Population of ground-state rotational levels in (α, 2nγ) reactions

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[ NuclearPhysics A124

(1969) 597--608; ( ~

North-HollandPublishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

P O P U L A T I O N O F G R O U N D - S T A T E R O T A T I O N A L LEVELS I N (~, 2n7) R E A C T I O N S s. J. MILLS and W. L. RAUTENBACH National Physical Research Laboratory, CSIR, Pretoria, South Africa Received 28 October 1968 Abstract: The relative intensities of ground-state rotational transitions in the nuclei 164Gd, le~Er, ~TsW, ~8°W, xs2Wand lt°Pt produced in (~, 2ny) reactions at energies between 19.2 MeV and 31.7 MeV, have been measured with a Ge(Li) detector. The results are compared with calculations based on the statistical description of compound nuclear reactions. It is shown that this model is not able to explain these experimental results as satisfactorily as in the case of isomeric cross-section ratios.

NUCLEAR REACTIONS ls*Sm, X62Dy,l~6,17s,18°Hf, 1880s (0c,2n~'), E= = 19.2--31.7 MeV; measured a(E; Er). Enriched targets, Ge(Li) detector. 1. Introduction

Since Morinaga and Gugelot i) have shown that (~, xnT) reactions preferentially populate the ground-state rotational band of deformed doubly even nuclei, the observation of the prompt gamma-ray cascade in this type of reaction has been developed into a very useful tool in nuclear spectroscopy. Measurements on these gamma rays also yield information on the particular nuclear reaction mechanism, especially on the effect of angular momentum on the decay of the compound nucleus. Results obtained in such a context will provide similar information as the well-known isomeric crosssection ratios 2,3), but the measurement of the prompt gamma rays (or conversion electrons) offers several advantages. Much more complete information can be obtained for each individual nucleus due to the fact that the populations of several angular momentum states can be measured. Furthermore, a large variety of product nuclei can be studied, because this method does not depend on the existence of suitable isomeric states. It is therefore in principle possible to study compound nuclei of which the decay should be nearly identical from the point of view of the statistical description of compound nuclear reactions 4-6). In such cases, comparison between experimental results and theory should provide a stringent test for the validity of both the theoretical reaction mechanisms assumed and the information deduced from best fits between theory and experiment. Although some investigations along these lines have previously been performed [see for instance refs. 7-~ 0)], there are no best fits over a range of incident energy. In the present work, however, the populations of levels in the ground-state rotational 597

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bands of lS4Gd, 164Er, 178W, iS°w, lSZw and 19°pt populated in (~, 2ny)reactions in the energy range 19.2 to 31.7 MeV, are considered ,. These nuclei cover the rareearth region of permanent defoI~ation reasonably well (19°pt actually lies just beyond this region), while the three tungsten isotopes provide a series of nearly identical cases from the point of view of the statistical theory. As is customary for measured isomeric cross-section ratios, the experimental results have been fitted with the statistical model of compound nuclear reactions.

2. Experimental details The experimental lay-out is shown schematically in fig. 1. The energy of the 31.7 MeV external alpha-particle cyclotron beam was varied by means of seven different sets of aluminium degrading foils mounted on a movable holder at the intermediatefocus position. The targets were also mounted on a movable holder with five target positions; one of them carried a thin fluorescent screen. After having traversed the target, the beam was stopped in a well-shielded Faraday collector connected to a current integrator. The targets were prepared from isotopically enriched oxides or the element in powder form (in the case of Os) by depositing a suspension of the powder in water on a 1 mg/cm 2 melinex backing stretched over an aluminium frame. After the powder film had dried, a drop of a dilute solution of VYNS in cyclo-hexanone was used to bind it to the backing. Additional particulars of the targets are given in table 1. TABLE 1 Target particulars

Target nucleus

Chemical form

xs2Sm ae2Dy X~6Hf l~SHf a*°Hf lssOs

Sm2 Oa Dy203 HfO2 HfO~ HfO2 Os

Approximate mean thickness (mg/cm~) 5.6 6.7 6.0 6.4 6.4 14.0

Isotopic enrichment a) (%) 99.06 91.04 81.0 89.14 93.8 87.7

~) As given by the supplier (Isotopes Division, Oak Ridge National Laboratory). Errors are estimated at less than 1 ~o.

The gamma-ray spectra were measured with a 2 cm a Ge(Li) detector placed at 90 ° with respect to the beam direction. During the experiment, the resolution for the 662 keV gamma ray of 137Cs was typically about 5 keV FWHM. The detection efficiency of the experimental arrangement was obtained as a function of gamma-ray energy by * The measurements on 1~8W, 18°W and ~8~W have already been reported in a preliminary short communication as), in which some aspects of the results have been discussed.

603

S. J. MILLS AND W. L. RAUTENBACH

means of a series of absolutely calibrated gamma-ray sources which could be mounted in the target position. For each garrlma-ray spectrum, a background spectrum was obtained for the same integrated beam current by interposing a 9 m m lead absorber between the target and the detector a). Corrections were made to the final results for the few transmitted g a m m a rays, which were recorded in the background spectra and were therefore incorrectly subtracted as background radiation in the analysis of the data.

3. Experimental results Fig. 2 shows a typical gamma-ray spectrum obtained. The observed ground-state rotational transitions in the product nucleus of the (ct, 2n) reaction are indicated. In 161~

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F i g . 2. G a m m a - r a y s p e c t r u m o b t a i n e d for a Ze2Dy203 t a r g e t b o m b a r d e d w i t h 26.9 M e V a l p h a p a r t i c l e s . G r o u n d - s t a t e r o t a t i o n a l t r a n s i t i o n s i n le4Er are i n d i c a t e d .

most spectra, the 2 + ~ 0 + transition in the target nucleus due to inelastic scattering of the alpha particles could also be identified. In each case a number of unidentified peaks were also observed. Some of them were characteristic of the particular target being irradiated, while others were common to all targets and therefore probably originated from the target backings and/or the oxygen in the oxides. However, as the interest of this work was centred on the rotational transitions in the ground-state bands of the (~, 2n) product nuclei, the origin of these peaks was not further investigated.

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or(6, 4)/(tr(4, 2) +?) 0.434-0.06 tr(8, 6)/tr(4, 2) 0.194-0.04 or(6, 4)/a(4, 2) 0.45±0.08 tr(8, 6)/a(4, 2) a(6, 4)/tr(4, 2) or(8, 6)/ix(4, 2) a(6, 4)/cr(4, 2) ix(8, 6)/tr(4, 2) ~r(6, 4)/a(4, 2) tr(8, 6)/tr(4, 2) ~r(2, 0)/t~(4, 2) ix(6, 4)/a(4, 2)

Measured ratio

4.094-1.15

0.474-0.13 0.254-0.09 0.364-0.07

0.614-0.08 0.18-t-0.04 0.484-0.05 0.21 -I-0.03 0.274-0.07

21.4

TABLE 2

2.594-0.47

0.454-0.11 0.215_0.08 0.454-0.08

0.644-0.08 0.344-0.06 0.554-0.07 0.28-4-0.05 0.374-0.09

23.4 0.764-0.10 0.36±0.06 0.615:0.07 0.29-4-0.05 0.464-0.09 0.124-0.06 0.594-0.12 0.334-0.08 0.51 4-0.08 0.164-0.06 2.194-0.33 0.274-0.05

25.2 0.744-0.10 0.434-0.07 0.654-0.08 0.374-0.06 0.47-4-0.08 0.084-0.04 0.654-0.12 0.364-0.08 0.544-0.07 0.284-0.05 1.774-0.23 0.324-0.06

26.9

Alpha-particle energy (MeV)

Measured cross-section ratios

0.634-0.08 0.38-4-0.06 0.69-t-0.08 0.434-0.07 0.484-0.07 0.134-0.04 0.664-0.11 0.404-0.08 0.554-0.08 0.254-0.06 1.604-0.24 0.33 4-0.06

28.6

0.594-0.10 0.404-0.07 0.704-0.09 0.45±0.07 0.474-0.06 0.154-0.03 0.734-0.11 0.514-0.09 0.724-0.13 0.224-0.07 1.464-0.18 0.41 4-0.07

30.2

0.554-0.13 0.35-4-0.07 0.784-0.12 0.594-0.10 0.494-0.07 0.204-0.06 0.754-0.13 0.544-0.11 0.785_0.19 0.124-0.11 1.354-0.19 0.424-0.07

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S. J. M I L L S A N D W . L. R A U T E N B A C H

Except in the case of 19°pt, the 2 + -> 0 + transitions have not been considered because of large experimental errors (due to incomplete resolution from other peaks) and uncertainties in the large internal conversion correction. Furthermore, the population of ground-state rotational levels above the 8 ÷ level could not be studied due to the low efficiency of the detector at these energies. The measured relative cross-sections a ( J , J - 2 ) for the production of the rotational transitions J ~ J - 2 are listed in table 2. All the cross sections are given relative to that of the 4 ÷ ~ 2 + transition in the particular case. These cross-section ratios are also shown in figs. 3 and 4, where, however, for the sake of ease of representation, the inverse of the ratio a(2, O)/a(4, 2) is plotted. These relative cross sections were obtained by determining the number of counts in the various peaks in the gamma-ray spectra and correcting for the efficiency of the detector and for internal conversion. Furthermore, it has been assumed that all the transitions have identical angular distributions within the errors with which they can be determined in the experiment s, ~2). All the errors specified are estimated standard deviations. No provision has been made for systematic errors except in the determination of the peak areas in the g a m m a - r a y spectra. However, all other systematic errors should be small in comparison with the total errors specified. In the case of 154Gd ' the cross-section ratios behave anomalously at alpha-particle energies above approximately 25 MeV and decrease with increasing alpha particle energy instead of increasing as is theoretically expected. This is probably due to a g a m m a - r a y peak, which is unresolved from the 4 ÷ ~ 2 ÷ gamma-ray peak and appears at approximately 25 MeV; its contribution to the total intensity of the composite peak increases as the alpha-particle energy is increased. However, if such a g a m m a ray does exist, it must have an energy nearly identical to that of the 4 + ~ 2 + transition. The same phenomenon is also observed in the case of the 8 + ~ 6 ÷ transition in ~S2W, but there it cannot be due to a c6mposite 4 ÷ ~ 2 + peak because there is no corresponding decrease in the ratio a(6, 4)/a(4, 2). It may therefore at first glance seem doubtful whether it is, in fact, the 8 ÷ --* 6 ÷ transition which has been analysed. However, the energy of 466 +_5 keV of the observed g a m m a ray falls within the energy limits of 458+ 10 keV specified by Lark and Morinaga 13) for the 8 + ~ 6 ÷ transition, and, furthermore, the intensity of this g a m m a ray (relative to that of the 4 ÷ ~ 2 ÷ transition) at an alpha-particle energy of 27 MeV agrees within experimental errors with their value for the 8 + ~ 6 ÷ transition. It has therefore been concluded that the observed transition at 466+__5 keV is the 8 ÷ --->6 ÷ member of the ground-state band o f ~82W. 4. Statistical-model calculations In the statistical-model calculations, we have essentially adopted the procedures o f Bishop et al. 6) as used in the analysis of isomeric cross-section ratios. However, as has been proposed by Sarantites and Pate 14), the level densities have been evaluated

(~t,2ny) REACTIONS

603

only for that part of the total excitation energy which is associated with thermal motion of the nucleons. The energy dependence of the level density therefore had to be included in the expression used for calculating the level densities, which was consequently taken to be of the form 15)

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where U is the excitation energy, J the angular momentum, t the thermodynamic temperature and a the spin-cut-off parameter. The level density parameter a was taken as t6) A/10.7, where A is the mass number of the nucleus. Furthermore, the effects of pairing of protons and of neutrons in the nucleus were also taken into account. This was performed in the way described by Vandenbosch et al. 17) with the pairing energy ~ taken from ref. 18) as 1.0 MeV. In the calculations, the effective moment-of-inertia J is then taken as a free parameter of which the value (expressed as a fraction of the rigid-body moment of inertia J R ) is varied to obtain the best agreement with the experimental results. We have shown 29) that this method of analysis yields much more realistic values o f J / J R than the method of Bishop et al. in which the total excitation energy of a nucleus is not separated into that associated with thermal motion and that associated with rotation, and in which the simpler level density 20,22)

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can therefore be used. Furthermore, it also constitutes a great improvement on the method of analysis used in the only two previous investigations similar to the present one 7.9), in which the calculations were performed with the simplest form of the level density in which the spin-cut-off parameter a is taken to be a constant; its value is adjusted to yield the best fit to the experimental results. The calculations have been performed both for dipole and for quadrupole gamma de-excitation of the final nucleus to the ground-state band. The arbitrary cut-off point o f this gamma cascade was chosen at an excitation energy of 2 MeV. Then, if the nth gamma transition is the last transition leading to an excitation energy Un above the 2 MeV cut-off level, the probability that the (n + 1)th gamma transition will populate one of the levels in the ground-state band has been taken as ( 2 - U n + ~ ) / ( U , - U , + ~ ) , and the probability that one more gamma ray is emitted before the "deciding" gammaray as (Un-2)/(U n- U,+I). Essentially this is still the same procedure as that of Bishop :t .al. in which, however, the number of gamma rays emitted before the deciding gamma ray does not vary smoothly with the initial excitation energy of the nucleus. Finally, it has been assumed that the deciding transition will populate with equal probabilities 9) all the members of the ground-state band which can be reached according to the appropriate triangular condition. The transmission coefficients of the alpha particles were calculated with Auerbach's ABACUS-2 optical-model programme 22) for a nuclear potential of Woods-Saxon

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Fig. 3. Comparison between experimental results and statistical-model calculations for dipole deexcitation o f the final nucleus. The open triangles, circles and squares are experimental points for the ratios a(4, 2)/a(2, 0), a(6, 4)/cr(4, 2) and or(8, 6)/~r(4, 2), respectively. In each case, the solid and dashed lines connect calculated values corresponding to the upper and the lower sets o f experimental points, respectively.

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606

S. J. MILLS AND W. L. RAUTENBACH

form 23) and a Coulomb potential resulting from a sphere with uniform charge distribution. The optical-model parameters were obtained by interpolating between the values of Huizenga and Igo 24). The neutron transmission coefficients were calculated for the diffuse-surface surface-absorption optica!-model potential of Bjorklund and Fernbach 25) using their parameters for a neutron energy of 4.1 MeV for all neutron energies. 5. Results of the calculations and discussion The results obtained in the calculations are shown in fig. 3 for dipole de-excitation and in fig. 4 for quadrupole de-excitation of the final nucleus. By inspection of these plots, estimates could in each case be made of the value of J / J R giving the best overall agreement with the experimental results. These "best values" of J / J R are listed in table 3. TABLE 3

Deduced best values of ,,C/JR Residual nucleus a54Gd l°4Er l~sW xs°W 18~W 19°Pt

Best value of "f/JR dipole de-excitation 0.60-0.90 0.50-0.65 0.30M).36 0.50-0,65 0.38-0.46 0.22-0.25

quadrupole de-excitation 0.80-1.20 0.80-1.00 0.40-4).45 0.75-1.10 0.60-0.75 0.32-0.40

The results show that the best fit obtained for each individual cross-section ratio is, in general, approximately as good as those obtained for isomeric cross-section ratios in comparable cases. However, due to the requirement that the same J / J R value must fit both cross-section ratios of each target, the over-all fits are much poorer. The results therefore reveal a weakness of the statistical model in describing the reaction mechanism of compound nuclear reactions which is not as evident when considering only one (isomeric) cross-section ratio. F r o m figs. 3 and 4, it is also clear that, except in the case of 178W, better individual fits are obtained for dipole rather than for quadrupole de-excitation of the final nucleus. This result is in agreement with those previously obtained for isomeric crosssection ratios 17,a6), and supports the general trend of assuming only dipole transitions in the gamma-ray cascade in the final nucleus. Although the measurements extend over the entire rare-earth deformed region, no simple behaviour with mass number is observed in this region. Exceptionally low best values of ~¢/JR were, however, obtained for 19°pt, in agreement with the fact that this nucleus actually falls just outside this deformed region and therefore has a very small moment of inertia.

(~t,gny) REACTIONS

607

Furthermore, no regular increase in the slope of the various experimental curves is observed as the spin of the final state increases. It would certainly not have been possible to assign spin values to the various levels on this basis, as has been done by Newton 27) in the case of the lSlTa(~, 2n)lSaRe reaction. In fact, the curve for the 8 + ~ 6 + transition in l s 2 w even reaches a maximum and then drops back to nearly zero at 31.7 MeV. On this information alone, the particular transition would not even have been identified as a rotational transition produced in the (~, 2n) reaction at all. As has previously been pointed out ~1), a comparison of the results obtained for 17SW, l S ° w and IS2w yields very interesting results. F r o m the point of view of the statistical description of compound nuclear reactions, these results should differ very little, as is evident from the nearly identical theoretical predictions for the same value of J / J a (see figs. 3 and 4). However, the experimental results obtained are quite different. Taken in conjunction with the difficulties encountered in fitting the two crosssection ratios for each nucleus with the same value of J / J R , this shows that some o f the assumptions underlying the statistical description of the processes taking place do not apply. The weakest part of this description probably is the simple model adopted for the gamma cascade following the evaporation of the two neutrons. Purely statistical considerations alone should not be applied to this de-excitation cascade in the final nucleus, since the more detailed effects of nuclear structure may be of considerable importance at such low excitation energies. Therefore, in conclusion, it must be stressed that great care must be exercised in using information derived from best fits of the statistical theory of compound nuclear reactions to experimental results. More investigations of the present kind will have to be performed before any definite conclusion can be reached about the general applicability of this method of analysis. The authors wish to express their appreciation to Dr. B. Spoelstra, Mr. A. S. M. de Jesus, Mr. J. M. Kuyl and the cyclotron staff for their help in obtaining the experimental data. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)

I-L Morinaga and P. C. Gugelot, Nucl. Phys. 46 (1963) 210 J. R. Huizenga and R. Vandenboseh, Phys. Rev. 120 (1960) 1305 R. Vandenbosch and J. R. Huizenga, Phys. Rev. 120 (1960) 1313 V. F. Weisskopf, Phys. Rev. 52 (1937) 294 J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (John Wiley, New York, 1952) C. T. Bishop, J. R. Huizenga and J. P. Hummel, Phys. Rev. 135 (1964) B401 G. B. Hansen, B. Elbek, K. A. Hagemann and W. F. Hornyak, Nucl. Phys. 47 (1963) 529 B. J. Shepherd, C. F. Williamson and I. Halpern, Phys. Rev. Lett. 17 (1966) 806 S. J~igare, Nucl. Phys. A95 (1967) 481 S. J~igare, Nucl. Phys. A95 (1967) 491 S.J. Mills and W. L. Rautenbach, Phys. Lett. 27B (1968) 207 J. O. Newton, F. S. Stephens, R. M. Diamond, K. Kotajima and E. Mathias, Nucl. Phys. A95 (1967) 357

608 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)

S. J. MILLSAND W. L. RAUTENBACH N. L. Lark and H. Morinaga, Nucl. Phys. 63 (1965) 466 D. G. Sarantites and B. D. Pate, Nucl. Phys. A93 (1967) 545 J. M. Lang and K. J. Le Couteur, Proc. Phys. Soc. 67A (1954) 586 D. B. Beard and A. McLellan, Phys. Rev. 131 (1963) 2664 R. Vandenbosch, L. Haskin and J. C. Norman, Phys. Rev. 137 (1965) B1134 P. E. Nemirovsky and Y. V. Adamchuk, Nucl. Phys. 39 (1962) 551 S. J. Mills, D. Sc. thesis, Potchefstroom University for Christian Higher Education (1968) unpublished H. A. Bethe, Revs. Mod. Phys. 9 (1937) 84 C. Bloch, Phys. Rev. 93 (1954) 1094 E. H. Auerbach, Brookhaven National Laboratory, unpublished R. D. Woods and D. S. Saxon, Phys. Rev. 95 (1954) 577 J. R. Huizenga and G. Igo, Nucl. Phys. 29 (1962) 462 F. Bjorklund and S. Fernbach, Phys. Rev. 109 (1958) 1296 D. G. Sarantites, Nucl. Phys. A93 (1967) 576 J. O. Newton, Nucl. Phys. A108 (1968) 353