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The photodisintegration of 40Ar
Nuclear Physics A398 (1983) 41 S-433 @ North-Holland Publishing Company
THE PHOTODISINTEGRATION
OF “Ad
R. A. SUTTON, P. D. ALLEN ++,M. N. THOMPSON and E. G. MUIRHEAD School of Physics, ~~i~er~~~yof M~~bo~r~e, PaTku~l~e,Victoria 3052, Ausmlia Received 16 November 1982 Abstract: High resolution measurements of the (y, n), (y, 2n), (y, p), (y, np) and (y, 2p) cross sections of 40Ar over a photon energy range of 10 to 28 MeV are reported. From this data, the total photon absorption cross section integrated to 26 MeV is found to be 434+40 MeV. mb. The results of a dynamic collective model (DCM) calculation compare favourably with the photoabsorption cross section, supporting the use of the DCM in this mass region. It is confirmed that isospin plays an important role in the decay of the ““Ar giant dipole resonance.
E
NUCLEAR REACTIONS 40Ar(y, n), (y, 2nh (Y, p), (x d), (x np). (y, 2~1, E = 10-28 MeV bremsstrahlung; measured reaction yields; deduced a(E) and total ofphotoabsorption). Comparison with dynamic collective model calculations.
1. Introduction In 2s-Id shell nuclei the giant dipole resonance (GDR) exhibits much fine struciure which is generally interpreted in terms of the shell model ‘, ‘). ~~la!~tative, if not quantitative, agreement has been obtained when multiparti~le-multihole terms are introduced, as in the collective correlations approach 3). On the other hand, medium weight nuclei (50 < A < 70) are described by the dynamic collective model where a similar mechanism produces structure consistent with that observed ex~rimentally, but where the model basis is collective rather than independent particle 4*5, . Recently at this laboratory and elsewhere systematic studies of the photonuclear cross sections of nuclei in the mass region 40 < A < 54 have been carried out 6- ‘I). Experimental evidence shows that the transition from highly structured cross sections in 2s-ld nuclei to the relatively smooth cross sections seen in 2p-If shell nuclei is quite rapid. 40Ar is of interest since it might reasonably be described using either the shell model or the dynamic collective model. The present study therefore offers evidence for the validity of these interpretations for a nucleus with properties intermediate between those of 2s-ld and 2p-l f shell nuclei. Investigation of the photodisintegration of *OAr should be especially useful since most of its decay i Work supported in part by the Australian Research Grant Committee. ++ Present address: Australian Radiation Laboratory, Yallambie, Victoria 3085, Australia. 415
R. A. Sutton et al. / Photodisintegration
416
of4’Ar
modes can be measured, thus avoiding the ambiguities associated with incomplete studies where not all the partial cross sections are measured. We report here high resolution measurements of cross sections for the reactions 40Ar(y, n), 40Ar(y,2n), 40Ar(y, d)+ (y, np) and 40Ar(y, 2~).
2. Experimental
details
40Ar cross sections were measured using the bremsstrahlung photon beam from the University of Melbourne 35 MeV betatron. Three separate types of experiments were necessary to measure the photoproton, photoneutron and (y, 2n) reactions. These are described in subsects. 2.1 and 2.2. The
2. I. ACTIVATION
MEASUREMENTS
The activation technique was used to measure the 40Ar(y, p), (y, d), (y, np) and (y, 2p) cross sections. In all these reactions the residual nuclei formed are unstable. The half-lives of the residual nuclei and the characteristic y-rays used to identify each reaction are listed in table 1. Yield curves were measured using samples of solid argon which were constructed as detailed below. Twelve identical thin-walled aluminium cylindrical bottles 12 cm in height and 8 cm in diameter were immersed in a bath of liquid nitrogen and filled with liquid argon. The liquid argon froze and remained stable for the period of several weeks required for the experiment. Each sample was always immersed in a small bath of liquid nitrogen during irradiation and counting except for approximately 30 s whilst the samples were being transferred. The decay y-rays from the various photoreactions were detected by three NaI detectors. These detectors were unable to resolve the 1.52 MeV y-ray produced by the 40Ar(y , P)~~C~ reaction from either the 1.46 MeV background 40K TABLE Thresholds Reaction
(Y. Go (;‘. n) (Y. P) (7%2n) (7. d) (7. np) (7, 2P) Columns
Threshold (MeV)
Residual nucleus
6.80 9.87 12.53 16.5 18.4 20.6 22.8
FS 39Ar Yl ‘*Ar YI YI 38S
4 and 5 list the half-lives
I
for photoreactions
of the residual
in ““Ar Half-life (mins)
Decay y-ray
55.6
1.27, 1.52
37.24 37.24 170
I .64. 2.17 1.64, 2.17 I .94
nuclei and the characteristic
(MeV)
y-rays emitted.
R. A. Sutton et al. / Photodisintegration
of 40Ar
417
electron capture y-ray or the 1.64 MeV y-rays from the 40Ar(y, np)38C1 reaction. Furthermore they were unable to separate the 1.29 MeV line due to the decay of 41Ar formed by neutron capture reactions, from the 1.27 MeV peak following the 40Ar(y p) reaction. Therefore, a Ge(Li) detector with its superior resolution but poore; efficiency, was also used in order to determine the strength of these y-rays in each of the two groups of unresolved peaks. No other residual activity interfered with important spectrum peaks. Yield curves for the 40Ar(y, p) and 40Ar(y, d) + (y, np) reactions were measured in 200 keV intervals from below the (y, p) threshold of 12.53 MeV up to 29 MeV. The targets were used cyclically so that at least ten half-lives elapsed before any one target was reused. Standard points on each target were measured regularly to check on the stability of both the target and the electronics. Each yield point was measured in the following way. A target was placed in a reproducible position in the collimated X-ray beam. In order to minimise deadtime in the counting system the irradiation time was varied from 50 min at low energy, to a few minutes at high energy. The photon dose was monitored by a thin-walled transmission ionization chamber 12) which was calibrated against a standard P2 chamber r3). Allowance was made for the decay of the activation products during the irradiation. After irradiation the target was removed and placed in a reproducible position within the counting apparatus. Starting exactly 5 min after the irradiation had ceased, y-ray spectra were accumulated for a fixed counting time of 50 min. Data for six yield curves were collected. The yield curves for the 40Ar(y, p) and 40Ar(y, np) reactions were derived from the raw data by taking the area under the appropriate spectrum peak and dividing by the dose. Corrections were made for the deadtime in the detectors and for the delay and counting times. The standard points were used to correct for the differences between individual targets. These differences were never more than 5%. The six yield curves were then averaged and corrected for the dose-monitor response. No evidence for the (y, 2p) reaction was found in these spectra. In order to obtain an estimate for the yield of this reaction a separate measurement was made at an energy of 29 MeV, with an irradiation time of three hours. The value for the ratio of the (y, 2p) yield to 0, np) yield at this energy was found to be (9+3)x 10e4. Absolute yield curves for the 40Ar(y, p) and 40Ar(y, np) reactions were obtained by normalizing to the known absolute yield of the 160(y, n) reaction 14,l’). An 160(y, n) relative yield curve was measured by counting the 0.511 MeV y-rays from the fi’ decay of “0. Identical irradiation and counting geometry was used with the argon containers filled with water as targets. After taking into account the energy dependence of the detector efficiencies, branching ratios for the measured oxygen and argon decays, and the different target densities, the ratio of the argon and oxygen yields was found. The density of solid argon was
R. A. Sutton et al. / Photodisintegration of 40Ar
418
assumed to be 1.65 gm/cm3, as measured at 40 K [ref. i6)]. The integrated cross section for the i60(y, n) reaction from 16 MeV to 26 MeV was taken to be 36 MeV. mb [refs. 14*15)]. The resulting absolute yield curves for the reactions 40Ar(y, p) and 40Ar(y, np) were analysed by the VBPL method “9 is) and the resulting cross sections are shown in figs. 1 and 2. Systematic uncertainties due to the normalization and correction procedures are estimated to be 15 y0 for the (y, p) reaction and 20% for the (y, np) reaction. 2.2. DIRECT
NEUTRON
DETECTION
The 40Ar(y xn) reactions were studied using a 47c BF, neutron counting facility which’has been described previously 19). Neutrons were counted during an 800 ps gate opening 20 ,USafter each beam pulse. The dose was monitored as is described in the previous section. The target chamber consisted of a steel cylinder of outside diameter 42.2 mm, length 2170 mm and wall thickness 2.77 mm, sealed with fusion-welded concave hemispherical end caps of thickness 1.22 mm. In order to minimise background, the length of the chamber was chosen so that each end cap was 400 mm outside the neutron detector. 2.2.1. Neutron production cross section. The target chamber was filled to a pressure of 11.7 MPa with natural argon (99.6% 40Ar) of 99.995% purity. Yields were measured under computer control from 9.5 MeV to 28 MeV in steps of 100 keV, with alternating increasing and decreasing energy sweeping. After
12.0 -
010 11
111
II 17
II
20 ENERGY
Fig. 1. The 40Ar(y, p) cross section. horizontal bars indicate the analysis
III
1
23 ( MeV)
26
Vertical bars represent bin widths which give
a
1
the statistical errors only and the a guide to the effective resolution.
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419
I’ 0
I
.
I
I..
I
I,
.I’
22
ENERGY
I
I
2.L
26
IMeVl
I
Fig. 2. The @Ar(y , d)+(y, np) cross section. Between the photodeuteron threshold of 18.4 MeV and the (y. np) threshold of 20.6 MeV only the (‘J. d) reaction contributes to the cross section. The same conventions are used as in fig. 1.
every tenth point a standard yield was measured at an energy of 26 MeV to enable correction for variation in detector and/or dose measuring efficiencies. The background yield with the target chamber evacuated was measured at 1 MeV intervals from 9 MeV to 28 MeV and was less than 10 % of the total yield at 26 MeV. The average yield curve was corrected for background, and for the variation of neutron detection efficiency along the target 2). The standard variable bin Penfold-Leiss (VBPL) unfolding technique ’ ‘) was applied using the code described in ref. is), to deduce the 40Ar neutron production cross section. 2.2.2. The (y, 2n) cross section. The (7, 2n) cross section was determined by a statistical analysis of the number of neutrons detected after each beam pulse [refs. 14,20)]. During a g’iven yield point the number of neutrons detected after each beam pulse was recorded only if the photon dose delivered during that pulse was within +5% of a selected value. These limits were chosen so that in the later analysis it could be assumed that the photon dose per pulse was effectively constant during that yield point. In practice, it was found that about 50% of beam pulses complied with this criterion. For each bremsstrahlung energy the number of detected neutrons per beam pulse was analysed by the iterative Newton-Raphson method to obtain yields of the (y, n) and (y, 2n) reactions. In the present experiment the variation of detector efficiency along the target prohibited further refinement of the yield values to obtain a best fit to the distribution. Therefore the accuracy of the results is somewhat limited.
420
R. A. Sutton et al. i Photodisintegration
of @Ar
The method described above does not require low count rates and thus is more accurate, given the same beam pulse repetition rate and neutron detection efficiency, than methods in which so-called “pile-up” events are avoided 21,22). The present analysis method is also preferable to Costa’s solution 20) which is mathematically elegant but diverges for low efficiency detectors because the effects of statistical fluctuations are not taken into account. The experimental set-up used to measure the (y, 2n) reaction was identical to that described in the previous section. The target chamber was filled with argon to a pressure of 2.76 MPa, a compromise between the requirements of the analysis procedure and of minimising background. Three yield curves were measured at energies from 16 MeV to 27 MeV in steps of 500 keV. A typical yield point was measured over a period of 30 min. Background was measured in the same way in 2 MeV intervals starting at 16 MeV. The accuracy obtainable in this experiment was limited by the relatively low maximum neutron detection efficiency of 15 %, the low beam pulse repetition rate of 50 Hz and in particular the variation of the detector efficiency over the length of the target. For this reason a point by point analysis of the data was not possible and so a curve, of a form derived from the statistical model with allowance for a proportion of direct reactions 23,24), was fitted to the yield data. The “direct fraction” parameter in this fit was taken to be 0.35 consistent with the work of Veyssikre et al. ‘) and a least chi-squared fit was obtained with a “level density” parameter of 13 MeV- ‘. This curve was used to calculate the 40Ar(y 2n) cross section (fig. 3c) from the total photoneutron production yield curvl. In using experimentally determined statistical model parameters it was assumed that the same structure occurs in both the (y, 2n) and the (y, xn) cross section. Using the (y, 2n) information the neutron production data was corrected for double counting of (y, 2n) events to derive the (y, sn) cross section shown in fig. 3a. 2.3. PHOTOABSORPTION
CROSS SECTION
The 40Ar(y, sn) cross section and the 40Ar(y, n) + (y, np) cross section derived from the photoneutron data are displayed in figs. 3a and 3b. The total photoabsorption cross section is estimated by adding the (y, p) cross section to the (y, sn) cross section. The result is shown in fig. 4e. One contribution to the total cross section that is not included is the (y, c() reaction. Reimann et al. 25) have shown that the (y, a) cross section is about 11% of the (y, p) cross section at an energy of 17.7 MeV. Hence we estimate that the (y, a) cross section comprises less than 1% of the total cross section at this energy. Other reactions are not expected to contribute significantly so that fig. 4e provides a good estimate of the total photoabsorption cross section.
R. A. Sutton et al.
Lo -
a
/ Photodisintegration of 4oAr
421
(al
16
20
ENERGY
IMeV)
28
Fig. 3. Cross sections for neutron production in 40Ar. (a) The measured “‘Ar photoneutron cross section a(y, sn) = cr(y, n)+u(y, np)+u(y, 2n). The present measurement (vertical bars) is compared to that by Veyssiere et al. ‘) (dots). (b) The 40Ar(y, n)+(y, np) cross section together with the (y, no) cross section derived from the data of Jury et al. “), assuming isotropic emission of neutrons (open circles). (c) The measured 40Ar(y, 2n) cross section, compared to the measurement of Veyssiere ‘) (dots). The same conventions are used as in fig. 1.
3. Discussion
A summary of the integrated cross sections and energy assignments to the structure of the measured photodisintegration cross sections can be found in tables 2 and 3. The estimated value of 434k40 MeV. mb for the photoabsorption cross section integrated to 26 MeV exhausts 73% of the Thomas-Reiche-Kuhn (TRK) dipole sum rule (60NZI.4 MeV . mb).
1
_ p-__--
_ _=--= _ --
E
_
-_
by lines.
Fig. 4. The “‘Ar photodisintegration cross sections: (a) the (7, n) cross section, (b) the (y, 2n) reaction, section, and (e) the estimated total absorption cross section. To aid easy comparison the component
i
1
3
(c) the (y, p) cross section, (d) the (7. d)+ (y, np) cross cross sections (a), (b), (c)and (d) are represented in (e)
R
p Y
N
R. A. Sutton et al. / Photodisintegration
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423
TABLE 2
Integrated
cross sections
for 40Ar photoreactions
Reaction
(MeEv, 21 21 27 27 26 26 26 26
(y. n) + (y, np)+ 2(~. 2n) (Y, n) + (Y, np) + (v, 24 (Y, 2n) i;, ;; + (Y, np) (~1 np) (Y, n) (Y, total)
= (Y,n)+(v, W+(Y.
P)+(Y.
d)+(y,
np)+(y,
2~)
s” adE (MeV mb) 529 + 30 382 f 30 148+15 232 f 20 61k 8 6& I 222 * 20 434 f 40
TABLE 3
Energy
assignments (Y,
sn)
(MeV) 11-13 14.7+0.2 16.3 kO.2 17.9kO.2 19.6kO.l 21.2kO.l 23.2f0.3
3.1. COMPARISON
WITH
OTHER
to structure
in “‘Ar
(Y.P) (McV)
16.9kO.3 19.5 kO.3 21.4kO.3 23.4kO.3
DATA
3.1.1. Photoproton measurements. Early experimental estimates of the integrated cross sections for the (y, p) and (y, np) reactions varied in magnitude by up to a factor of five 26- 31). Reasonable agreement was obtained in later experiments [refs. 32-34)]. The results of these latter measurements and the present one are given in table 4 and are consistent if allowance is made for the differing upper energy limits. Penfold and Garwin measured the energy dependence of the (y, p) and (y, np) reactions with coarse resolution 29). In that measurement the (y, p) cross section reached a maximum at 23.5 MeV, while the (y, np) cross section peaked at 27.5 MeV. The overall shape of the cross sections reported in ref. 29) correlate well with the present measurement, although the tine structure that we observe was not resolved. 3.1.2. Photoneutron measurements. Early measurements of the photoneutron reactions showed a featureless cross section with a maximum of 30 to 40 mb at an energy of 18 to 20 MeV [refs. 26*35- 37)]. Later experiments demonstrated
R. A. Sutton et al. / Photodisintegration of @‘Ar
424
TABLE 4
Integrated
cross sections
Reference
Present
experiment
Penfold
and Garwin
“)
Dosch ef al. 32) Dodge
and Barber
Hofmann
33)
et a/. 34)
“) As renormalised
by Dosch
obtained
from photoproton
(MEV) e
s” a(y, p)dE (MeV mb)
26 29 33 33 34 30 32.5
61j7
8
experiments s” u(y, np)dE (MeV mb) 6k
(Y. 2~) yield (Y, np) yield
1 9*3x
91 lOOk 15
1om4
22 25klO 3.5 x 10-3
62-111 104+15
et al. 32).
the existence of some tine structure in the 40Ar giant resonance. The 40Ar(y, no) differential cross section measured at 90” by Lokan er al. 3*), identified twenty seven resonances in the energy range from 10.4 MeV to 12.5 MeV. This structure is unresolved in our experiment since the resolution in this region exceeds 1 MeV. The (y, no) measurement was later extended up to 23 MeV by Jury et al. 39). The cross section shown in fig. 3b (open circles) is obtained by multiplying their differential cross section by 471 on the assumption of an isotropic angular distribution. The structure at 17.7 MeV and 19.5 MeV corresponds to that observed in the (y, sn) cross-section measurement. The (y, no) cross section at 17.7 MeV is approximately 4 mb, compared to 38 mb for the (y, sn) reaction. Thus the (y, no) decay channel constitutes a relatively small proportion of the giant resonance. The 40Ar photoneutron measurement of Veyssiere et al. ‘) can be directly compared to the present measurement and is shown in fig. 3a. The magnitudes of the total photoneutron cross section are in agreement up to 20 MeV and the integrated strength up to 26.7 MeV from the Saclay measurement is 393 f28 MeV . mb compared with the value of 382 + 30 MeV * mb integrated to 27 MeV obtained here. However there is less consistency concerning the tine structure above 18 MeV. The peaks observed at 19.6 MeV, 21.2 MeV and 23.2 MeV have no obvious counterparts in the Saclay measurement. The validity of these structures is supported by the present measurement of the (y, p) cross section which shows similar features, particularly at 21 and 23 MeV (see table 3). Since different techniques were used for these two experiments they provide mutually supporting evidence. Also, the (y, no) cross section measurement by Jury et al. shows structure at 17.7 MeV and 19.4 MeV [ref. 39)] (see fig. 3b). The (y, 2n) cross section measured by Veyssiere et al. is compared to the present measurement in fig. 3c. Considering the limitations of the techniques used to derive the cross sections the agreement is quite good.
R. A. Sutton et al. / Photodisintegration of 40Ar 3.2. COMPARISON
425
WITH THEORY
3.2.1. The dynamic collectioe model. The dynamic collective model (DCM) has not generally been applied to nuclei as light as 40Ar since the validity of using a collective basis with so few nucleons has been questioned 40). However the agreement between the structure predicted by the DCM and the experimental results for f%isotopes suggest that these qualms are unjustified 8*41,42). Experiments have shown that 40Ar is spherical 43,44), therefore it is possible to compare the GDR of 40Ar with the predictions of the dynamic collective model applied to spherical nuclei by Huber, Danos, Weber and Greiner 5). The DCM is an extension of the hydrodynamic model, taking into account the interaction with the low-energy collective states 4). Huber et al. calculate the low-energy states assuming that these vibrations are harmonic 5). In the case of 40Ar this will only be an approximation since the two-phonon Of, 2+ and 4+ states are not degenerate 45). Huber et al. calculate eigenstates and transition strengths to the dipole states on the assumption that the interaction between the giant dipole resonance and the low energy vibrations is adiabatic. The parameters that determine the cross section are the unperturbed giant resonance energy E,, the quadrupole phonon energy E, and the average vibrational amplitude /IO. It is found that the spectrum of the l- states depends strongly on PO and weakly on E,. Variation in E, mainly causes a shift in the spectrum. Huber et al. provide results of their calculations of the dipole strengths as a function of /IO for various values of E,, with E, = 18 MeV. For a nucleus with given fro, E, and E,, they show that the slight change in spectrum due to using E, # 18 MeV can be compensated for by replacing flo with Do = &POE,. The energy E, of the first excited 2+ state in 40Ar is equal to 1.46 MeV [ref. 45)]. The value of /IO is 0.22 from deuteron scattering studies by Hinterberger et al. 46) and Sen and Darden 44). Coulomb scattering work by Nakai et al. 43) suggests that B(E,, O+ + 2+) = 3.2 x 10-50 e* . cm4. The deformation parameter is derived from the expression PO = 47c[B(E2, 0’ + 2’)]*/3ZR”, giving a value of 0.23 if R = 1.25& [ref. 47)]. The closest parameters to these given in ref. 5, are for a spectrum of dipole states with /IO = 0.25 and E, = 1.6 MeV. This spectrum is shown by the bars in fig. 5. E, has been assumed to be 19 MeV, and the spectrum shifted accordingly. Thus the correct value of PO for 40Ar is between 0.23 and 0.24. The effect of using a high value of b. in the calculation is partially counteracted by the use of a higher value of E,. Since no information is available concerning the damping of the giant resonance the width of each state is regarded as a free parameter and is adjusted to obtain the best tit to the absorption cross section. The widths used varied from 3 MeV at low energy to 1.2 MeV at high energy. The calculated cross section is shown as the full curve in fig. 5. It can be seen that the DCM correctly predicts the relative energy of the inter-
426
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of 40Ar
1 ,
L
0
12
16 ENERGY
20
2L
28
(MeV)
Fig. 5. The total absorption cross section compared with the predictions of the dynamic collective model ‘). The vertical bars show the calculated dipole strengths. The solid line represents the photoabsorption cross section derived from these dipole strengths (see text).
mediate structure in the GDR above 17 MeV. The agreement between the individual peaks of the experimental cross section and the DCM prediction is excellent. The calculation also accounts quite well for the relative strength observed in the absorption cross section between 16 MeV and 23 MeV. However several discrepancies are evident. More structure exists at lower energies than is predicted, and the calculation underestimates the strength both at low and high energies. The lack of agreement in the low-energy region is not surprising as non-collective excitations are expected which are neglected in the calculation. Similar disagreement concerning the strength at higher energies has been observed for 2p-If shell nuclei with somewhat higher atomic weights ‘341*42). Nevertheless the DCM seems to provide a reasonable explanation of the observed structure in the GDR of 40Ar. 3.2.2. Isospin effects in the decay of the GDR. The nature of the interaction between the electric dipole field and a nucleus leads to the isospin selection rule AT = 0, f 1, with T = 0 to T = 0 transitions prohibited. El photon absorption by a non-self-conjugate nucleus, initially in the ground state TO = $(N -Z), therefore populates states of isospin T, and T,+ 1. These states of different isospin form two components of the GDR refered to as the T, and the T, resonances. It has been predicted 48) that the T, and T, components are separated in energy by an amount AE = E, -E, = 6O(T,+ 1)/A. The relative integrated
R. A. Suiton et al. 1 Photodisintegration of 40Ar
427
energy-weighted cross sections of these two components are given by Fallieros and Goulard 49). Essential experimental confirmation of these predictions has been given for nuclei in this mass region by the work reported by Thompson 5o). The decay by neutron or proton emission from these isospin components is partially governed by isospin conservation laws. This is illustrated by the energy level diagram for the decay of argon, shown in fig. 6. In the residual nuclei only the lowest level with the indicated value of isospin is shown. Where this level is not the ground state, the energy has been calculated from the known reaction Q-value of the appropriate isobaric analogue state using the semiempirical formula for the coulomb displacement energies derived by Anderson et al. 51). The numbers associated with each decay mode (indicated by the arrows) are the isospin coupling coefficients. The effects of isospin should be evident in the partial cross sections for neutron and proton decay. Simplifying somewhat, one can predict that the T, resonance will dominate the (y, p) reaction, since the neutron decay from these states to T = 3 states in 39Ar is prohibited. The T, resonance will be more evident in the (y, sn) cross section due to a larger number of states available for neutron decay and the Coulomb barrier inhibition of the proton decay. We therefore tentatively identify the cross section strength at 21-24 MeV in the (y, p) cross section as due to decay of the T, resonance. Since the predicted isospin splitting is 4.5 MeV for 40Ar the T, resonance should be centered around 17 MeV. This corresponds to h, location of the major strength in the total photoneutron cross section and the smaller structure seen in the (y, p) cross section. The effects of isospin should also be evident in the dinucleon reactions. If these reactions are two stage sequential decays through intermediate states in 39C1 and 39Ar then the competition between the (y, n)(n) and (y, n)(p) reactions and between the (y, p)(n) and (y, p)(p) reactions will be influenced by the isospin selection rules in .a similar manner to the initial (y, n) and (y, p) reactions (see fig. 6). For example below 27 MeV the isospin selection rules forbid (y, 2n) reactions through T = $ states in 39Ar and therefore these states can only decay through the (y, n)(p) reaction. The above arguments can be put on a quantitative level. The calculation is an extension of the method of Pywell 7, to include sequential two-nucleon decay through intermediate states in the A - 1 nucleus. The T, and T, components of the absorption cross section are represented by single lorentzians whose separation and relative strengths are fixed, consistent with the predictions of ref.48). In the absence of any further theoretical information, the widths of each resonance and the centroid energy of the GDR were regarded as free parameters to be adjusted to give the best chi-squared lit to the measured total photon absorption cross section. The final widths obtained were 8.0 MeV and 5.0 MeV for the T, and T, resonances respectively. The absorption cross
428
R. A. Sutton et al.
I Photodisintegrarion
qf40Ar
80
3 265 c lo
10
2 l&L "L
lo
T’
T<
“Cl
(Zl,dI
0
L
xcitation new ,. (MeVl
Fig. 6. Decay given isospin.
modes of the GDR in 40Ar The indicated states are those of minimum energy for the The arrows represent isospin allowed transitions with values of the squared ClebschGordan
coupling
coefficients
marked.
section, the two lorentzian fit and the T, and T, components are shown in fig. 7a. The decay of the GDR is calculated assuming a statistical decay mechanism, taking into account the isospin selection rules, Coulomb and angular momentum barriers and geometric factors. Level density parameters for 39Ar, 38Ar and 3EC1 were obtained from the data given by Beckerman 52). In the absence of specific data for 39C1 these were assumed to be the same as for j9K.
R. A. Sutton et al. / Photodisintegration of 4QAr
429
For comparison the cross sections were also calculated from the same fitted absorption cross section using the same method except that the isospin effects were not included. The results of these calculations are shown as the full (with isospin) and broken (without isospin) curves in figs. 7b7e compared with the measured cross sections. Within the limits of the model lorentzians, the shape of the (y, n) and (y, p) cross sections are well reproduced by the calculation which includes isospin. The calculated (y, p) cross section has the correct magnitude but the peak energy is about 1 MeV low. Note that if isospin effects are ignored the (y, p) cross section is more than a factor of ten too small. The (y, n) reaction is relatively insensitive to isospin effects but a marginal improvement is evident when isospin is included. In fig. 7c the (y, 2n) cross section is plotted. The theoretical and experimental curves are in agreement only if isospin effects are included. In the case of the (y, np) reaction there is poor agreement between theory and experiment in each case (fig. 7e). Overall it is evident that including the isospin effects markedly improves the agreement with the major decay modes. The main discrepancy is the gross over-estimation of the (y, np) reaction. Most of this calculated strength is due to the (y, n)(p) reaction and arises because the T = $ states in 39Ar are assumed to be of pure isospin and cannot decay by emission of a neutron. This assumption that no isospin mixing is present is not easily justifiable since the density of T = t states is much greater than that of T = 5 states in this region. The maximum likely effect of isospin mixing on the reaction cross sections was estimated by repeating the calculation as described above but including 100% mixing, so that the T = 2 states in 39Ar and the T = $ states in j9C1 were assumed to have T = t and T = 3 character respectively for subsequent decays. The results of this calculation are shown as the dot-dash curves in figs. 7c and 7e. The (y, p) and (y, n) cross sections are unaffected since the isospin mixing only occurs at energies above the dinucleon reaction thresholds. Most of the strength from the higher excited states in 39Ar is now channelled away from the (y, np) cross section into the (y, 2n) reaction. The calculated location of the (y, np) cross section maximum now agrees with experiment, and the height of the cross section decreases to about half that of the experimental value. Both dinucleon cross sections are seen to lie between the two extreme calculations using the assumption of 0 and loo’? isospin mixing. Therefore it appears that the inclusion of a proportion of isospin mixing in the calculation would produce agreement with the experimental values. From the preceding discussion it is evident that isospin significantly affects the decay of the GDR in 40Ar . The agreement with the data is improved if some isospin mixing is included. It seems reasonable to suppose that the remaining discrepancies between the calculated and experimental results are due to the simplifications used in the theory, viz: (i) the use of a relatively simple
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R. A. Sutton et ai. / P~otodisintegrati~n
of 40Ar
431
level density formula, and (ii) the assumption that the T, and T, resonances can be described by simple lorentzians despite the structure evident in the absorption cross section.
4. Conclusion The photodisintegration of 40Ar has been investigated by measuring the partial cross sections 40Ar(y, n), 40Ar(y, p), 40Ar(y, d)+ (y, np), 40Ar(y, 2nj and “OAr(y, 2~). Combining these results gives an accurate estimate of the total photoabsorption cross section. More structure is resolved in the present experiment than in earlier measurements and the structure is mutually confirmed in the two independent measurements of the cross sections for proton and neutron decay. The total photoabsorption cross section has been compared with the predictions of the dynamic collective theory. This calculation was able to account for the energy of all structure observed above 17 MeV, which suggests that the DCM approach is valid for 40Ar despite its relatively low atomic weight. However the calculation underestimates the strength below 17 MeV and above 23 MeV. Hence the application to 40Ar of refined DCM calculations 4*), in which some of the approximations of the treatment given here are improved would be of interest. The competition between the various modes of decay has been interpreted as evidence for isospin effects on the GDR of 40Ar. It is shown that a simple isospin-constrained two lorentzian fit to the total absorption cross section, together with decays described by the statistical model and isospin conservation laws are able to account for the principal modes of decay. Hence the photodisintegration of “Ar is consistent with isospin splitting of the GDR. The results of the present experiments suggest some further aspects of theory that would be of particular interest. The success of both the isospin-statistical model approach and the dynamic collective theory raises the issue of the relationship between the two. The approaches are complementary in that the DCM predicts the absorption cross section whereas isospin and the statistical model determine the decay of the GDR. However, the isospin approach requires the presence of two groups of states with definite isospin that are separated in energy and have different strengths. In order to unify these two concepts the DCM must be capable of generating these states. At present this is beyond the scope of the collective theories 53). In view of the results for 40Ar and for other nuclei in refs. 6- “) this shouId be an important consideration in the future devetopment of the collective theory.
432
R. A. Sution et al. / Photodisintegration of 40Ar
The authors wish to thank members of the betatron group for assistance during the experiment. One of us (P.D.A.) gratefully acknowledges the support of an Australian Post Graduate Research Award during the period of this work.
References 1) A. Veyssitre, H. Be& R. Berg&e, P. Carlos, A. Lepretre and A. De Miniac, Nucl. Phys. A227 (1974) 513 P. D. Allen, E. G. Muirhead and D. V. Webb, Nucl. Phys. A357 (1981) 171 D. Drechsel, J. B. Seabom and W. Greiner, Phys. Rev. 162 (1967) 983 M. Danos and W. Greiner, Phys. Rev. 134 (1964) 284 M. G. Huber, M. Danos, H. J. Weber and W. Greiner, Phys. Rev. 155 (1967) 1073 S. Oikawa and K. Shoda, Nucl. Phys. A277 (1977) 301 R. E. Pywell and M. N. Thompson, Nucl. Phys. A318 (1979) 416 R. Sutton, M. N. Thompson, M. Sugawara, T. Saito and H. Tsubota, Nucl. Phys. A339 (1980) 125 R. E. Pywell, M. N. Thompson, K. Shoda, M. Sugawara, T. Saito, H. Tsubota, H. Miyase, J. Uegaki, T. Tamae, H. Ohashi, and T. Urano, Austral. J. Phys. 33 (1980) 685 10) Y. I. Assatiri and M. N. Thompson, Nucl. Phys. A357 (1981) 429 11) P. D. Harty and M. N. Thompson, Austral. J. Phys. 34 (1981) 505 12) R. S. Hicks, Ph. D. thesis, University of Melbourne (1972), unpublished 13) J. S. Pruitt and S. R. Domen, N. B. S. Monograph 48 (1962) 14) P. D. Allen, Ph. D. thesis, University of Melbourne (1979), unpublished 15) Su Su, Ph. D. thesis, University of Melbourne (1977), unpublished 16) G. W. Kaye and T. H. Laby, Tables of physical and chemical constants (Longman, 1975) 17) E. Bramanis, T. K. Deague, R. S. Hicks, R. J. Hughes, E. G. Muirhead, R. H. Sambell and R. J. J. Stewart, Nucl. Instr. 100 (1972) 59 18) P. D. Allen, Su Su and E. G. Muirhead, Comp. Phys. 21 (1980) 163 19) R. H. Sambell and B. M. Spicer, Nucl. Phys. A205 (1973) 139 20) S. Costa, Nucl. Instr. 21 (1963) 129 21) H. Beil, R. Berg&e and A. Veyssiere, Nucl. Instr. 67 (1969) 293 22) J. G. Woodworth, K. G. McNeill, J. W. Jury, R. A. Alvarez, B. L. Berman, D. D. Faul and P. Meyer, Phys. Rev. Cl9 (1979) 1667 23) J. M. Blatt and W. F. Weiskophf, Theoretical nuclear physics (Wiley, New York, 1952) 24) H. H. Thies and B. M. Spicer, Austral. J. Phys. 13 (1960) 905 25) M. A. Reimann, J. R. MacDonald and J. B. Warren, Nucl. Phys. 66 (1965) 465 26) D. McPherson, E. Pederson and L. Katz, Can. J. Phys. 32 (1954) 593 27) B. M. Spicer, Phys. Rev. 100 (1955) 791 28) I. P. Iavor, ZhETF (USSR) 34 (1958) 1420; JETP (Sov. Phys.) 34 (1958) 983 29) A. S. Penfold and E. L. Garwin, Phys. Rev. 114 (1958) 1139 30) P. Brix, A. Kording and K. H. Lindenberger, Z. Phys. 154 (1959) 569 31) V. Emma, C. Milone, R. Rinzivillo and A. Rubbino, Nuovo Cim. 14 (1959) 62 32) H. G. Dosch, K. H. Lindenberger and P. Brix, Nucl. Phys. 18 (1960) 615 33) W. R. Dodge and W. C. Barber, Phys. Rev. 127 (1962) 1746 34) W. Hofmann, G. Kraft and R. Mundhenke, Z. Phys. 225 (1969) 303 35) G. A. Ferguson, J. Halpem, R. Nathans and P. F. Yergin, Phys. Rev. 96 (1954) 776 36) R. W. Fast, P. A. Flourney, R. S. Tickle and W. D. Whitehead, Phys. Rev. 118 (1960) 535 37) D. Ehhalt, R. Kosiek and R. Pfeiffer, Z. Phys. 187 (1965) 210 38) K. H. Lokan, N. K. Sherman, R. W. Gellie, J. W. Jury, J. I. Lodge and R. G. Johnson, Phys. Rev. Lett. 28 (1972) 1526 39) J. W. Jury, J. I. Lodge, K. H. Lokan, N. K. Sherman and R. W. Gellie, Can. J. Phys. 51 (1973) 1176 40) E. M. Diener, J. F. Amann, P. Paul and S. L. Blatt, Phys. Rev. C3 (1971) 2303 41) J. I. Weiss, Austral. J. Phys. 34 (1981) 627 2) 3) 4) 5) 6) 7) 8) 9)
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J. I. Weiss, Z. Phys. A300 (1981) 329 K. Nakai, J. L. Quebert, F. S. Stevens and R. M. Diamond, Phys. Rev. Lett. 24 (1970) 903 S. Sen and S. E. Darden, Nucl. Phys. A226 (1976) 173 P. M. Endt and C. van der Leun, Nucl. Phys. A310 (1978) 1 F. Hinterberger, G. Mairle, U. Schmidt-Rohr, G. J. Wagner and P. Turek, Nucl. Phys. All5 (1968) 570 F. Hinterberger, G. Mairle, U. Schmidt-Rohr and G. J. Wagner, Nucl. Phys. All1 (1968) 265 R. t). Akytiz and S. Fallieros, Phys. Rev. Lett. 27 (1971) 1016 S. Fallieros and B. Goulard, Nucl. Phys. Al47 (1970) 593 M. N. Thompson, in Nuclear interactions, conference held in Canberra, Aug 28 - Sept 1, 1978, ed. B. A. Robson, vol. 92 (Springer, Berlin, 1979) p. 208 J. D. Anderson, C. Wong and J. W. McClure, Phys. Rev. 138 (1965) B615 M. Beckerman, Nucl. Phys. A278 (1977) 333 T. J. Bowles, R. J. Holt, H. E. Jackson, R. M. Laszewski, R. D. McKeown, A. M. Natham and J. R. Specht, Phys. Rev. C24 (1981) 1940
THE PHOTODISINTEGRATION
OF “Ad
R. A. SUTTON, P. D. ALLEN ++,M. N. THOMPSON and E. G. MUIRHEAD School of Physics, ~~i~er~~~yof M~~bo~r~e, PaTku~l~e,Victoria 3052, Ausmlia Received 16 November 1982 Abstract: High resolution measurements of the (y, n), (y, 2n), (y, p), (y, np) and (y, 2p) cross sections of 40Ar over a photon energy range of 10 to 28 MeV are reported. From this data, the total photon absorption cross section integrated to 26 MeV is found to be 434+40 MeV. mb. The results of a dynamic collective model (DCM) calculation compare favourably with the photoabsorption cross section, supporting the use of the DCM in this mass region. It is confirmed that isospin plays an important role in the decay of the ““Ar giant dipole resonance.
E
NUCLEAR REACTIONS 40Ar(y, n), (y, 2nh (Y, p), (x d), (x np). (y, 2~1, E = 10-28 MeV bremsstrahlung; measured reaction yields; deduced a(E) and total ofphotoabsorption). Comparison with dynamic collective model calculations.
1. Introduction In 2s-Id shell nuclei the giant dipole resonance (GDR) exhibits much fine struciure which is generally interpreted in terms of the shell model ‘, ‘). ~~la!~tative, if not quantitative, agreement has been obtained when multiparti~le-multihole terms are introduced, as in the collective correlations approach 3). On the other hand, medium weight nuclei (50 < A < 70) are described by the dynamic collective model where a similar mechanism produces structure consistent with that observed ex~rimentally, but where the model basis is collective rather than independent particle 4*5, . Recently at this laboratory and elsewhere systematic studies of the photonuclear cross sections of nuclei in the mass region 40 < A < 54 have been carried out 6- ‘I). Experimental evidence shows that the transition from highly structured cross sections in 2s-ld nuclei to the relatively smooth cross sections seen in 2p-If shell nuclei is quite rapid. 40Ar is of interest since it might reasonably be described using either the shell model or the dynamic collective model. The present study therefore offers evidence for the validity of these interpretations for a nucleus with properties intermediate between those of 2s-ld and 2p-l f shell nuclei. Investigation of the photodisintegration of *OAr should be especially useful since most of its decay i Work supported in part by the Australian Research Grant Committee. ++ Present address: Australian Radiation Laboratory, Yallambie, Victoria 3085, Australia. 415
R. A. Sutton et al. / Photodisintegration
416
of4’Ar
modes can be measured, thus avoiding the ambiguities associated with incomplete studies where not all the partial cross sections are measured. We report here high resolution measurements of cross sections for the reactions 40Ar(y, n), 40Ar(y,2n), 40Ar(y, d)+ (y, np) and 40Ar(y, 2~).
2. Experimental
details
40Ar cross sections were measured using the bremsstrahlung photon beam from the University of Melbourne 35 MeV betatron. Three separate types of experiments were necessary to measure the photoproton, photoneutron and (y, 2n) reactions. These are described in subsects. 2.1 and 2.2. The
2. I. ACTIVATION
MEASUREMENTS
The activation technique was used to measure the 40Ar(y, p), (y, d), (y, np) and (y, 2p) cross sections. In all these reactions the residual nuclei formed are unstable. The half-lives of the residual nuclei and the characteristic y-rays used to identify each reaction are listed in table 1. Yield curves were measured using samples of solid argon which were constructed as detailed below. Twelve identical thin-walled aluminium cylindrical bottles 12 cm in height and 8 cm in diameter were immersed in a bath of liquid nitrogen and filled with liquid argon. The liquid argon froze and remained stable for the period of several weeks required for the experiment. Each sample was always immersed in a small bath of liquid nitrogen during irradiation and counting except for approximately 30 s whilst the samples were being transferred. The decay y-rays from the various photoreactions were detected by three NaI detectors. These detectors were unable to resolve the 1.52 MeV y-ray produced by the 40Ar(y , P)~~C~ reaction from either the 1.46 MeV background 40K TABLE Thresholds Reaction
(Y. Go (;‘. n) (Y. P) (7%2n) (7. d) (7. np) (7, 2P) Columns
Threshold (MeV)
Residual nucleus
6.80 9.87 12.53 16.5 18.4 20.6 22.8
FS 39Ar Yl ‘*Ar YI YI 38S
4 and 5 list the half-lives
I
for photoreactions
of the residual
in ““Ar Half-life (mins)
Decay y-ray
55.6
1.27, 1.52
37.24 37.24 170
I .64. 2.17 1.64, 2.17 I .94
nuclei and the characteristic
(MeV)
y-rays emitted.
R. A. Sutton et al. / Photodisintegration
of 40Ar
417
electron capture y-ray or the 1.64 MeV y-rays from the 40Ar(y, np)38C1 reaction. Furthermore they were unable to separate the 1.29 MeV line due to the decay of 41Ar formed by neutron capture reactions, from the 1.27 MeV peak following the 40Ar(y p) reaction. Therefore, a Ge(Li) detector with its superior resolution but poore; efficiency, was also used in order to determine the strength of these y-rays in each of the two groups of unresolved peaks. No other residual activity interfered with important spectrum peaks. Yield curves for the 40Ar(y, p) and 40Ar(y, d) + (y, np) reactions were measured in 200 keV intervals from below the (y, p) threshold of 12.53 MeV up to 29 MeV. The targets were used cyclically so that at least ten half-lives elapsed before any one target was reused. Standard points on each target were measured regularly to check on the stability of both the target and the electronics. Each yield point was measured in the following way. A target was placed in a reproducible position in the collimated X-ray beam. In order to minimise deadtime in the counting system the irradiation time was varied from 50 min at low energy, to a few minutes at high energy. The photon dose was monitored by a thin-walled transmission ionization chamber 12) which was calibrated against a standard P2 chamber r3). Allowance was made for the decay of the activation products during the irradiation. After irradiation the target was removed and placed in a reproducible position within the counting apparatus. Starting exactly 5 min after the irradiation had ceased, y-ray spectra were accumulated for a fixed counting time of 50 min. Data for six yield curves were collected. The yield curves for the 40Ar(y, p) and 40Ar(y, np) reactions were derived from the raw data by taking the area under the appropriate spectrum peak and dividing by the dose. Corrections were made for the deadtime in the detectors and for the delay and counting times. The standard points were used to correct for the differences between individual targets. These differences were never more than 5%. The six yield curves were then averaged and corrected for the dose-monitor response. No evidence for the (y, 2p) reaction was found in these spectra. In order to obtain an estimate for the yield of this reaction a separate measurement was made at an energy of 29 MeV, with an irradiation time of three hours. The value for the ratio of the (y, 2p) yield to 0, np) yield at this energy was found to be (9+3)x 10e4. Absolute yield curves for the 40Ar(y, p) and 40Ar(y, np) reactions were obtained by normalizing to the known absolute yield of the 160(y, n) reaction 14,l’). An 160(y, n) relative yield curve was measured by counting the 0.511 MeV y-rays from the fi’ decay of “0. Identical irradiation and counting geometry was used with the argon containers filled with water as targets. After taking into account the energy dependence of the detector efficiencies, branching ratios for the measured oxygen and argon decays, and the different target densities, the ratio of the argon and oxygen yields was found. The density of solid argon was
R. A. Sutton et al. / Photodisintegration of 40Ar
418
assumed to be 1.65 gm/cm3, as measured at 40 K [ref. i6)]. The integrated cross section for the i60(y, n) reaction from 16 MeV to 26 MeV was taken to be 36 MeV. mb [refs. 14*15)]. The resulting absolute yield curves for the reactions 40Ar(y, p) and 40Ar(y, np) were analysed by the VBPL method “9 is) and the resulting cross sections are shown in figs. 1 and 2. Systematic uncertainties due to the normalization and correction procedures are estimated to be 15 y0 for the (y, p) reaction and 20% for the (y, np) reaction. 2.2. DIRECT
NEUTRON
DETECTION
The 40Ar(y xn) reactions were studied using a 47c BF, neutron counting facility which’has been described previously 19). Neutrons were counted during an 800 ps gate opening 20 ,USafter each beam pulse. The dose was monitored as is described in the previous section. The target chamber consisted of a steel cylinder of outside diameter 42.2 mm, length 2170 mm and wall thickness 2.77 mm, sealed with fusion-welded concave hemispherical end caps of thickness 1.22 mm. In order to minimise background, the length of the chamber was chosen so that each end cap was 400 mm outside the neutron detector. 2.2.1. Neutron production cross section. The target chamber was filled to a pressure of 11.7 MPa with natural argon (99.6% 40Ar) of 99.995% purity. Yields were measured under computer control from 9.5 MeV to 28 MeV in steps of 100 keV, with alternating increasing and decreasing energy sweeping. After
12.0 -
010 11
111
II 17
II
20 ENERGY
Fig. 1. The 40Ar(y, p) cross section. horizontal bars indicate the analysis
III
1
23 ( MeV)
26
Vertical bars represent bin widths which give
a
1
the statistical errors only and the a guide to the effective resolution.
R. A. Sutton et al. / Photodisintegration of @Ar
419
I’ 0
I
.
I
I..
I
I,
.I’
22
ENERGY
I
I
2.L
26
IMeVl
I
Fig. 2. The @Ar(y , d)+(y, np) cross section. Between the photodeuteron threshold of 18.4 MeV and the (y. np) threshold of 20.6 MeV only the (‘J. d) reaction contributes to the cross section. The same conventions are used as in fig. 1.
every tenth point a standard yield was measured at an energy of 26 MeV to enable correction for variation in detector and/or dose measuring efficiencies. The background yield with the target chamber evacuated was measured at 1 MeV intervals from 9 MeV to 28 MeV and was less than 10 % of the total yield at 26 MeV. The average yield curve was corrected for background, and for the variation of neutron detection efficiency along the target 2). The standard variable bin Penfold-Leiss (VBPL) unfolding technique ’ ‘) was applied using the code described in ref. is), to deduce the 40Ar neutron production cross section. 2.2.2. The (y, 2n) cross section. The (7, 2n) cross section was determined by a statistical analysis of the number of neutrons detected after each beam pulse [refs. 14,20)]. During a g’iven yield point the number of neutrons detected after each beam pulse was recorded only if the photon dose delivered during that pulse was within +5% of a selected value. These limits were chosen so that in the later analysis it could be assumed that the photon dose per pulse was effectively constant during that yield point. In practice, it was found that about 50% of beam pulses complied with this criterion. For each bremsstrahlung energy the number of detected neutrons per beam pulse was analysed by the iterative Newton-Raphson method to obtain yields of the (y, n) and (y, 2n) reactions. In the present experiment the variation of detector efficiency along the target prohibited further refinement of the yield values to obtain a best fit to the distribution. Therefore the accuracy of the results is somewhat limited.
420
R. A. Sutton et al. i Photodisintegration
of @Ar
The method described above does not require low count rates and thus is more accurate, given the same beam pulse repetition rate and neutron detection efficiency, than methods in which so-called “pile-up” events are avoided 21,22). The present analysis method is also preferable to Costa’s solution 20) which is mathematically elegant but diverges for low efficiency detectors because the effects of statistical fluctuations are not taken into account. The experimental set-up used to measure the (y, 2n) reaction was identical to that described in the previous section. The target chamber was filled with argon to a pressure of 2.76 MPa, a compromise between the requirements of the analysis procedure and of minimising background. Three yield curves were measured at energies from 16 MeV to 27 MeV in steps of 500 keV. A typical yield point was measured over a period of 30 min. Background was measured in the same way in 2 MeV intervals starting at 16 MeV. The accuracy obtainable in this experiment was limited by the relatively low maximum neutron detection efficiency of 15 %, the low beam pulse repetition rate of 50 Hz and in particular the variation of the detector efficiency over the length of the target. For this reason a point by point analysis of the data was not possible and so a curve, of a form derived from the statistical model with allowance for a proportion of direct reactions 23,24), was fitted to the yield data. The “direct fraction” parameter in this fit was taken to be 0.35 consistent with the work of Veyssikre et al. ‘) and a least chi-squared fit was obtained with a “level density” parameter of 13 MeV- ‘. This curve was used to calculate the 40Ar(y 2n) cross section (fig. 3c) from the total photoneutron production yield curvl. In using experimentally determined statistical model parameters it was assumed that the same structure occurs in both the (y, 2n) and the (y, xn) cross section. Using the (y, 2n) information the neutron production data was corrected for double counting of (y, 2n) events to derive the (y, sn) cross section shown in fig. 3a. 2.3. PHOTOABSORPTION
CROSS SECTION
The 40Ar(y, sn) cross section and the 40Ar(y, n) + (y, np) cross section derived from the photoneutron data are displayed in figs. 3a and 3b. The total photoabsorption cross section is estimated by adding the (y, p) cross section to the (y, sn) cross section. The result is shown in fig. 4e. One contribution to the total cross section that is not included is the (y, c() reaction. Reimann et al. 25) have shown that the (y, a) cross section is about 11% of the (y, p) cross section at an energy of 17.7 MeV. Hence we estimate that the (y, a) cross section comprises less than 1% of the total cross section at this energy. Other reactions are not expected to contribute significantly so that fig. 4e provides a good estimate of the total photoabsorption cross section.
R. A. Sutton et al.
Lo -
a
/ Photodisintegration of 4oAr
421
(al
16
20
ENERGY
IMeV)
28
Fig. 3. Cross sections for neutron production in 40Ar. (a) The measured “‘Ar photoneutron cross section a(y, sn) = cr(y, n)+u(y, np)+u(y, 2n). The present measurement (vertical bars) is compared to that by Veyssiere et al. ‘) (dots). (b) The 40Ar(y, n)+(y, np) cross section together with the (y, no) cross section derived from the data of Jury et al. “), assuming isotropic emission of neutrons (open circles). (c) The measured 40Ar(y, 2n) cross section, compared to the measurement of Veyssiere ‘) (dots). The same conventions are used as in fig. 1.
3. Discussion
A summary of the integrated cross sections and energy assignments to the structure of the measured photodisintegration cross sections can be found in tables 2 and 3. The estimated value of 434k40 MeV. mb for the photoabsorption cross section integrated to 26 MeV exhausts 73% of the Thomas-Reiche-Kuhn (TRK) dipole sum rule (60NZI.4 MeV . mb).
1
_ p-__--
_ _=--= _ --
E
_
-_
by lines.
Fig. 4. The “‘Ar photodisintegration cross sections: (a) the (7, n) cross section, (b) the (y, 2n) reaction, section, and (e) the estimated total absorption cross section. To aid easy comparison the component
i
1
3
(c) the (y, p) cross section, (d) the (7. d)+ (y, np) cross cross sections (a), (b), (c)and (d) are represented in (e)
R
p Y
N
R. A. Sutton et al. / Photodisintegration
of “OAr
423
TABLE 2
Integrated
cross sections
for 40Ar photoreactions
Reaction
(MeEv, 21 21 27 27 26 26 26 26
(y. n) + (y, np)+ 2(~. 2n) (Y, n) + (Y, np) + (v, 24 (Y, 2n) i;, ;; + (Y, np) (~1 np) (Y, n) (Y, total)
= (Y,n)+(v, W+(Y.
P)+(Y.
d)+(y,
np)+(y,
2~)
s” adE (MeV mb) 529 + 30 382 f 30 148+15 232 f 20 61k 8 6& I 222 * 20 434 f 40
TABLE 3
Energy
assignments (Y,
sn)
(MeV) 11-13 14.7+0.2 16.3 kO.2 17.9kO.2 19.6kO.l 21.2kO.l 23.2f0.3
3.1. COMPARISON
WITH
OTHER
to structure
in “‘Ar
(Y.P) (McV)
16.9kO.3 19.5 kO.3 21.4kO.3 23.4kO.3
DATA
3.1.1. Photoproton measurements. Early experimental estimates of the integrated cross sections for the (y, p) and (y, np) reactions varied in magnitude by up to a factor of five 26- 31). Reasonable agreement was obtained in later experiments [refs. 32-34)]. The results of these latter measurements and the present one are given in table 4 and are consistent if allowance is made for the differing upper energy limits. Penfold and Garwin measured the energy dependence of the (y, p) and (y, np) reactions with coarse resolution 29). In that measurement the (y, p) cross section reached a maximum at 23.5 MeV, while the (y, np) cross section peaked at 27.5 MeV. The overall shape of the cross sections reported in ref. 29) correlate well with the present measurement, although the tine structure that we observe was not resolved. 3.1.2. Photoneutron measurements. Early measurements of the photoneutron reactions showed a featureless cross section with a maximum of 30 to 40 mb at an energy of 18 to 20 MeV [refs. 26*35- 37)]. Later experiments demonstrated
R. A. Sutton et al. / Photodisintegration of @‘Ar
424
TABLE 4
Integrated
cross sections
Reference
Present
experiment
Penfold
and Garwin
“)
Dosch ef al. 32) Dodge
and Barber
Hofmann
33)
et a/. 34)
“) As renormalised
by Dosch
obtained
from photoproton
(MEV) e
s” a(y, p)dE (MeV mb)
26 29 33 33 34 30 32.5
61j7
8
experiments s” u(y, np)dE (MeV mb) 6k
(Y. 2~) yield (Y, np) yield
1 9*3x
91 lOOk 15
1om4
22 25klO 3.5 x 10-3
62-111 104+15
et al. 32).
the existence of some tine structure in the 40Ar giant resonance. The 40Ar(y, no) differential cross section measured at 90” by Lokan er al. 3*), identified twenty seven resonances in the energy range from 10.4 MeV to 12.5 MeV. This structure is unresolved in our experiment since the resolution in this region exceeds 1 MeV. The (y, no) measurement was later extended up to 23 MeV by Jury et al. 39). The cross section shown in fig. 3b (open circles) is obtained by multiplying their differential cross section by 471 on the assumption of an isotropic angular distribution. The structure at 17.7 MeV and 19.5 MeV corresponds to that observed in the (y, sn) cross-section measurement. The (y, no) cross section at 17.7 MeV is approximately 4 mb, compared to 38 mb for the (y, sn) reaction. Thus the (y, no) decay channel constitutes a relatively small proportion of the giant resonance. The 40Ar photoneutron measurement of Veyssiere et al. ‘) can be directly compared to the present measurement and is shown in fig. 3a. The magnitudes of the total photoneutron cross section are in agreement up to 20 MeV and the integrated strength up to 26.7 MeV from the Saclay measurement is 393 f28 MeV . mb compared with the value of 382 + 30 MeV * mb integrated to 27 MeV obtained here. However there is less consistency concerning the tine structure above 18 MeV. The peaks observed at 19.6 MeV, 21.2 MeV and 23.2 MeV have no obvious counterparts in the Saclay measurement. The validity of these structures is supported by the present measurement of the (y, p) cross section which shows similar features, particularly at 21 and 23 MeV (see table 3). Since different techniques were used for these two experiments they provide mutually supporting evidence. Also, the (y, no) cross section measurement by Jury et al. shows structure at 17.7 MeV and 19.4 MeV [ref. 39)] (see fig. 3b). The (y, 2n) cross section measured by Veyssiere et al. is compared to the present measurement in fig. 3c. Considering the limitations of the techniques used to derive the cross sections the agreement is quite good.
R. A. Sutton et al. / Photodisintegration of 40Ar 3.2. COMPARISON
425
WITH THEORY
3.2.1. The dynamic collectioe model. The dynamic collective model (DCM) has not generally been applied to nuclei as light as 40Ar since the validity of using a collective basis with so few nucleons has been questioned 40). However the agreement between the structure predicted by the DCM and the experimental results for f%isotopes suggest that these qualms are unjustified 8*41,42). Experiments have shown that 40Ar is spherical 43,44), therefore it is possible to compare the GDR of 40Ar with the predictions of the dynamic collective model applied to spherical nuclei by Huber, Danos, Weber and Greiner 5). The DCM is an extension of the hydrodynamic model, taking into account the interaction with the low-energy collective states 4). Huber et al. calculate the low-energy states assuming that these vibrations are harmonic 5). In the case of 40Ar this will only be an approximation since the two-phonon Of, 2+ and 4+ states are not degenerate 45). Huber et al. calculate eigenstates and transition strengths to the dipole states on the assumption that the interaction between the giant dipole resonance and the low energy vibrations is adiabatic. The parameters that determine the cross section are the unperturbed giant resonance energy E,, the quadrupole phonon energy E, and the average vibrational amplitude /IO. It is found that the spectrum of the l- states depends strongly on PO and weakly on E,. Variation in E, mainly causes a shift in the spectrum. Huber et al. provide results of their calculations of the dipole strengths as a function of /IO for various values of E,, with E, = 18 MeV. For a nucleus with given fro, E, and E,, they show that the slight change in spectrum due to using E, # 18 MeV can be compensated for by replacing flo with Do = &POE,. The energy E, of the first excited 2+ state in 40Ar is equal to 1.46 MeV [ref. 45)]. The value of /IO is 0.22 from deuteron scattering studies by Hinterberger et al. 46) and Sen and Darden 44). Coulomb scattering work by Nakai et al. 43) suggests that B(E,, O+ + 2+) = 3.2 x 10-50 e* . cm4. The deformation parameter is derived from the expression PO = 47c[B(E2, 0’ + 2’)]*/3ZR”, giving a value of 0.23 if R = 1.25& [ref. 47)]. The closest parameters to these given in ref. 5, are for a spectrum of dipole states with /IO = 0.25 and E, = 1.6 MeV. This spectrum is shown by the bars in fig. 5. E, has been assumed to be 19 MeV, and the spectrum shifted accordingly. Thus the correct value of PO for 40Ar is between 0.23 and 0.24. The effect of using a high value of b. in the calculation is partially counteracted by the use of a higher value of E,. Since no information is available concerning the damping of the giant resonance the width of each state is regarded as a free parameter and is adjusted to obtain the best tit to the absorption cross section. The widths used varied from 3 MeV at low energy to 1.2 MeV at high energy. The calculated cross section is shown as the full curve in fig. 5. It can be seen that the DCM correctly predicts the relative energy of the inter-
426
R. A. Sutton et al. / Photodisintegration
of 40Ar
1 ,
L
0
12
16 ENERGY
20
2L
28
(MeV)
Fig. 5. The total absorption cross section compared with the predictions of the dynamic collective model ‘). The vertical bars show the calculated dipole strengths. The solid line represents the photoabsorption cross section derived from these dipole strengths (see text).
mediate structure in the GDR above 17 MeV. The agreement between the individual peaks of the experimental cross section and the DCM prediction is excellent. The calculation also accounts quite well for the relative strength observed in the absorption cross section between 16 MeV and 23 MeV. However several discrepancies are evident. More structure exists at lower energies than is predicted, and the calculation underestimates the strength both at low and high energies. The lack of agreement in the low-energy region is not surprising as non-collective excitations are expected which are neglected in the calculation. Similar disagreement concerning the strength at higher energies has been observed for 2p-If shell nuclei with somewhat higher atomic weights ‘341*42). Nevertheless the DCM seems to provide a reasonable explanation of the observed structure in the GDR of 40Ar. 3.2.2. Isospin effects in the decay of the GDR. The nature of the interaction between the electric dipole field and a nucleus leads to the isospin selection rule AT = 0, f 1, with T = 0 to T = 0 transitions prohibited. El photon absorption by a non-self-conjugate nucleus, initially in the ground state TO = $(N -Z), therefore populates states of isospin T, and T,+ 1. These states of different isospin form two components of the GDR refered to as the T, and the T, resonances. It has been predicted 48) that the T, and T, components are separated in energy by an amount AE = E, -E, = 6O(T,+ 1)/A. The relative integrated
R. A. Suiton et al. 1 Photodisintegration of 40Ar
427
energy-weighted cross sections of these two components are given by Fallieros and Goulard 49). Essential experimental confirmation of these predictions has been given for nuclei in this mass region by the work reported by Thompson 5o). The decay by neutron or proton emission from these isospin components is partially governed by isospin conservation laws. This is illustrated by the energy level diagram for the decay of argon, shown in fig. 6. In the residual nuclei only the lowest level with the indicated value of isospin is shown. Where this level is not the ground state, the energy has been calculated from the known reaction Q-value of the appropriate isobaric analogue state using the semiempirical formula for the coulomb displacement energies derived by Anderson et al. 51). The numbers associated with each decay mode (indicated by the arrows) are the isospin coupling coefficients. The effects of isospin should be evident in the partial cross sections for neutron and proton decay. Simplifying somewhat, one can predict that the T, resonance will dominate the (y, p) reaction, since the neutron decay from these states to T = 3 states in 39Ar is prohibited. The T, resonance will be more evident in the (y, sn) cross section due to a larger number of states available for neutron decay and the Coulomb barrier inhibition of the proton decay. We therefore tentatively identify the cross section strength at 21-24 MeV in the (y, p) cross section as due to decay of the T, resonance. Since the predicted isospin splitting is 4.5 MeV for 40Ar the T, resonance should be centered around 17 MeV. This corresponds to h, location of the major strength in the total photoneutron cross section and the smaller structure seen in the (y, p) cross section. The effects of isospin should also be evident in the dinucleon reactions. If these reactions are two stage sequential decays through intermediate states in 39C1 and 39Ar then the competition between the (y, n)(n) and (y, n)(p) reactions and between the (y, p)(n) and (y, p)(p) reactions will be influenced by the isospin selection rules in .a similar manner to the initial (y, n) and (y, p) reactions (see fig. 6). For example below 27 MeV the isospin selection rules forbid (y, 2n) reactions through T = $ states in 39Ar and therefore these states can only decay through the (y, n)(p) reaction. The above arguments can be put on a quantitative level. The calculation is an extension of the method of Pywell 7, to include sequential two-nucleon decay through intermediate states in the A - 1 nucleus. The T, and T, components of the absorption cross section are represented by single lorentzians whose separation and relative strengths are fixed, consistent with the predictions of ref.48). In the absence of any further theoretical information, the widths of each resonance and the centroid energy of the GDR were regarded as free parameters to be adjusted to give the best chi-squared lit to the measured total photon absorption cross section. The final widths obtained were 8.0 MeV and 5.0 MeV for the T, and T, resonances respectively. The absorption cross
428
R. A. Sutton et al.
I Photodisintegrarion
qf40Ar
80
3 265 c lo
10
2 l&L "L
lo
T’
T<
“Cl
(Zl,dI
0
L
xcitation new ,. (MeVl
Fig. 6. Decay given isospin.
modes of the GDR in 40Ar The indicated states are those of minimum energy for the The arrows represent isospin allowed transitions with values of the squared ClebschGordan
coupling
coefficients
marked.
section, the two lorentzian fit and the T, and T, components are shown in fig. 7a. The decay of the GDR is calculated assuming a statistical decay mechanism, taking into account the isospin selection rules, Coulomb and angular momentum barriers and geometric factors. Level density parameters for 39Ar, 38Ar and 3EC1 were obtained from the data given by Beckerman 52). In the absence of specific data for 39C1 these were assumed to be the same as for j9K.
R. A. Sutton et al. / Photodisintegration of 4QAr
429
For comparison the cross sections were also calculated from the same fitted absorption cross section using the same method except that the isospin effects were not included. The results of these calculations are shown as the full (with isospin) and broken (without isospin) curves in figs. 7b7e compared with the measured cross sections. Within the limits of the model lorentzians, the shape of the (y, n) and (y, p) cross sections are well reproduced by the calculation which includes isospin. The calculated (y, p) cross section has the correct magnitude but the peak energy is about 1 MeV low. Note that if isospin effects are ignored the (y, p) cross section is more than a factor of ten too small. The (y, n) reaction is relatively insensitive to isospin effects but a marginal improvement is evident when isospin is included. In fig. 7c the (y, 2n) cross section is plotted. The theoretical and experimental curves are in agreement only if isospin effects are included. In the case of the (y, np) reaction there is poor agreement between theory and experiment in each case (fig. 7e). Overall it is evident that including the isospin effects markedly improves the agreement with the major decay modes. The main discrepancy is the gross over-estimation of the (y, np) reaction. Most of this calculated strength is due to the (y, n)(p) reaction and arises because the T = $ states in 39Ar are assumed to be of pure isospin and cannot decay by emission of a neutron. This assumption that no isospin mixing is present is not easily justifiable since the density of T = t states is much greater than that of T = 5 states in this region. The maximum likely effect of isospin mixing on the reaction cross sections was estimated by repeating the calculation as described above but including 100% mixing, so that the T = 2 states in 39Ar and the T = $ states in j9C1 were assumed to have T = t and T = 3 character respectively for subsequent decays. The results of this calculation are shown as the dot-dash curves in figs. 7c and 7e. The (y, p) and (y, n) cross sections are unaffected since the isospin mixing only occurs at energies above the dinucleon reaction thresholds. Most of the strength from the higher excited states in 39Ar is now channelled away from the (y, np) cross section into the (y, 2n) reaction. The calculated location of the (y, np) cross section maximum now agrees with experiment, and the height of the cross section decreases to about half that of the experimental value. Both dinucleon cross sections are seen to lie between the two extreme calculations using the assumption of 0 and loo’? isospin mixing. Therefore it appears that the inclusion of a proportion of isospin mixing in the calculation would produce agreement with the experimental values. From the preceding discussion it is evident that isospin significantly affects the decay of the GDR in 40Ar . The agreement with the data is improved if some isospin mixing is included. It seems reasonable to suppose that the remaining discrepancies between the calculated and experimental results are due to the simplifications used in the theory, viz: (i) the use of a relatively simple
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R. A. Sutton et ai. / P~otodisintegrati~n
of 40Ar
431
level density formula, and (ii) the assumption that the T, and T, resonances can be described by simple lorentzians despite the structure evident in the absorption cross section.
4. Conclusion The photodisintegration of 40Ar has been investigated by measuring the partial cross sections 40Ar(y, n), 40Ar(y, p), 40Ar(y, d)+ (y, np), 40Ar(y, 2nj and “OAr(y, 2~). Combining these results gives an accurate estimate of the total photoabsorption cross section. More structure is resolved in the present experiment than in earlier measurements and the structure is mutually confirmed in the two independent measurements of the cross sections for proton and neutron decay. The total photoabsorption cross section has been compared with the predictions of the dynamic collective theory. This calculation was able to account for the energy of all structure observed above 17 MeV, which suggests that the DCM approach is valid for 40Ar despite its relatively low atomic weight. However the calculation underestimates the strength below 17 MeV and above 23 MeV. Hence the application to 40Ar of refined DCM calculations 4*), in which some of the approximations of the treatment given here are improved would be of interest. The competition between the various modes of decay has been interpreted as evidence for isospin effects on the GDR of 40Ar. It is shown that a simple isospin-constrained two lorentzian fit to the total absorption cross section, together with decays described by the statistical model and isospin conservation laws are able to account for the principal modes of decay. Hence the photodisintegration of “Ar is consistent with isospin splitting of the GDR. The results of the present experiments suggest some further aspects of theory that would be of particular interest. The success of both the isospin-statistical model approach and the dynamic collective theory raises the issue of the relationship between the two. The approaches are complementary in that the DCM predicts the absorption cross section whereas isospin and the statistical model determine the decay of the GDR. However, the isospin approach requires the presence of two groups of states with definite isospin that are separated in energy and have different strengths. In order to unify these two concepts the DCM must be capable of generating these states. At present this is beyond the scope of the collective theories 53). In view of the results for 40Ar and for other nuclei in refs. 6- “) this shouId be an important consideration in the future devetopment of the collective theory.
432
R. A. Sution et al. / Photodisintegration of 40Ar
The authors wish to thank members of the betatron group for assistance during the experiment. One of us (P.D.A.) gratefully acknowledges the support of an Australian Post Graduate Research Award during the period of this work.
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