Inelastic scattering of deuterons from strontium and yttrium

Nuclear Physics 39 (1962) 139--146; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by pbotoprint or microfilm without written permission from the publisher

INELASTIC SCATTERING OF DEUTERONS FROM STRONTIUM AND YTTRIUM E. W. H A M B U R G E R

Departamento de Ftsica, Faculdade de Filosofia, CMneias e Letras, Universidade de S~o Paulo, S. Paulo, Brasil Received 16 July 1962 Abstract: Targets of natural strontium and yttrium were bombarded with 15 MeV deuterons. Scattered particles were magnetically analysed and detected in nuclear emulsions. Angular distributions between 25 ° and 85 ° were obtained for the deuterons corresponding to the Sr 88 levels at 1.835 and 2.74 MeV. Other strontium levels were observed at 0.85 MeV (probably the 0.869 MeV level of SrS0, 1.114-0.02 MeV (probably the 1.080 MeV level of SrS6), 3.204-0.05 MeV, 3.61 +0.025 MeV, 4.024-0.025 MeV, 4.274-0.03 MeV. Yttrium exposures were made at 30 °, 60 ° and 85 °. The following levels of ya9 were observed: 1.510±0.010, 1.7424-0.010, 2.2274-0.010, 2.5334-0.015, 2.8864-0.015, 3,1354-0.020, 3.744-0.02, 4.024-0.03, 4.20±0.03, 4.344-0.03, 4.494-0.03 MeV and perhaps 4.794-0.04 MeV.

1. Introduction and Experimental Procedure Inelastic deuteron scattering has not been studied very often until recently. The present experiment is a continuation of the work of Cohen and Price 1) and aimed at gathering more information on the mechanism of the reactions and at obtaining data on the levels of Sr 88 and ya9. The irradiations were made at the University of Pittsburgh cyclotron. The scattering system and the data processing have been described previously 2, a). The incident energy was 15 MeV. The scattered particles passed through a magnetic analyser and were detected in nuclear emulsions. The emulsions were scanned at the Universidade de S~o Paulo. Exposures were made at twelve scattering angles between 25 ° and 85 ° with the strontium target and at three angles, 30 °, 60 ° and 85 °, with the yttrium target. The strontium target was prepared by evaporation onto a gold backing and transferred to the scattering chamber in vacuum 3). The thickness was estimated from the measured energy loss of the deuterons in the strontium layer and was ~ 2.6 mg/cm 2. The yttrium target was also prepared by evaporation t; it was self-supporting, with a thickness o f 0.47 mg/cm 2. Both targets had appreciable contaminations of oxygen, carbon and probably nitrogen, as can be seen from the elastic peaks due to these elements in the spectra o f figs. 1 and 2. All peaks in the strontium spectrum (fig. 1) show a low energy tail, due probably to non-uniformity of the target. The full width at half maximum of the peaks in the strontium spectrum is ~ 70 keV; in the yttrium t The author thanks Mr. G. Fodor for making the target. 139

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EXCITATION

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141

INELASTIC SCATTERING OF DEUTERONS

spectrum it is ~ 36 keV. The better resolution for the yttrium work is due to the better target, to the closing down o f the width of the object slit for the b e a m analysing magnet and to convenient orientation of the target plane *). The absolute cross sections were calculated from the target thicknesses and from the known efficiency of the magnetic analyser ~) and are estimated to be correct within + 40 9/0 for the strontium work and within + 30 ~ for the yttrium work. The errors given in the angular distribution figures and in table 2 refer only to the relative cross sections. The excitation energies were obtained from the calibration curve of the magnetic analyser 5), which could be checked with the positions of the elastic groups from the target contaminants and of the well known level at 1.835 MeV in Sr as. 2. Results

for Strontium

2.1. ELASTIC SCATTERING The experiment was designed to measure the inelastic scattering. At the larger angles, however, it was also possible to measure the intensity of the elastically scattered group. Fig. 3 shows the angular distribution obtained~ The results for gold agree well with the work of Cindro and Wall 6); no absolute cross sections were measured for gold, however. Strontium seems to show sharper structure than the elements in this mass region studied by Cindro and Wall. The errors at small angles are large because it became difficult to separate the strontium and gold peaks. Below 45 ° the density of tracks in 3

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142

E.W.

HAMBURGER

the emulsion was too high to permit counting. The ratio of the absolute cross section to the Rutherford cross section is approximately the same as found by Cindro and Wall for nearby elements. This is an indication that the absolute cross section scale is approximately correct. 2.2. I N E L A S T I C

SCATTERING

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GROUPS

Only two levels give rise to strong inelastic groups: the 1.835 MeV (2 +) and 2.74 MeV (3-) states of Sr ss. This is in agreement with previous (p, p') and (d, d') work (refs. 7) and 1), respectively) and confirms the idea 8) that inelastic scattering reactions excite collective states preferentially, since these two states presumably are respectively quadrupole and octupole vibrational states. It also affords another example where it is shown that the "anomalous" groups found in inelastic scattering at Q ~ - 2 . 5 MeV 7, 9) are due to excitation of 3- levels. I

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In Cohen and Rubin's (p, p') experiment 7) a strong group appeared at 2.57 MeV excitation. No such strong group was found in the present work. At a few angles there were indications of a weak group at 2.5 MeV excitation; if this group exists its intensity is ~0 of that of the 2.74 MeV group. Figs. 4 and 5 show the angular distributions for the two strong groups. The large anisotropies suggest a direct interaction mechanism. The general features of the distributions are the same as those found for Zr(d, d') by Cohen and Price 1): a

INELASTIC SCATTERING OF DEUTERONS

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large forward peak at 0 < 30 °, a secondary peak or hump at 0 ~ 60 ° and very small values at 0 ~, 80 °. The inelastic diffraction scattering model 1o) predicts that the angular distributions for the elastic scattering and for the excitation of the 3- state be in phase with each other (i.e. the peaks and valleys occurring at the same angles) but out of phase with the 2 + state. Inspection of figs. 3, 4 and 5 shows that not much can be said concerning the relative phase of the elastic group but that the forward peak for the 3- group occurs at ~ 32 °, where the 2 + group is already near a minimum. The data are consistent with the prediction of the model. I

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Fig. 5. A n g u l a r distribution for the Sr88(d, d') Sr 88. 2.74 M e V (3-) reaction. At the two largest angles the group was n o t identified; u p p e r limits o n its cross section are shown.

Cohen and Price 1) found a strong correlation between the cross section for exciting a given level by (d, d') scattering and the values of the Coulomb excitation parameter B(E2) for that level. From their systematics (cf. fig. 22 of ref. 1)) and the present results, one obtains the following estimate of B(E2) for the 1.835 MeV level: 0.04 x 10 -48 e 2 c m 4. The uncertainty in the (d, d') absolute cross section corresponds to an uncertainty of a factor ~ 3 in B(E2). On the other hand Ofer and Schwarzschild 1~) measured the mean lifetime of this level; from their results one deduces 12) B(E2) = (0.13±0.03)x 10-4% 2 cm 4. The agreement is satisfactory. 2.3. O T H E R I N E L A S T I C G R O U P S

Table 1 gives the excitation energies and estimated errors of the levels identified at three or more angles.

144

E. W. HAMBURGER

The groups at Ex ~ 0.85 and 1.11 MeV were identified only at angles larger than 60°; they probably correspond to the known states at 0.87 MeV in Sr 87 and at 1.08 MeV in Sr a6, respectively. I f this assignment is correct the cross sections for these groups are large, o f the same order of magnitude as for the Sr 8s 1.835 and 2.74 MeV TABLE 1 Energy levels identified in Sr(d, d') with estimated errors Isotope

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This work

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0.85 1.11 -/- 0.02 1.835 (calib.) 2.744-0.015 3.20-4-0.05 3.61 4-0.025 4.02+0.025 4.274-0.03

=) Errors estimated by t h e present author.

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INELASTIC SCATTERING OF DEUTERONS

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levels. For example, at 60 ° we have a 0 A 1 M e V ) = 0.4___0.2 mb/sr and at 85 ° tr(0.87 M e V ) = 0.2+_0.1 mb/sr. The group at 3.20 MeV was identified only at 60 °, 70 ° and perhaps at 40 °. Its cross section at 60 ° (assuming that it is a level of Sr aS) is 0.045+_0.011 mb/sr. Partial angular distributions for the other groups are shown in fig. 6. The cross sections were computed assuming the groups to be due to Sr 8s. The anisotropies seem to be quite large, of the order of a factor 2. The accuracy is poor because of the small peak to background ratio. 3. Results for Yttrium The spectrum at 60 ° is shown in fig. 2. Group no. 1, corresponding to the 1.52 MeV level of ya9, is covered by the oxygen elastic in the figure; it was, however, identified at 30 °. The group at 3.108 MeV excitation (group no. 6) is significantly broader than the experimental resolution. The 30 ° data suggest that it corresponds to a doublet of levels, ~ 25 keV apart. Between 4.45 and 4.7 MeV (i.e. between groups no. 11 and 12) there seem to be several unresolved and weakly excited states. Table 2 gives the observed level energies and cross sections, with the estimated uncertainties. At 85 ° the cross sections are small and only the strongest levels could be identified. The excitation energies of groups 1 to 6 agree, within the quoted errors, with previous (n, n'v) experiments 13, 14). The spectrum at 60 ° can be compared with the work of Cohen and Price 1), who used a poorer target. Cohen and Price found strong peaks at 1.41, 1.53 and 2.29 MeV which we did not see. Comparison with fig. 2 suggests that oxygen and carbon contaminations may have affected the older results. The excitation energies found in the present experiment are systematically lower than those of 1el. x) by ~ 50 keV. The TABLE 2 Results for the ys, (d, d') reaction Group no.

1 2 3 4 5 6 7 8 9 10 11 12

Energy levels (MeV) •

Ref. 13) 0.915+0.005 1.52 4-0.015 1.75 4-0.018 2.24 i 0 . 0 2 2 2.55 4-0.025 2.87 4-0.029 3.10 +0.031

a(30 o)

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a(85 o)

This work

(mb/sr)

(mb/sr)

(mb/sr)

1.5104-0.010 1.7424-0.010 2.2274-0.010 2.533:~0.015 2.886±0.015 3.135±0.020 *) 3.74 4-0.02 4.02 4-0.03 4.20 ±0.03 4.34 i 0 . 0 3 4.49 4-0.03 (4.79 4-0.04)

0.354-10 ~ 0.41 ± 1 0 ~ 0.48+ 8 ~ 0.664- 6 ~ 0.564- 7 ~ 0.25±12~ 0.184-15 ~ 0.16±15 ~ 0.23+12% 0.07-4-50 ~o 0.074- 50 ~

a) Broad group, probably corresponds to two levels.

0.294- 10 ~ 0.164- 9 ~o 0.294- 7~o 0.254- 8 ~ 0.11+14~o 0.104-15 0.114-14 ~ 0.15-1-12 ~o 0.03-4-50 ~o 0.05i40 ~

0.10±30 ~/o 0.07~30 % 0.06 4- 50 %

146

E. W. HAMBURGER

well known isomer level at 0.915 MeV is not observably excited, as already noted by Cohen and Price. Upper limits on its cross sections from the present work are: at 30 °, 0.14 mb/sr and at 60 °, 0.10 mb/sr. The (p, p') reaction on yttrium 7) excites strongly levels of ya9 at 2.22, 2.52, 2.87 and 3.86 MeV. Except for the last one, these are probably the same levels strongly excited in the present work. The spins and parities of the yS9 levels studied in this experiment are not known. It is difficult to deduce anything about the structure of the various levels from a(d, d') measurement without angular distributions. We merely note that the groups at 2.533, 2.886 and 3.13 5 MeV seem to have similar angular distributions (the ratio of the cross sections at 30 ° and at 60 ° is the same for the three groups) and are at the correct energy to correspond to the "anomalous" peak of Cohen. These levels may therefore be analogous to the 3 - state at 2.74 MeV in Sr s8 and correspond to a collective octupole vibration of the nucleus. The author gratefully acknowledges the important help of Professor B.L. Cohen in this experiment, the hospitality of the Radiation Laboratory of the University of Pittsburgh where the plates were exposed and the support o f Professor J. Goldemberg. The plates were scanned efficiently by A. M. Motta, D. O. Borges and E. Zacharias. The work was partially supported by the Conselho Nacional de Pesquisas (Brasil).

References

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

B. L. Cohen and R. E. Price, Phys. Rev. 123 (1961) 283 R. S. Bender et aL, Rev. Sci. Instr. 23 (1952) 542 E. W. Hamburger, Ph.D. Thesis, University of Pittsburgh (1959) B. L. Cohen, Rev. Sci. Instr. 30 (1959) 415 B. L. Cohen, private communication N. Cindro and N. S. Wall, Phys. Rev. 119 (1960) 1340 B. L. Cohen and A. G. Rubin, Phys. Rev. 111 (1958) 1568 B. L. Cohen, Phys. Rev. 116 (1959) 426 B. L. Cohen, Phys. Rev. 105 (1957) 1549; B. L. Cohen and S. Mosko, Phys. Rev. 106 (1957) 995 J. S. Blair, Phys. Rev. 115 (1959) 928 S. Ofer and A. Schwarzschild, Phys. Rev. Lett. 3 (1959) 384 Alder Bohr, Huus, Mottelson and Winther, Rev. Mod. Phys. 28 (1956) 432, eq. IV. 3. Trehan, Shafroth and Van Patter, Bull. Am. Phys. Soc. 7 (1962) 82, Y6 Nuclear Data Sheets, National Research Council, Washington 25, D. C.