 0.57

0.56 1.25 0.86 1.39 0.59 0.77 0.69 0.37 1.10 0.93 1.33 1.10 1.10 0.48 0.62

0.59 1.47 0.90 1.54 0.63 0.92 0.71 0.42 1.10 0.98 1.76 1.01 1.24 0.47 0.59

0.0 0.1 0.5 0.1 0.8 0.0 1.1 0.2 2.2 1.4 0.0 1.0 20.3 5.6 0.1

0.2 0.2 0.7 0.2 0.4 0.1 0.7 0.5 2.6 1.0 0.0 1.3 — 4.3 0.3

34.4 2.46 0:43+0:18 −0:18 1:54+0:30 −0:26

12.5 0.96 0:57+0:18 −0:18 1:77+0:35 −0:29

−0:02 −0:19 −1:61

+0:99 +0:26 +1:16 +0:26 −1:20 +1:57 +0:64 −0:57 −5:16 +1:54 +0:26

elements MJ are presented in Table 27. For even–even targets with I = 0, the matrix elements are obtained directly from the likelihood analysis in terms of MJ . For I = 0 nuclei, the matrix elements MJ were obtained from the spreading widths w , using the level spacings DJ . For I = 1=2 targets the reported values of DJ and MJ are for spin J = 1. For these nuclides the spins of the p-wave resonances were measured in dedicated -ray spectroscopic measurements [78,153,154]. For targets with higher spins we used the approximation DJ 2D0 , where D0 is the observed level spacing for s-wave resonances. Except for 93 Nb and 133 Cs, the values of the matrix elements are concentrated in a rather narrow range—between 0.5 and 3.0 meV. The large error bars on MJ do not allow a test of the dependence of the matrix elements on level density. The :uctuations of the MJ values are approximately the same size as the measurement error. Calculations of the weak root-mean-squared matrix elements have been performed recently by Rodin and Urin [120] in the framework of the so-called ‘semimicroscopic’ approach to the problem of the strong and weak mean Kelds in nuclei. This theory focuses on an adequate representation of the particle–hole couplings to the multi-quasiparticle conKgurations and uses the same nuclear matter parameters which were proven to provide a good description of the neutron and radiative strength functions for all nuclei. A comparison of the calculated values with the TRIPLE results for MJ was performed in [120], and shows qualitative agreement (within a factor of three).

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Table 27 Weak matrix elements and level spacings A

DJ (eV)

MJ (meV)

Refs.

81

110 ± 10 190 ± 16 60 ± 5 220 ± 65 24 ± 2 217 ± 61 182 ± 33 33 ± 4 28 ± 3 33 ± 4 22 ± 1 79 ± 6 25 ± 3 60 ± 7 23 ± 3 130 ± 15 41 ± 4

600 17 ± 2 21 ± 3

3 60:6

[4] [125] [132] [134] [134] [134] [134] [97] [97] [121] [136] [133] [102] [102] [102] [108] [126] [8] [135] [41]

Br a Nb 103 Rh 104 Pd 105 Pd 106 Pd 108 Pd 107 Ag 109 Ag 113 Cd 115 In 117 Sn 121 Sb 123 Sb 127 I 131 Xea 133 Cs 139 Laa 232 Th 238 U 93

a

1:2+0:5 −0:4 1:9+2:5 −0:9 0:6+0:3 −0:2 1:9+1:8 −0:9 65:6 1:2+0:5 −0:3 0:8+0:5 −0:3 1:3+0:6 −0:4 0:7+0:2 −0:1 0:6+0:4 −0:2 1:4+0:9 −0:5 1:3+2:7 −0:7 0:5+0:3 −0:2

1 0:06+0:25 −0:02

3 1:1+0:3 −0:2 0:7+0:3 −0:2

MJ values estimated as Vsp .

A method for calculating MJ that is based on the statistical model, but includes a realistic residual nucleon interaction was developed by Flambaum and Vorov [60]. For thorium they predict values of 2.08 and 3.57 meV for two theoretical options that take into account the residual particle–hole interactions. Another theoretical prediction is given in Ref. [34] as MJ = √ 1:3 × 10−8 AueF DJ . In this expression, the quantities MJ , DJ , and the eFective excitation energy ueF = Eb − Epair have the dimensions eV. With A = 110, ueF = 6 MeV, and DJ = 26 eV, the predicted value of MJ is 1.7 meV. Again there is qualitative agreement with the experimental value MJ  = 0:98 ± 0:20 meV obtained from the MJ -results for Ag, Cd, Sn, Sb, and I. The average level spacing for this group of nuclei is 26 eV. The higher theoretical values were obtained with the conventional choice of the weak interaction parameters, which could indicate an overestimate of the eFective nucleon–nucleon coupling constants in nuclei. The important issue of using the experimental MJ values in order to extract information about the meson–nucleon coupling constants for the weak interaction in nuclei was discussed by Tomsovic [141]. A recent result for 238 U [142] in the framework of the statistical spectroscopy approach with the use of the DDH weak coupling constants F and FA is in qualitative agreement with experiment. This time, however, the theoretical value of MJ is about a factor of 3 smaller than the experimental value. Thus there appears to be qualitative agreement between the experimental values of the weak matrix elements and a variety of theoretical descriptions. Here we wish to make a remark

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concerning future theoretical work on MJ2 . Until the present the goal of the theoretical eForts has been to calculate the spreading width of the weak interaction for some model weak interaction. The usual choice of the ‘best’ interaction from Desplanques et al. [48] leads only to qualitative agreement with the experimental results. We urge that future theoretical eForts not be limited to the ‘best’ interaction, but that they give the real symmetric matrix Bij (A) that relates the weak spreading width for each nucleus (mass number A) to all participating couplings {Fj }:  w (A)= ij Bij (A)Fi Fj . The availability of the theoretical results in this form will allow existing and future experimental results for weak spreading widths to be used to constrain the weak interaction couplings. 7.3. General summary The TRIPLE Collaboration was formed to study parity violation in neutron resonances. The spallation neutron facility at LANSCE provided the opportunity to extend the eFective neutron energy region of the Dubna pioneering study from 10 –20 eV to several hundred eV. This extension of the energy range enabled the measurement of many resonances per nuclide—this was crucial both to answering general questions concerning the PNC eFect in neutron resonances and to performing detailed analysis of the data. Following preliminary measurements, an entire new experimental system was designed and fabricated—:ux monitor, polarizing Klter, spin :ipper, neutron detector array, guide Keld over the entire :ight path, and -ray detector array. A data acquisition system was designed and a sequencing procedure adopted to satisfy the special requirements of this experiment. We studied 20 diFerent nuclides and measured the longitudinal asymmetries for several hundred p-wave resonances. In the process a large number of new resonances were observed, particularly for the p-wave resonances. Isotopic identiKcation was achieved through the use of small isotopically enriched samples that were studied with the -ray detector array. Measurements by the group at IRMM (Geel) established the spins of a number of resonances, which proved very helpful in the analysis. A multi-level analysis code was developed that correctly includes the beam resolution function, Doppler broadening, and the neutron detector resolution. Essentially all of the data were analyzed with this code FITXS. The neutron resonance energies and widths (gn values) were determined. The orbital angular momentum values were determined from a Bayesian analysis of the widths. The longitudinal asymmetries were determined for each p-wave resonance. Either the weak matrix element or the weak spreading width was determined directly from the experimental longitudinal asymmetries. The procedure is spelled out in Section 3. Although it is not possible in general to determine the individual weak matrix elements, it is possible to determine the rms weak matrix element (or spreading width) for a given nuclide. The spectroscopic information is very important. For some cases we had complete information concerning the resonance spins, which enabled us to validate our analysis procedures. The spirit of the analysis approach was to include all available spectroscopic information and then to average over the remaining unknown parameters. For targets with I = 0, the diMculty with lack of spectroscopic information is accentuated, particularly the lack of information about the entrance projectile spins. The maximum likelihood method works well for this problem. In favorable cases, one can obtain the rms weak matrix element directly, and then determine the weak spreading width.

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When it is necessary to Kt directly to the weak spreading width, the rms matrix element is determined from the spreading width. There is a nonstatistical anomaly in 232 Th, where the 10 longitudinal asymmetries observed up to 250 eV all have the same sign. There is evidence that this is a phenomenon restricted to 232 Th, as suggested in Table 1, which lists the signs of all of the statistically signiKcant parity violation eFects observed in our measurements. All attempts to explain the sign correlation as a general eFect led to unreasonably large values of the weak single particle matrix element. The fact that at higher energies in 232 Th there are PNC eFects with the opposite sign, supports the local doorway explanation. Unfortunately, none of the proposed explanations that incorporate some special feature of the nuclide 232 Th seem likely. The most reasonable explanation is that the eFect is due to a local doorway and is simply a random statistical event [82]. The results for the spreading widths are listed in Table 25 and for the matrix elements in Table 27. Some general conclusions can be reached from these results. The statistical ansatz for parity violation in compound nuclei appears to be justiKed—consistent with all other information concerning the behavior of the nuclear many-body system at high excitation energies [77]. The data are consistent with the view that every resonance has a parity admixture. Those resonances with the appropriate J value that do not display an experimental PNC eFect simply have a parity admixture below the threshold of observability for the particular set of experimental conditions. The values of the rms weak matrix element MJ obtained in these measurements are qualitatively consistent with the predictions of a variety of theoretical approaches. The experimental value of the weak interaction spreading width w = 1:8 × 10−7 eV agrees with theoretical expectations. The weak spreading widths are consistent with a constant or slowly varying mass dependence. There is evidence of local :uctuations in the spreading widths—perhaps similar to those observed in isospin symmetry breaking [80]. A more detailed quantitative comparison, emphasizing the values obtained for diFerent mass regions and the apparent anomalies for speciKc nuclei, requires additional theoretical eFort. Acknowledgements We would like to express our appreciation to all of our fellow members of the TRIPLE Collaboration whose joint eForts led to the parity violation results reported in this review. Over the years, the authors have proKted from discussions on the experimental and theoretical aspects of parity violation in the compound nucleus with many colleagues to all of whom we are very grateful. EIS would like to thank physicists and staF assistants of the Triangle Universities Nuclear Laboratory for their support and hospitality while this manuscript was prepared. This work was supported in part by the U.S. Department of Energy, OMce of High Energy and Nuclear Physics, under grant DE-FG02-97-ER41042 and by the U.S. Department of Energy, OMce of Energy Research, under contract W-7405-ENG-36. References [1] Yu.G. Abov, P.A. Krupchitsky, Yu.A. Oratovsky, Phys. Lett. 12 (1964) 25. [2] E.G. Adelberger, W.C. Haxton, Ann. Rev. Nucl. Part. Sci. 35 (1985) 501.

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