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Parity nonconservation in neutron resonances
Nuclear 0
Physics
North-Holland
A398 (1983) 93-106 Publishing
Company
PARITY NONCONSERVATION
IN NEUTRON RESONANCES
V. P. ALFIMENKOV, S. B. BORZAKOV, VO VAN THUAN, YU. D. MAREEV, L. B. PIKELNER, A. S. KHRYKIN and E. 1. SHARAPOV Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, USSR Received 5 July 1982 (Revised 6 October 1982)
Abstract: Experiments to observe the parity nonconserving effects in *‘Br, “‘Cd, “‘Sn, “‘I, ‘j9La and 238U are described. The measurements were performed with a beam of polarized neutrons from the pulsed reactor IBR-30 at Dubna. A dependence of total cross sections on neutron helicity was discovered in the following resonances: 0.88 eV “Br, 4.53 eV “‘Cd, 1.33 eV “‘Sn, and 0.75 eV ‘39La. The effect has a resonance character and is in agreement with theoretical predictions made in the framework of the model of mixing compound states. The paper contains experimental estimates for the mixing coefficients and matrix elements.
E
NUCLEAR REACT!ONS “Br, sured transmission. ‘*Br, “*Cd, dependence,
’ t’Cd. “‘Sn, ‘3’La(polarized n, X), E = 0.5-5 eV. mea“sSn, ““La resonances deduced o(total) neutron helicity p-wave parity nonconservation effect.
1. Introduction
In 1964 an experiment was proposed ‘) to observe rotation of the neutron spin due to parity nonconserving (P-odd)effects for a beam oftransverse polarized neutrons passing through an unpolarized target. Further papers 2-6) considered, in addition to the spin rotation, the difference between the total cross sections for the two helicity states of longitudinally polarized neutrons. All the above-mentioned papers discussed the P-odd effects connected with single-particle processes, i.e. the nuclei were considered to have no internal degrees of freedom. The estimates of the effects were on the verge ofexperimental possibilities of their observation. In the middle of the sixties, after the experimental observation of P-odd effects in ytransitions of nuclei ‘), it was established that the excited states of the nucleus can have mixed parity. However, only in the middle of 1980 has there appeared the first theoretical paper s) on the connection of both the neutron spin rotation and helicity dependence of the total cross section with the parity mixing in nuclear compound states. This paper pointed out that such mixing must enhance considerably the P-odd effects, and that they should be strongest for neutrons with energies lying in the p-resonance region. In ref. 8, the effects for p-resonances in medium mass and heavy nuclei were estimated. The spin 93
94
V. P. AiJinenkou
et ul. ] Parity ~~n-~ons~~~ati#~
rotation angle (in radians) and the relative change in neutron transmission under spin reversal appeared to be of the order of 10-2-10- 1 for a target of one attenuation length thickness at resonance. In the beginning of 1980 in Grenoble an experiment ‘) with an unpolarized “‘Sn target and 1.7meVneutrons wascarriedout whichrevealedtheeffectsofspinrotationfor transverse polarized neutrons and the helicity dependence of the total cross section for longitudinally polarized neutrons. The following results were obtained : the neutron spin rotated by the angle v, = -(3.7f0.3) x 10m5 rad/cm t and the relative change in transmission at a reverse of helicity was A = -(9.78 k4.01) x 10F6. Ref. 9, was met with much interest and has stimulated both theoretical and experimental studies in this field. The experiment lo) made in Leningrad on a beam of polarized neutrons with E, N 2 x 10m2 eV repeated with higher accuracy the measurement of the helicity dependence of the neutron cross section for “‘Sri, and gave new data on a ‘39La target. was found to be The relative change in cross section (a, -[I_),@++ (6.2+0.7)x 10m6for ‘~‘Snand(9.0~ 1.4) x 10m6for ‘39La. It wasshown that theeffect is connected only with the capture component of the cross section, i.e. with the compound states of nuclei. All the later theoretical works in this field ” - I5 ) explained the observed effects as being due to the mixing of compound states with energies near to the neutron binding energy, having equal spins and opposite parities. In fact, at thermal neutron energies both ’ “Sn and ‘39La have weak resonances (E, = 1.3 eV for “‘Sn and E, = 0.75 eV for ’ 39La) which are p-resonances with a high probability, i.e. their parity is the opposite to that of the conventional s-resonances for these nuclei and for this energy region. Toensure thecorrectnessoftheexplanationproposedinref. *)for theP-oddeffectsit is neccessary to show experimentally that the effects are enhanced considerably as the neutron energy approaches the corresponding p-resonance energy. Ref. l’) showed that the explanation of the observed effects may demand the introduction of a new weak force considerably exceeding the conventional parity-violating one. The present paper gives the results of the experiment performed in the Laboratory of Neutron Physics of the Joint Institute for Nuclear Research in order to investigate the helicity dependence of total cross sections in the vicinity of presonances for several nuclei. These results were partly reported earlier in refs, * 6- 1*).
2. Main principles of the theory and of the measuring procedure For convenience we first outline the theory of the P-odd dependence of the total cross section on neutron helicity. We follow ref. I’) and assume that the contribution of + The sign of the spin rotation is changed 9, following a private communication positive sign corresponds to a right-handed rotation about the momentum.
with B. Heckel. A
V. P. Alfimenkov et al. / Parity non-conservation
95
potential scattering to this dependence is negligible, i.e. we shall consider only the resonant part of interaction (processes going through the formation of compound states). Here, the parity-conserving terms, Ho, of the hamiltonian describing the compound nucleus give rise to states with energy Ei, parity q, spin J and wave functions rplJ(E). The presence in the hamiltonian ofa small P-odd component Hw will change to a slight degree each of the states. The new states will not have definite parity, but will keep the same spin values. The wave function $f(E) of each of these states in the vicinity of the energy Ei will in first-order perturbation theory be:
$i(E) = qlJ(E)+C aij(E)qy(E).
i
(1)
Here, the summation is over statesj with the same spin as the state i, but with opposite parity If. The mixing coefficient aij can be written as follows:
Compound states ofthe nucleus-neutron system are revealed in the form ofresonances in the neutron-nucleus interaction cross section. Resonances excited by neutrons with the orbital Imomenta I = 0,1,2,. . . are called s-, p-, d-resonances, respectively. Resonances with even- and odd-l correspond to the compound states with opposite parities. For low energy neutrons the capture cross section decreases rapidly with increasing I due to the increasing centrifugal potential barrier. Therefore, we can limit our studies to s- and p-resonances. If the target nucleus has spin Z, then the spins of s-resonances may take values J = Z-t+ and spins of p-resonances take values .Z = Z&i; I+;. Only p-resonances with the same spin may take part in mixing with s-resonances, since compound states with the wave function ll/J have definite spin values. Let us assume that the matrix elements entering eq. (2) are about the same for different j. Then for a p-resonance in the first approximation it suffices to take into account only the contribution of the nearest s-resonance in eq. (l), since the expression for c1 contains an energy denominator. Let us consider the effect due to such mixing in the total cross section near a p-resonance. The wave function of the corresponding compound state is:
II/,(E)= cp,(E) + Wrp,(E),
(3)
where o! =
’
We are dealing with plane waves describing neutron beams of different helicities in a system of reference with the origin at the centre of the nucleus and the z-axis in the
96
direction orbital
V.. P. Alfmenkov
of the neutron momenta,
et al. 1 Parity non-conservation
momentum.
if limited
The expansion
of these waves over the neutron
to the terms with I < 2, can be written
in the form:
where k is the neutron wave number, xt are the wave functions describing the neutron spin with.projections +i to the z-axis, and e(l,j,j,) are the eigenfunctions of the total momentumj of the neutron with phases chosen according to Landau and Lifshitz 19). Capture in the state $,(E) (eq. (3)) of a neutron described by the wave function (4) may take place via p-wave (2nd and 3rd terms in (4)) and via s-wave (1st term in (4)). The capture amplitudes caused by the 1st and 2nd terms interfere in the total cross section and, according to eq. (4) the interference term changes its sign with the change of neutron helicity. The corresponding equation for the resonance cross section gpf of neutrons with a positive and negative helicity looks as follows:
a,[1 f9(k)],
gp+ = where g,, = (n/k’)gri(k)r,/[(E cross section in the p-resonance
P(k)
(5)
is the conventional - E,)’ ++ri] without polarization and
= 2a
Breit-Wigner
C(k) r&(k) FpqTpj-’ J
Here, g is the statistical spin factor, k is the neutron energy and total width of the p-resonance; T:(k),
(6)
wave number, E, and rP are the T:(k) are the neutron widths of
the s- and p-resonances for a neutron of wave number k. They are connected to the and with the wave numbers k,,, at resonance by the following widths, [&,I,,,, equations
C’(k) = [CL
0 ;
‘2
r;(k) =
[r;l,,,
s
T&k) is the part of T;(k) corresponding
to the p-resonance
0 3. ;
P
capture
the total angular momentumj = 3. In eq. (6) the sign of the root and the contribution of r;, (channel mixture) are unknown. For an estimate one can .9(k) may be rewritten as follows
of neutrons
with
into fg = f 3: + l-i+ put r;, z r;. Then
(7)
The estimates made in ref. ‘) for some p-resonances give B(k) = 1O-2-1O-1.
in medium
mass and heavy nuclei
V. P. Alfimenkov
et al. 1 Parity non-conservation
91
The dependence ofthe resonance cross section on neutron helicity near an s-resonance is considered in a similar way and gives a Y(k) value smaller by a factor of Pf/rG N 104lo5 than for the p-resonance. The observation of such a small relative change in cross section seems to be nowadays beyond experimental possibilities. Now let us pass to the experimental study of the P-odd dependence of the total cross section on neutron helicity. In this case one should measure the change in transmission through the target due to a small change in CJunder a reverse of neutron helicity. The optimal target thickness n nuclei /cm2 for the best accuracy should meet the requirement na = 2. Thicker samples give a gain in transmission effect, but reduce the statistical accuracy due to low neutron intensity behind the target. Since (T= l&20 b in the presonance region, then the optimal thickness ofthe target is n = (l-2) x 1O23nuclei/cm2. In the experiments with polarized neutrons the so-called transmission effect is usually measured. In our case it is convenient to present it in the form:
where I,, I, are the intensities of the transmitted beam of neutrons polarized in parallel and antiparallel directions to the neutron momentum, respectively;& is the neutron polarization. Eq. (8) can be transformed into: E = -tanh$(a+
-cr_),
(9)
where c + is the cross section of the target nucleus for neutrons with positive and negative helicity. In the study of parity-violating effects (n(o+ - o_)l +Z 1 and eq. (9) can be written in a simpler form: E =
-$l(fJ+ -a_).
(10)
Hence, the experimentally obtained transmission effect allows one to find a change in total cross section da = ‘T, --6_ under reversal of helicity. In the framework of the model discussed above, the dependence of the total cross section on neutron helicity in the p-wave resonance region is described with eq. (5). Thus we obtain: E =
-iH(k)
(11)
From the latter equation it follows that B(k) most naturally characterizes P-odd experimental effects in the total cross section near p-resonances. This value is especially convenient at the p-resonance itself where it is practically constant and the value of b,, can be found with high accuracy from transmission measurements. In measurements far from the resonance where either no data on bp are available or one is not sure about the correctness of eq. (5), it seems reasonable to report the experimental values of do.
98
E P. Alfimenkov 5
et al. / Parity nun-conservation 6
6
3
9
Fig. 1. Experimental arrangement: 1 - reactor, 2 - evacuated neutron guide tube, 3 - monitors, 4 - collimators, 5 - polarized proton target, 6 - electromagnets of the guide Field, 7 - current sheet, 8 - solenoid, 9 - sample, IO - neutron detector. Arrows along the neutron beam path show the direction of magnetic field.
3. Experiment Transmission measurements were performed by the time-of-flight method on the beam of polarized neutrons from the IBR-30 reactor of the Laboratory of Neutron Physics of the Joint Institute for Nuclear Research. The flight path was 58 m long. measurements in the energy range up to I.5 eV were carried out with a neutron pulse duration of 70 ps and a reactor mean power of 20 kW. In order to improve resolution at higherneutronenergiesweused theboostermodeoftheIBR-30reactorwith theelectron accelerator. In this case the pulse duration was 4 ,us and the mean power about 5 kW. The experimental arrangement is shown in fig. 1. The beam of unpolarized neutrons was guided to the polarizer installed at a distance of 32 m from the reactor core. The proton polarized target was used as a polarizer. The target was a single crystal La,Mg,(NO,)i, * 24H,O with an area of 25 cm’ and 17 mm thick. The solid effect ‘l) was used to polarize the protons in the crystallized water of the single crystal. A magnetic field of H = 20 kOe was applied to the target, perpendicular to the neutron beam. Small variations in the field strength (by 40 Oe) ~rmitted the protons to be polarized both parallel and antiparallel to the field direction. The beam transmitted through the proton target acquires a polarization in the direction of proton polarization, since the (n, p) cross section in the singlet state considerably exceeds the triplet one 22). Our target with the proton polarization fD = 0.5-0.6 provided a neutron polarizationf, about equal to the proton polarization, the intensity loss being a factor of 10. The polarized beam was guided and its polarization changed in the following way. The polarized neutron beam passed the gaps of the two electromagnets WithequalfieldsH = 2OOOe.Thedirectionofthelieldofthefirstmagnet wasthesameasthatappliedtotheprotontarget.Thedirectionoftheothermagneticfield could bemadeeitherparallelorantiparallel to the proton target field. A thincoppersheet (0.5 mm) was placed between the two magnets and ~r~ndicular to the beam. The current in it produced on its surface a H = 50 Oe magnetic field. The current through the sheet was not switched off during the measurement. The direction of the current in the
V. P. Alfimenkov et al. / Parity non-conservation
99
sheet was such that its magnetic field on the side of the first magnet had the same direction as the field of the first magnet. In the case of parallel fields the direction of the field in both magnets is the same along the whole path from the proton target to the second magnet. The neutrons arrive at the field ofthe second magnet with the polarization they hadleaving the proton target. When the direction of the current in the second magnet is changed there appears across the current sheet an area where the magnetic field changes abruptly its direction and thus the condition for nonadiabatic transmission is created for neutrons. They pass through the sheet keeping their space orientation of polarization and arrive at the second magnet with the polarization reversed relative to the magnetic field. A solenoid with a field of H = 200 Oe in the direction of the neutron momentum is installed behind the second magnet. The distance between the back edge of the second magnet and the front edge ofthe solenoid is 100 mm. Measurements ofthe magnetic fields have shown that the field in the neutron beam cross-section region turns from transverse in the second magnet to longitudinal in the solenoid along a distance of 200 mm. The direction of polarization of slow neutrons in this field follows adiabatically the direction of the field, i.e. the beam in the solenoid is longitudinally polarized. The calculation performed on a computer using the data on magnetic field measurements shows that the loss in neutron polarization due to the imperfect reverse does not exceed 1@15 % at a neutron energy E = 50 eV. Toreduce theinfluenceofthesecondmagnetreversingfieldon thelieldnear theproton target and the influence of the solenoid on the field near the current sheet the dimensions of the magnets in the direction of the beam were made rather large (600 mm each). The solenoid was 500 mm long which permitted thick enough samples to be placed inside. The neutrons transmitted through the sample went along the evacuated neutron guide tube to the neutron detector. We used as a detector either a liquid scintillation detector 24)or a scintillation detector with Li glass. A fast polarization reversal was made every 40 set to reduce the effects of beam and apparatus instability. The sign of the proton target polarization was changed every 50 h. Thus the neutron polarization and the sign of the P-odd effect were reversed without changing the experimental conditions. This allowed us to account for systematic errors due to instrumental effects. The total measuring time amounted to 200-300 h for every target. An automatic system based on a TPA minicomputer 25) was used for the acquisition of the time spectra and monitor spectra. Spectra N, and N, correspond to 50 h of data acquisition with the neutron spins parallel and antiparallel to their momentum. Figs. 2-5 (upper) give such spectra near the investigated p-resonances for several samples studied. The N, and N, spectra obtained in runs with a fixed proton polarization were then summed to yield two pairs of spectra N, and N,. These pairs allowed us to find for each channel the value of experimental transmission effect for both proton polarization directions :
(12)
V. P. Alfimenkov et al./ Parity non-conservation
100
0.88
-:A 4
m
,o
Qr
I
3
z
2
1
-30 2.0 1.6 1.21.0 0.6 150
200
250
0,6 300
0.4 350
Erl
400
t
Fig. 2. Part of the time-of-flight spectrum (above) and the transmission effect (below) for “Br. The number and arrows show the position and energy of the p-resonance; E, is the energy of the neutron, in eV, t is the time of flight.
120
Fig. 3. Part
1?, :,>, ,: E”
q:
of the time-of-flight
140
160
spectrum
160
200
220
240
and the transmission
t
effect for “‘Cd
V. P. Alfimenkov et al. / Parity non-conservation
101
-20 2.0 1.81.6 1.4 1,2 LI
350
Fig. 4. Part
of the time-of-flight
400
450
spectrum
and
1.0 500
0.8 En I' 550 1
the transmission
effect for “‘Sn.
050
t
0
.
.i'0 -50 -
\/
3 -100 t
'\ *
' I
\ I' b
-150 -200 -
1.0 0.9 0.8 0.7 110 120
Fig. 5. Part of the time-of-flight
0,6
130 140 150
spectrum
0.5 En
160 170
and the transmission
t
effect for ‘39La.
102
V. P. A!fimenkov
et al. ,I Parity non-conservation
These values were tested for agreement and then averaged to have a final value of EeXp for the given sample. Figs.2-5(lower)showe,,,forthedifferent samplesandneutronenergyintervals. Here, Eexpvalues are averaged over groups of channels, the number of channels in the group being increased as the size of the effect decreases. The experimental points in the figures are in the middle of each region over which the average was made. The solid curves are least squares fits of these points to eq. (11). The parameters E,, rp and gr; were determined from the N, and N, spectra for the majority ofthe resonances. Two resonances (one in “Brand one in l”I) were previously not known. We have observed them in separate transmission measurements through thick samples. An isotope assignment of the p-resonance in bromine was made on the basis of the y-spectra following radiative neutron capture. The values 9(k) for p-resonances in the samples were found from E,,~in the following way. If the Doppler and resolution broadening of the experimentally observed resonance is negligible (as in the Br and Sn cases), then the experimental values of N, and N, are proportional to the values of I, and I, in (8) and E,_, = E. For these cases 9(k) was obtained from E_ by the least squares method, using eq. (11) and known data on the target thickness and the parameters of the resonance. If the broadening of the resonance cannot be neglected (La and Cd), then E_(E) in the energy channel and 9(k,)are related by
E,_(E) = - na,9(k,)
m R(E, ~)#(E’~-““~~~~)dE -s - Oooo R(,&‘,E’)e-“~Od’E”&’ s -co
(13)
Here, (TVis the cross section at the maximum of the investigated resonance ; (P(E’) is the function 26) which accounts for the distortion of the cross section due to the Doppler effect ; R(E, E’) is the resolution function dependent on the neutron burst shape and the width of the analyzer time channel. After computing the integrals in eq. (13), the values of for each channel of the analyzer. The B(k,) were found from experimental values of EeXp final value for 9(k,) was obtained as a weighted average value over all the channels.
4. Results and discussion The total cross-section dependence on helicity of neutrons was investigated for 11 weak resonances at a low energy in the nuclei *‘Br, lllCd, “‘Sn, l”I, 139La, 238U. Within high probability they may be considered to be p-wave resonances, since their neutron widths are 3-4 orders ofmagnitude less than the corres~nding,average~eutron widths of s-resonances. The spins of all these resonances are unknown. If the spins are I +$, a P-odd effect is expected. If the spins are I -t-s, then no P-odd effect is expected.
V. P. Alfimenkov et al. / Parity non-conservation
103
A P-odd dependence of total cross section on neutron helicity was observed experimentally in 4 resonances: ‘lBr(E, = 0.88 eV), “‘Cd(E, = 4.53 eV), “‘Sn(E, = 1.33 eV) and ‘j’La(E P = 0.75 eV). The corresponding dependences of E,,~(E) are shown in figs. 2-5. For the 7 resonances left we estimated only the upper limits for the transmission effect. Table 1summarizes p(k,) values obtained from experimental data on all the resonances. There are also given the thicknesses of the targets and the parameters of p-resonances [for 238U from ref. 27), others were obtained in the experiment reported here]. Ifit is known which s-resonances mix with the p-resonance, then from the 9(k,) value and eqs. (7) and (3) one may derive the magnitudes of the mixing coefficients a and the matrix elements (slH,Jp). However, the absence ofdata on spins ofp-resonances and on channel mixture of P; widths prevents us from obtaining unambiguous values. The last columns in table 1 give the results of calculations of Ial and (s(H,lp)l under the assumption that the s-resonances with maximum T;/(E, - ,Q2 value mixes with the presonance. The parameters E, andgr; of these resonances from refs. 27*28) are also listed in table 1. The values of l(sl~wlp)l in table 1 give a lower estimate if it is assumed that the effect is caused by mixing with only one s-resonance. From table 1 it is seen that the values of 9(k,) for different resonances vary in a wide range from lo- 1to lo- 3, the latter corresponding to the accuracy of measurements. The maximum value of9(k,) = 7.3 x 10e2 was obtained for the ‘39La nucleus, where the presonance is the weakest ofall those observed and the s-resonance is anomalously strong. The values of (aland l(slHwlp)l are estimates only, since we are not certain which of the one or possibly more s-resonances mixes with the investigated p-resonance. If an sresonance with negative energy takes part in mixing, then additional uncertainties appear. A comparatively reliable combination of these parameters gT,“/E% may be derived from the thermal capture cross section, but only under the assumption of one negative level contribution to the thermal cross section. An attempt to obtain separately E, and gri does not as a rule give reliable results. Consequently, the estimates for l(s(H,lp) in the case of mixed negative s-resonances appear to be more accurate than (al estimates, since to obtain the latter the separate values are required, while for the former it practically s&ices to use gT,“/Ef. In the case of p-resonances, in which the P-odd effect was observed, the Ialestimates lie in the interval (l-10) x 10e5. The lslH,lp)( estimates are dispersed within the interval (0.3-3) x 10e3 eV. In two cases where no effect wasobserved (a resonance in 1l ‘Cd at E, = 6.9 eV and a resonance in 1271at E = 7.6 eV) the matrix element may be of the order of 10d3 eV though the measuringPaccuracy was insufficient. In other cases (2 resonances in lz71 and 3 resonances in 238U) the matrix elements were either less than 0.2 x 1O-3 eV or equal to zero because of the spin of the p-resonance was I +$. It seems interesting to compare our results on Y(k,) with the data on helicity effect measurements with thermal neutrons. They are available for the “‘Sn, ‘j9La [ref. ‘“)I and Br [ref. “)I nuclei in the form of Si’*,,= As/2a, where r~ is
1.3
“‘Sn
eV)
r,
1.5
238~
11.32+0.02 19.5OkO.2
4.41 &0.01
0.75+0.01
I .25
‘39La
(25) (25)
(25)
45+
5
130+20
7.6 +O.l 90*10 90+10
230 + 20
I .33 &O.Ol
10.4 +0.1 14.0 io.2
163klO 143+13
190*20
(lo-’
4.53 + 0.03 6.94kO.07
0.88 +O.Ol
(2)
3.9
,271
2.05
1.1
*‘Br
“‘Cd
n (10z3 nuclei/cm2)
Nucleus
1.5
3.5 * 6 140 *70
11.1+
0.3 0.2
+40 220
+ 2
*
I
,O.l
+0.1
20.9
+O.l
6.671032
-48.6
37.7
-29
-4
101.0
(e?)
values and results
TABLE
0.3
+ 5 &- 8
3.6+
320 150
13
19
107 108
5.8k
(1 O”‘eV)
Experimental
kO.4
+0.7
1.9
kO.5
0.59t_o.o1
84
4.3
5.5
0.95
9.7
.4P (IO-” eV) y&4
55
- 2.5 * 2.s 0 kl
3.713.7
73
0.3kO.4 1.31: I.0
11.2+8.0
4.5+ 1.3
-8.2k2.2 4.1 k3.3
24
&k,) (lo-‘)
+0.2
1.7 1-1.7 0 io.7
1.7 +-I.?
2.6
0.3 kO.4 0.6 ~0.5
1.8 +1.3
I .25kO.35
9.4 +2.5 3.8 23.0
3.0 &OS
(,&
kO.4
0.08 TO.08 0 kO.01
0.04~0.04
1.28+0.12
0.1 kO.1 0.15~0.11
0.5
0.38+0.10
O.80*0.22 0.42 + 0.33
3.0 20.5
(10e3 eV)
iK.~lff&)l
p
3 2 b % g 2. i:
‘;
c.
2
$2 a
3 [:
-2
&
V. P. Aljbnenkov et al. / Parity non-conservation
105
the total cross section. The following relationship exists for Pti, and .Y(k,): (14)
where crOis the resonance part of the cross section in the maximum of the p-resonance. One can easily derive the above relationship from eq. (5) under assumption that the thermal point is near enough to the p-resonance for eq. (5) to hold. Table 2 summarizes our results on cr,,and P(k,), data on c and Pti, from refs. lo, 29),as well as 9$, values calculated with eq. (14). The agreement between Pth and 9’: can be considered good enough having in mind that Y,,, and .P(k,) differ by 3 and more orders of magnitude. TABLE 2 Comparison
of the effects of resonance
and thermal
.@(k ) (lo-p3)
Nucleus
R,,
“‘Sn
1.33
1.6kO.2
‘39La
0.75
2.8 +0.4
73
*5
19.6k2.0
*‘Br
0.88
0.9+0.1
24
+4
15.5k1.5
“‘Cd
4.53
3.8 kO.5
4.5kl.3
-8.2k2.2
neutrons
3.7kO.4
29
k4 ‘*)
.‘p%
(10-h)
(10-y
6.2kO.7
14.5k5.5
9.oi1.4 19.6 f 2.0 “)
9.3 +2.9 16.2k5.1 0.4 b)
“) Data from ref. 29) recalculated per Br isotope. b, Upper estimate for IYf,l obtained using ref. 13)
5. Conclusions
The present work has shown that the P-odd dependence of the total cross section on neutron helicity has the clear-cut resonance behaviour predicted in ref. “). The effect is explainable in the frame of the presently used idea of the universal weak interaction, and there is no need to introduce any new parity-violating force. All existing experimental data on the helicity dependence of the total cross section are in good agreement with the ideas developed in refs. 8*12).There are indications of the universal character of the effect, since the corresponding matrix elements determining the parity mixing of nuclear. levels are approximately the same. For the further deepening of our understanding of this phenomena, one should try to perform higher accuracy measurements on a much larger number of p-resonances. In conclusion the authors are indebted to, and express their gratitude to, I. M. Frank
106
V. P. Aljimenkov
and V. I. Luschikovfor Ignatovich,
et al. / Parity non-conservation
their interest in the work, to G. G. Bunatian,
S. G. Kadmensky,
0. P. Sushkov,
V. V. Flambaum,
D. F. Zaretsky, V. I. Furman
Shapiro for useful discussions and to M. B. Bunin, S. I. Negovelov, their help during the measurements.
V. K.
and I. S.
B. A. Rodionov
for
References I) F. C. Michel, Phys. Rev. 133 (1964) 8329 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)
L. Stodolsky, Phys. Lett. 50B (1974) 352 M. Forte, Inst. Phys. Conf. Ser., No. 42, 1978, ch. 2, p. 86 G. Karl and D. Tadic, Phys. Rev. Cl6 (1977) 172 A. Barroso and D. Tadic, Nucl. Phys. A294 (1978) 376 A. Barroso and F. Margaca, J. of Phys. G6 (1980) 657 Yu. G. Abov et al., Phys. Lett. 12 (1964) 25 0. P. Sushkov and V. V. Flambaum, JETP Pis’ma 32 (1980) 377 M. Forte et al., Phys. Rev. Lett. 45 (1980) 2088 E. A. Kolomensky et al., Phys. Lett. 1078 (1981) 272 L. Stodolsky, Phys. Lett. 96B (1980) 127
12) 13) 14) 15) 16) 17) 18) 19)
0. P. Sushkov and V. V. Flambaum, Usp. Fiz. Nauk 136 (1982) 2 V. E. Bunakov and V. P. Gudkov, Z. Phys. 303 (1981) 285 G. A. Lobov, preprint ITEP, No. 30, M., 1980; preprint ITEP, No. 145, M., 1981 I. S. Shapiro, JETP Pis’ma 35 (1982) 275 V. P. Alfimenkov et al., JETP Pis’ma 34 (1981) 308 V. P. Aliimenkov et a/., JETP Pis’ma 35 (1982) 42 V. P. Alfimenkov et al., JINR, P3-82-86, Dubna, 1982 L. D. Landau and E. M. Lifshitz, Course of theoretical physics: quantum mechanics (Pergamon, London, 1958) 1. M. Frank, Particles and nucleus, 1972, vol. 2, part. 4, p. 805 C. D. Jeffries, Dynamic nuclear orientation (Interscience, New York, 1963) Yu. V. Taran and F. L. Shapiro, JETP 44 (1963) 2185 V. 1. Luschikov et al., Yad. Fiz. 10 (1969) 1178 H. Malecki et al., JINR, 13-6609, Dubna, 1972 V. A. Vagov e/ al., JINR, D13-7616, Dubna, 1974 W. Lamb, Phys. Rev. 55 (1939) 190 S. F. Mughabghab and D. I. Garber, Neutron cross sections, BNL-325, 3rd ed., vol. I, 1973 S. F. Mughabghab et al., Neutron cross sections, vol. 1, part A, 1981 V. A. Vesna et a/., JETP Pis’ma 35 (1982) 351
20) 21) 22) 23) 24) 25) 26) 27) 28) 29)
Physics
North-Holland
A398 (1983) 93-106 Publishing
Company
PARITY NONCONSERVATION
IN NEUTRON RESONANCES
V. P. ALFIMENKOV, S. B. BORZAKOV, VO VAN THUAN, YU. D. MAREEV, L. B. PIKELNER, A. S. KHRYKIN and E. 1. SHARAPOV Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, USSR Received 5 July 1982 (Revised 6 October 1982)
Abstract: Experiments to observe the parity nonconserving effects in *‘Br, “‘Cd, “‘Sn, “‘I, ‘j9La and 238U are described. The measurements were performed with a beam of polarized neutrons from the pulsed reactor IBR-30 at Dubna. A dependence of total cross sections on neutron helicity was discovered in the following resonances: 0.88 eV “Br, 4.53 eV “‘Cd, 1.33 eV “‘Sn, and 0.75 eV ‘39La. The effect has a resonance character and is in agreement with theoretical predictions made in the framework of the model of mixing compound states. The paper contains experimental estimates for the mixing coefficients and matrix elements.
E
NUCLEAR REACT!ONS “Br, sured transmission. ‘*Br, “*Cd, dependence,
’ t’Cd. “‘Sn, ‘3’La(polarized n, X), E = 0.5-5 eV. mea“sSn, ““La resonances deduced o(total) neutron helicity p-wave parity nonconservation effect.
1. Introduction
In 1964 an experiment was proposed ‘) to observe rotation of the neutron spin due to parity nonconserving (P-odd)effects for a beam oftransverse polarized neutrons passing through an unpolarized target. Further papers 2-6) considered, in addition to the spin rotation, the difference between the total cross sections for the two helicity states of longitudinally polarized neutrons. All the above-mentioned papers discussed the P-odd effects connected with single-particle processes, i.e. the nuclei were considered to have no internal degrees of freedom. The estimates of the effects were on the verge ofexperimental possibilities of their observation. In the middle of the sixties, after the experimental observation of P-odd effects in ytransitions of nuclei ‘), it was established that the excited states of the nucleus can have mixed parity. However, only in the middle of 1980 has there appeared the first theoretical paper s) on the connection of both the neutron spin rotation and helicity dependence of the total cross section with the parity mixing in nuclear compound states. This paper pointed out that such mixing must enhance considerably the P-odd effects, and that they should be strongest for neutrons with energies lying in the p-resonance region. In ref. 8, the effects for p-resonances in medium mass and heavy nuclei were estimated. The spin 93
94
V. P. AiJinenkou
et ul. ] Parity ~~n-~ons~~~ati#~
rotation angle (in radians) and the relative change in neutron transmission under spin reversal appeared to be of the order of 10-2-10- 1 for a target of one attenuation length thickness at resonance. In the beginning of 1980 in Grenoble an experiment ‘) with an unpolarized “‘Sn target and 1.7meVneutrons wascarriedout whichrevealedtheeffectsofspinrotationfor transverse polarized neutrons and the helicity dependence of the total cross section for longitudinally polarized neutrons. The following results were obtained : the neutron spin rotated by the angle v, = -(3.7f0.3) x 10m5 rad/cm t and the relative change in transmission at a reverse of helicity was A = -(9.78 k4.01) x 10F6. Ref. 9, was met with much interest and has stimulated both theoretical and experimental studies in this field. The experiment lo) made in Leningrad on a beam of polarized neutrons with E, N 2 x 10m2 eV repeated with higher accuracy the measurement of the helicity dependence of the neutron cross section for “‘Sri, and gave new data on a ‘39La target. was found to be The relative change in cross section (a, -[I_),@++ (6.2+0.7)x 10m6for ‘~‘Snand(9.0~ 1.4) x 10m6for ‘39La. It wasshown that theeffect is connected only with the capture component of the cross section, i.e. with the compound states of nuclei. All the later theoretical works in this field ” - I5 ) explained the observed effects as being due to the mixing of compound states with energies near to the neutron binding energy, having equal spins and opposite parities. In fact, at thermal neutron energies both ’ “Sn and ‘39La have weak resonances (E, = 1.3 eV for “‘Sn and E, = 0.75 eV for ’ 39La) which are p-resonances with a high probability, i.e. their parity is the opposite to that of the conventional s-resonances for these nuclei and for this energy region. Toensure thecorrectnessoftheexplanationproposedinref. *)for theP-oddeffectsit is neccessary to show experimentally that the effects are enhanced considerably as the neutron energy approaches the corresponding p-resonance energy. Ref. l’) showed that the explanation of the observed effects may demand the introduction of a new weak force considerably exceeding the conventional parity-violating one. The present paper gives the results of the experiment performed in the Laboratory of Neutron Physics of the Joint Institute for Nuclear Research in order to investigate the helicity dependence of total cross sections in the vicinity of presonances for several nuclei. These results were partly reported earlier in refs, * 6- 1*).
2. Main principles of the theory and of the measuring procedure For convenience we first outline the theory of the P-odd dependence of the total cross section on neutron helicity. We follow ref. I’) and assume that the contribution of + The sign of the spin rotation is changed 9, following a private communication positive sign corresponds to a right-handed rotation about the momentum.
with B. Heckel. A
V. P. Alfimenkov et al. / Parity non-conservation
95
potential scattering to this dependence is negligible, i.e. we shall consider only the resonant part of interaction (processes going through the formation of compound states). Here, the parity-conserving terms, Ho, of the hamiltonian describing the compound nucleus give rise to states with energy Ei, parity q, spin J and wave functions rplJ(E). The presence in the hamiltonian ofa small P-odd component Hw will change to a slight degree each of the states. The new states will not have definite parity, but will keep the same spin values. The wave function $f(E) of each of these states in the vicinity of the energy Ei will in first-order perturbation theory be:
$i(E) = qlJ(E)+C aij(E)qy(E).
i
(1)
Here, the summation is over statesj with the same spin as the state i, but with opposite parity If. The mixing coefficient aij can be written as follows:
Compound states ofthe nucleus-neutron system are revealed in the form ofresonances in the neutron-nucleus interaction cross section. Resonances excited by neutrons with the orbital Imomenta I = 0,1,2,. . . are called s-, p-, d-resonances, respectively. Resonances with even- and odd-l correspond to the compound states with opposite parities. For low energy neutrons the capture cross section decreases rapidly with increasing I due to the increasing centrifugal potential barrier. Therefore, we can limit our studies to s- and p-resonances. If the target nucleus has spin Z, then the spins of s-resonances may take values J = Z-t+ and spins of p-resonances take values .Z = Z&i; I+;. Only p-resonances with the same spin may take part in mixing with s-resonances, since compound states with the wave function ll/J have definite spin values. Let us assume that the matrix elements entering eq. (2) are about the same for different j. Then for a p-resonance in the first approximation it suffices to take into account only the contribution of the nearest s-resonance in eq. (l), since the expression for c1 contains an energy denominator. Let us consider the effect due to such mixing in the total cross section near a p-resonance. The wave function of the corresponding compound state is:
II/,(E)= cp,(E) + Wrp,(E),
(3)
where o! =
’
We are dealing with plane waves describing neutron beams of different helicities in a system of reference with the origin at the centre of the nucleus and the z-axis in the
96
direction orbital
V.. P. Alfmenkov
of the neutron momenta,
et al. 1 Parity non-conservation
momentum.
if limited
The expansion
of these waves over the neutron
to the terms with I < 2, can be written
in the form:
where k is the neutron wave number, xt are the wave functions describing the neutron spin with.projections +i to the z-axis, and e(l,j,j,) are the eigenfunctions of the total momentumj of the neutron with phases chosen according to Landau and Lifshitz 19). Capture in the state $,(E) (eq. (3)) of a neutron described by the wave function (4) may take place via p-wave (2nd and 3rd terms in (4)) and via s-wave (1st term in (4)). The capture amplitudes caused by the 1st and 2nd terms interfere in the total cross section and, according to eq. (4) the interference term changes its sign with the change of neutron helicity. The corresponding equation for the resonance cross section gpf of neutrons with a positive and negative helicity looks as follows:
a,[1 f9(k)],
gp+ = where g,, = (n/k’)gri(k)r,/[(E cross section in the p-resonance
P(k)
(5)
is the conventional - E,)’ ++ri] without polarization and
= 2a
Breit-Wigner
C(k) r&(k) FpqTpj-’ J
Here, g is the statistical spin factor, k is the neutron energy and total width of the p-resonance; T:(k),
(6)
wave number, E, and rP are the T:(k) are the neutron widths of
the s- and p-resonances for a neutron of wave number k. They are connected to the and with the wave numbers k,,, at resonance by the following widths, [&,I,,,, equations
C’(k) = [CL
0 ;
‘2
r;(k) =
[r;l,,,
s
T&k) is the part of T;(k) corresponding
to the p-resonance
0 3. ;
P
capture
the total angular momentumj = 3. In eq. (6) the sign of the root and the contribution of r;, (channel mixture) are unknown. For an estimate one can .9(k) may be rewritten as follows
of neutrons
with
into fg = f 3: + l-i+ put r;, z r;. Then
(7)
The estimates made in ref. ‘) for some p-resonances give B(k) = 1O-2-1O-1.
in medium
mass and heavy nuclei
V. P. Alfimenkov
et al. 1 Parity non-conservation
91
The dependence ofthe resonance cross section on neutron helicity near an s-resonance is considered in a similar way and gives a Y(k) value smaller by a factor of Pf/rG N 104lo5 than for the p-resonance. The observation of such a small relative change in cross section seems to be nowadays beyond experimental possibilities. Now let us pass to the experimental study of the P-odd dependence of the total cross section on neutron helicity. In this case one should measure the change in transmission through the target due to a small change in CJunder a reverse of neutron helicity. The optimal target thickness n nuclei /cm2 for the best accuracy should meet the requirement na = 2. Thicker samples give a gain in transmission effect, but reduce the statistical accuracy due to low neutron intensity behind the target. Since (T= l&20 b in the presonance region, then the optimal thickness ofthe target is n = (l-2) x 1O23nuclei/cm2. In the experiments with polarized neutrons the so-called transmission effect is usually measured. In our case it is convenient to present it in the form:
where I,, I, are the intensities of the transmitted beam of neutrons polarized in parallel and antiparallel directions to the neutron momentum, respectively;& is the neutron polarization. Eq. (8) can be transformed into: E = -tanh$(a+
-cr_),
(9)
where c + is the cross section of the target nucleus for neutrons with positive and negative helicity. In the study of parity-violating effects (n(o+ - o_)l +Z 1 and eq. (9) can be written in a simpler form: E =
-$l(fJ+ -a_).
(10)
Hence, the experimentally obtained transmission effect allows one to find a change in total cross section da = ‘T, --6_ under reversal of helicity. In the framework of the model discussed above, the dependence of the total cross section on neutron helicity in the p-wave resonance region is described with eq. (5). Thus we obtain: E =
-iH(k)
(11)
From the latter equation it follows that B(k) most naturally characterizes P-odd experimental effects in the total cross section near p-resonances. This value is especially convenient at the p-resonance itself where it is practically constant and the value of b,, can be found with high accuracy from transmission measurements. In measurements far from the resonance where either no data on bp are available or one is not sure about the correctness of eq. (5), it seems reasonable to report the experimental values of do.
98
E P. Alfimenkov 5
et al. / Parity nun-conservation 6
6
3
9
Fig. 1. Experimental arrangement: 1 - reactor, 2 - evacuated neutron guide tube, 3 - monitors, 4 - collimators, 5 - polarized proton target, 6 - electromagnets of the guide Field, 7 - current sheet, 8 - solenoid, 9 - sample, IO - neutron detector. Arrows along the neutron beam path show the direction of magnetic field.
3. Experiment Transmission measurements were performed by the time-of-flight method on the beam of polarized neutrons from the IBR-30 reactor of the Laboratory of Neutron Physics of the Joint Institute for Nuclear Research. The flight path was 58 m long. measurements in the energy range up to I.5 eV were carried out with a neutron pulse duration of 70 ps and a reactor mean power of 20 kW. In order to improve resolution at higherneutronenergiesweused theboostermodeoftheIBR-30reactorwith theelectron accelerator. In this case the pulse duration was 4 ,us and the mean power about 5 kW. The experimental arrangement is shown in fig. 1. The beam of unpolarized neutrons was guided to the polarizer installed at a distance of 32 m from the reactor core. The proton polarized target was used as a polarizer. The target was a single crystal La,Mg,(NO,)i, * 24H,O with an area of 25 cm’ and 17 mm thick. The solid effect ‘l) was used to polarize the protons in the crystallized water of the single crystal. A magnetic field of H = 20 kOe was applied to the target, perpendicular to the neutron beam. Small variations in the field strength (by 40 Oe) ~rmitted the protons to be polarized both parallel and antiparallel to the field direction. The beam transmitted through the proton target acquires a polarization in the direction of proton polarization, since the (n, p) cross section in the singlet state considerably exceeds the triplet one 22). Our target with the proton polarization fD = 0.5-0.6 provided a neutron polarizationf, about equal to the proton polarization, the intensity loss being a factor of 10. The polarized beam was guided and its polarization changed in the following way. The polarized neutron beam passed the gaps of the two electromagnets WithequalfieldsH = 2OOOe.Thedirectionofthelieldofthefirstmagnet wasthesameasthatappliedtotheprotontarget.Thedirectionoftheothermagneticfield could bemadeeitherparallelorantiparallel to the proton target field. A thincoppersheet (0.5 mm) was placed between the two magnets and ~r~ndicular to the beam. The current in it produced on its surface a H = 50 Oe magnetic field. The current through the sheet was not switched off during the measurement. The direction of the current in the
V. P. Alfimenkov et al. / Parity non-conservation
99
sheet was such that its magnetic field on the side of the first magnet had the same direction as the field of the first magnet. In the case of parallel fields the direction of the field in both magnets is the same along the whole path from the proton target to the second magnet. The neutrons arrive at the field ofthe second magnet with the polarization they hadleaving the proton target. When the direction of the current in the second magnet is changed there appears across the current sheet an area where the magnetic field changes abruptly its direction and thus the condition for nonadiabatic transmission is created for neutrons. They pass through the sheet keeping their space orientation of polarization and arrive at the second magnet with the polarization reversed relative to the magnetic field. A solenoid with a field of H = 200 Oe in the direction of the neutron momentum is installed behind the second magnet. The distance between the back edge of the second magnet and the front edge ofthe solenoid is 100 mm. Measurements ofthe magnetic fields have shown that the field in the neutron beam cross-section region turns from transverse in the second magnet to longitudinal in the solenoid along a distance of 200 mm. The direction of polarization of slow neutrons in this field follows adiabatically the direction of the field, i.e. the beam in the solenoid is longitudinally polarized. The calculation performed on a computer using the data on magnetic field measurements shows that the loss in neutron polarization due to the imperfect reverse does not exceed 1@15 % at a neutron energy E = 50 eV. Toreduce theinfluenceofthesecondmagnetreversingfieldon thelieldnear theproton target and the influence of the solenoid on the field near the current sheet the dimensions of the magnets in the direction of the beam were made rather large (600 mm each). The solenoid was 500 mm long which permitted thick enough samples to be placed inside. The neutrons transmitted through the sample went along the evacuated neutron guide tube to the neutron detector. We used as a detector either a liquid scintillation detector 24)or a scintillation detector with Li glass. A fast polarization reversal was made every 40 set to reduce the effects of beam and apparatus instability. The sign of the proton target polarization was changed every 50 h. Thus the neutron polarization and the sign of the P-odd effect were reversed without changing the experimental conditions. This allowed us to account for systematic errors due to instrumental effects. The total measuring time amounted to 200-300 h for every target. An automatic system based on a TPA minicomputer 25) was used for the acquisition of the time spectra and monitor spectra. Spectra N, and N, correspond to 50 h of data acquisition with the neutron spins parallel and antiparallel to their momentum. Figs. 2-5 (upper) give such spectra near the investigated p-resonances for several samples studied. The N, and N, spectra obtained in runs with a fixed proton polarization were then summed to yield two pairs of spectra N, and N,. These pairs allowed us to find for each channel the value of experimental transmission effect for both proton polarization directions :
(12)
V. P. Alfimenkov et al./ Parity non-conservation
100
0.88
-:A 4
m
,o
Qr
I
3
z
2
1
-30 2.0 1.6 1.21.0 0.6 150
200
250
0,6 300
0.4 350
Erl
400
t
Fig. 2. Part of the time-of-flight spectrum (above) and the transmission effect (below) for “Br. The number and arrows show the position and energy of the p-resonance; E, is the energy of the neutron, in eV, t is the time of flight.
120
Fig. 3. Part
1?, :,>, ,: E”
q:
of the time-of-flight
140
160
spectrum
160
200
220
240
and the transmission
t
effect for “‘Cd
V. P. Alfimenkov et al. / Parity non-conservation
101
-20 2.0 1.81.6 1.4 1,2 LI
350
Fig. 4. Part
of the time-of-flight
400
450
spectrum
and
1.0 500
0.8 En I' 550 1
the transmission
effect for “‘Sn.
050
t
0
.
.i'0 -50 -
\/
3 -100 t
'\ *
' I
\ I' b
-150 -200 -
1.0 0.9 0.8 0.7 110 120
Fig. 5. Part of the time-of-flight
0,6
130 140 150
spectrum
0.5 En
160 170
and the transmission
t
effect for ‘39La.
102
V. P. A!fimenkov
et al. ,I Parity non-conservation
These values were tested for agreement and then averaged to have a final value of EeXp for the given sample. Figs.2-5(lower)showe,,,forthedifferent samplesandneutronenergyintervals. Here, Eexpvalues are averaged over groups of channels, the number of channels in the group being increased as the size of the effect decreases. The experimental points in the figures are in the middle of each region over which the average was made. The solid curves are least squares fits of these points to eq. (11). The parameters E,, rp and gr; were determined from the N, and N, spectra for the majority ofthe resonances. Two resonances (one in “Brand one in l”I) were previously not known. We have observed them in separate transmission measurements through thick samples. An isotope assignment of the p-resonance in bromine was made on the basis of the y-spectra following radiative neutron capture. The values 9(k) for p-resonances in the samples were found from E,,~in the following way. If the Doppler and resolution broadening of the experimentally observed resonance is negligible (as in the Br and Sn cases), then the experimental values of N, and N, are proportional to the values of I, and I, in (8) and E,_, = E. For these cases 9(k) was obtained from E_ by the least squares method, using eq. (11) and known data on the target thickness and the parameters of the resonance. If the broadening of the resonance cannot be neglected (La and Cd), then E_(E) in the energy channel and 9(k,)are related by
E,_(E) = - na,9(k,)
m R(E, ~)#(E’~-““~~~~)dE -s - Oooo R(,&‘,E’)e-“~Od’E”&’ s -co
(13)
Here, (TVis the cross section at the maximum of the investigated resonance ; (P(E’) is the function 26) which accounts for the distortion of the cross section due to the Doppler effect ; R(E, E’) is the resolution function dependent on the neutron burst shape and the width of the analyzer time channel. After computing the integrals in eq. (13), the values of for each channel of the analyzer. The B(k,) were found from experimental values of EeXp final value for 9(k,) was obtained as a weighted average value over all the channels.
4. Results and discussion The total cross-section dependence on helicity of neutrons was investigated for 11 weak resonances at a low energy in the nuclei *‘Br, lllCd, “‘Sn, l”I, 139La, 238U. Within high probability they may be considered to be p-wave resonances, since their neutron widths are 3-4 orders ofmagnitude less than the corres~nding,average~eutron widths of s-resonances. The spins of all these resonances are unknown. If the spins are I +$, a P-odd effect is expected. If the spins are I -t-s, then no P-odd effect is expected.
V. P. Alfimenkov et al. / Parity non-conservation
103
A P-odd dependence of total cross section on neutron helicity was observed experimentally in 4 resonances: ‘lBr(E, = 0.88 eV), “‘Cd(E, = 4.53 eV), “‘Sn(E, = 1.33 eV) and ‘j’La(E P = 0.75 eV). The corresponding dependences of E,,~(E) are shown in figs. 2-5. For the 7 resonances left we estimated only the upper limits for the transmission effect. Table 1summarizes p(k,) values obtained from experimental data on all the resonances. There are also given the thicknesses of the targets and the parameters of p-resonances [for 238U from ref. 27), others were obtained in the experiment reported here]. Ifit is known which s-resonances mix with the p-resonance, then from the 9(k,) value and eqs. (7) and (3) one may derive the magnitudes of the mixing coefficients a and the matrix elements (slH,Jp). However, the absence ofdata on spins ofp-resonances and on channel mixture of P; widths prevents us from obtaining unambiguous values. The last columns in table 1 give the results of calculations of Ial and (s(H,lp)l under the assumption that the s-resonances with maximum T;/(E, - ,Q2 value mixes with the presonance. The parameters E, andgr; of these resonances from refs. 27*28) are also listed in table 1. The values of l(sl~wlp)l in table 1 give a lower estimate if it is assumed that the effect is caused by mixing with only one s-resonance. From table 1 it is seen that the values of 9(k,) for different resonances vary in a wide range from lo- 1to lo- 3, the latter corresponding to the accuracy of measurements. The maximum value of9(k,) = 7.3 x 10e2 was obtained for the ‘39La nucleus, where the presonance is the weakest ofall those observed and the s-resonance is anomalously strong. The values of (aland l(slHwlp)l are estimates only, since we are not certain which of the one or possibly more s-resonances mixes with the investigated p-resonance. If an sresonance with negative energy takes part in mixing, then additional uncertainties appear. A comparatively reliable combination of these parameters gT,“/E% may be derived from the thermal capture cross section, but only under the assumption of one negative level contribution to the thermal cross section. An attempt to obtain separately E, and gri does not as a rule give reliable results. Consequently, the estimates for l(s(H,lp) in the case of mixed negative s-resonances appear to be more accurate than (al estimates, since to obtain the latter the separate values are required, while for the former it practically s&ices to use gT,“/Ef. In the case of p-resonances, in which the P-odd effect was observed, the Ialestimates lie in the interval (l-10) x 10e5. The lslH,lp)( estimates are dispersed within the interval (0.3-3) x 10e3 eV. In two cases where no effect wasobserved (a resonance in 1l ‘Cd at E, = 6.9 eV and a resonance in 1271at E = 7.6 eV) the matrix element may be of the order of 10d3 eV though the measuringPaccuracy was insufficient. In other cases (2 resonances in lz71 and 3 resonances in 238U) the matrix elements were either less than 0.2 x 1O-3 eV or equal to zero because of the spin of the p-resonance was I +$. It seems interesting to compare our results on Y(k,) with the data on helicity effect measurements with thermal neutrons. They are available for the “‘Sn, ‘j9La [ref. ‘“)I and Br [ref. “)I nuclei in the form of Si’*,,= As/2a, where r~ is
1.3
“‘Sn
eV)
r,
1.5
238~
11.32+0.02 19.5OkO.2
4.41 &0.01
0.75+0.01
I .25
‘39La
(25) (25)
(25)
45+
5
130+20
7.6 +O.l 90*10 90+10
230 + 20
I .33 &O.Ol
10.4 +0.1 14.0 io.2
163klO 143+13
190*20
(lo-’
4.53 + 0.03 6.94kO.07
0.88 +O.Ol
(2)
3.9
,271
2.05
1.1
*‘Br
“‘Cd
n (10z3 nuclei/cm2)
Nucleus
1.5
3.5 * 6 140 *70
11.1+
0.3 0.2
+40 220
+ 2
*
I
,O.l
+0.1
20.9
+O.l
6.671032
-48.6
37.7
-29
-4
101.0
(e?)
values and results
TABLE
0.3
+ 5 &- 8
3.6+
320 150
13
19
107 108
5.8k
(1 O”‘eV)
Experimental
kO.4
+0.7
1.9
kO.5
0.59t_o.o1
84
4.3
5.5
0.95
9.7
.4P (IO-” eV) y&4
55
- 2.5 * 2.s 0 kl
3.713.7
73
0.3kO.4 1.31: I.0
11.2+8.0
4.5+ 1.3
-8.2k2.2 4.1 k3.3
24
&k,) (lo-‘)
+0.2
1.7 1-1.7 0 io.7
1.7 +-I.?
2.6
0.3 kO.4 0.6 ~0.5
1.8 +1.3
I .25kO.35
9.4 +2.5 3.8 23.0
3.0 &OS
(,&
kO.4
0.08 TO.08 0 kO.01
0.04~0.04
1.28+0.12
0.1 kO.1 0.15~0.11
0.5
0.38+0.10
O.80*0.22 0.42 + 0.33
3.0 20.5
(10e3 eV)
iK.~lff&)l
p
3 2 b % g 2. i:
‘;
c.
2
$2 a
3 [:
-2
&
V. P. Aljbnenkov et al. / Parity non-conservation
105
the total cross section. The following relationship exists for Pti, and .Y(k,): (14)
where crOis the resonance part of the cross section in the maximum of the p-resonance. One can easily derive the above relationship from eq. (5) under assumption that the thermal point is near enough to the p-resonance for eq. (5) to hold. Table 2 summarizes our results on cr,,and P(k,), data on c and Pti, from refs. lo, 29),as well as 9$, values calculated with eq. (14). The agreement between Pth and 9’: can be considered good enough having in mind that Y,,, and .P(k,) differ by 3 and more orders of magnitude. TABLE 2 Comparison
of the effects of resonance
and thermal
.@(k ) (lo-p3)
Nucleus
R,,
“‘Sn
1.33
1.6kO.2
‘39La
0.75
2.8 +0.4
73
*5
19.6k2.0
*‘Br
0.88
0.9+0.1
24
+4
15.5k1.5
“‘Cd
4.53
3.8 kO.5
4.5kl.3
-8.2k2.2
neutrons
3.7kO.4
29
k4 ‘*)
.‘p%
(10-h)
(10-y
6.2kO.7
14.5k5.5
9.oi1.4 19.6 f 2.0 “)
9.3 +2.9 16.2k5.1 0.4 b)
“) Data from ref. 29) recalculated per Br isotope. b, Upper estimate for IYf,l obtained using ref. 13)
5. Conclusions
The present work has shown that the P-odd dependence of the total cross section on neutron helicity has the clear-cut resonance behaviour predicted in ref. “). The effect is explainable in the frame of the presently used idea of the universal weak interaction, and there is no need to introduce any new parity-violating force. All existing experimental data on the helicity dependence of the total cross section are in good agreement with the ideas developed in refs. 8*12).There are indications of the universal character of the effect, since the corresponding matrix elements determining the parity mixing of nuclear. levels are approximately the same. For the further deepening of our understanding of this phenomena, one should try to perform higher accuracy measurements on a much larger number of p-resonances. In conclusion the authors are indebted to, and express their gratitude to, I. M. Frank
106
V. P. Aljimenkov
and V. I. Luschikovfor Ignatovich,
et al. / Parity non-conservation
their interest in the work, to G. G. Bunatian,
S. G. Kadmensky,
0. P. Sushkov,
V. V. Flambaum,
D. F. Zaretsky, V. I. Furman
Shapiro for useful discussions and to M. B. Bunin, S. I. Negovelov, their help during the measurements.
V. K.
and I. S.
B. A. Rodionov
for
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