Quadrupole moments in the cadmium isotopes

Volume 61B, number 3

PHYSICS LETTERS

29 March 1976

QUADRUPOLE MOMENTS IN THE CADMIUM ISOTOPES M.T. ESAT, D.C. KEAN, R.H. SPEAR and R.A.I. BELL Department of Nuclear Physics, The Australian National University, Canberra, Australia

Received 30 January 1976 Contrary to theoretical predictions and previous experimental results, a new systematic study of the static quadrupole moments Q2÷ in the even-masscadmium isotopes using the re-orientation effect shows no evidence of significant variation in Q2+ with mass number. For ll6Cd, B(E2:0 +-~ 2+) is found to be 20% lower than the previously adopted value. The variation with mass number of the static quadrupole moments Q2 ÷ of the lowest 2 + states in the cadmium isotopes has recently aroused considerable interest due to both conflicting experimental evidence [1-3] and difficulties of theoretical interpretation [2-5]. Fig. 1 shows results extracted from a data survey by Christy and Hausser [1 ], and some more recent data reported for 106Cd and l°SCd by Hall et al. [3]. Apart from the obvious conflicts for 106Cd and 108Cd, the value for ll6Cd is surprisingly large in magnitude compared to the now generally accepted value of - 0 . 4 eb for the exhaustively studied neighbouring isotope 114Cd (the values for Q2 ÷ considered herein all assume [6, 7] that interference from higher 2 + states in Coulomb excitation of the cadmium isotopes is constructive). Also shown in fig. 1 are the results of a particle-vibration coupling calculation by Sips [4] (which has been extensively criticized by Broglia et al. [8]) and a boson-expansion calculation by Sorensen [5]. These two calculations disagree strongly with each other, and because of the confused experimental situation it is not possible to decide which is in better agreement with data. In the present work we have endeavoured to determine the variation of Q2 ÷ with mass number by applying a common technique to all the even cadmium isotopes. The only previous attempt to do this was made by Steadman et al. [2], who obtained a variation with mass similar to that shown for ref. [ 1] in fig. 1. Coulomb excitation probabilities for 4He and 160 projectiles were determined for 106,110,112,114,116Cd by direct measurements of the elastic and inelastic yields observed in an annular surface barrier detector. Typical energy resolutions of 24 keV and 105 keV were ob242

tained for 4He and 160 projectiles, respectively. In order to minimize the low-energy tail on the elastic peaks, detectors [9] with a high collection field were used, and the beam collimator was made sufficiently large ( ~ 4.5 mm dia) that little beam was intercepted by it, so reducing the effects of slit scattering. The resuiting uncertainty in mean scattering angle is negligible at the extreme backward angles used. Examples of spectra obtained are shown in fig. 2. The targets consisted of cadmium chloride evaporated onto a thin carbon backing; isotopic enrichments, in order of increasing mass number, were 82, 97, 97, 98, and 94%. The ratio of inelastic peak height to background in the 4He data (which largely determines the B(E2) values) ranged from 50 to 350, corresponding to an order of magnitude improvement over that achieved in previous investigations [10, 11 ] ; for 160 projectiles the ratio ranged from 10 to 30, which is similar to that obtained previously. The relative numbers of counts in the overlapping elastic and inelastic peaks in the 160 data were extracted using two different procedures. In one, an elastic lineshape obtained from the scattering of 160 on an enriched target of 118Sn (which has a high first excited state and so gives a clean low-energy tall) was used to unfold the elastic and inelastic peaks, only the peak positions and heights being allowed to vary in the fitting procedure. In the alternative unfolding procedure, the peaks were fitted by an analytic function representing a skewed gaussian with exponential tail, the width and tail parameters being free to vary in the fitting procedure. This method allows for variations in the peak shape from one run to another due to variations in target and beam quality, and the fits obtained were

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Fig. 1. Experimental results and theoretical predictions for the variation of the quadrupole moment of the first 2+ state across the cadmium isotopes. For the present data, the statistical errors are approximately half the total errors shown. much better than with the standard 118Sn lineshapes. However the two different unfolding procedures gave the same inelastic/elastic ratio to within 0.5%. As an additional check, spectra obtained at the same bombarding energy but with peak-to-valley ratios differing by a factor of two, were analysed and found to give the same inelastic/elastic ratio within the statistical error (~- 0.8%). Further support for the reliability of the unfolding procedure is provided by the fact that the results were found to be consistent over a range of bombarding energies corresponding to considerable changes in the inelastic/elastic ratio. It is concluded that systematic errors in the analysis of the 160 spectra are less than 0.8%. The analysis o f the 4He spectra was carried out both by lineshape fitting and linear background subtraction, the consistency of the results indicating that errors in the analysis were less than 0.5%. The effect o f uncertainties in the isotopic composition of the targets is greatest for the 116Cd + 160 data, where the l l 2 c d elastic peak must be subtracted from the spectrum in the region of the 116Cd inelastic peak; in this case an uncertainty of 0.2% in the ll6Cd excitation probability is introduced through the isotopic analysis error quoted by the suppliers. The intensities of other elastic peaks in the spectra indicated that

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29 March 1975

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Fig. 2. Spectra of 8.5 MeV 4He and 44 MeV 1 6 0 ions scattered from ll6Cd for 01ab = 171.6 ° and 174.6 °, respectively. Contributions from other isotopes have been subtracted from the data. The lines through the data points show least-squares fits to the spectra. the isotopic composition of the targets is in satisfactory agreement with the supplier's assay so that possible effects of isotopic fractionation during target manufacture have been ignored. Examination of the 4He spectra between 0.8 and 13.5 MeV bombarding energy showed that within twice the statistical error of the background there was no contamination of the targets by elements with mass number between 70 and 127. There is no indication in our data of Coulomb-nuclear interference below 10 MeV for 4He projectiles or below 44 MeV for 160 projectiles. The beam energy was calibrated to an accuracy o f 0.5 X 10 3 using ThC c~particle sources and the D(160, n)17F reaction. Details regarding experimental procedures and methods of analysis will be presented in a forthcoming publication, along with results for 108Cd, which could not be studied in the present work due to temporary non-availability of suitably enriched target material. 243

Volume 61B, number 3

PHYSICS LETTERS

29 March 1976

Table 1 B(E2; 0 +-~ 2+), Q2÷ and normalized x 2 values obtained from the present experiment. ×2 is calculated using statistical errors only. n is the number of data points used in the fit. Isotope

E2+(MeV)

B(E2; 0 ÷ ~ 2+) (e2b 2)

Q2+(eb)

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n

l°6Cd

0.633 0.658 0.617 0.559 0.513

0.384 0.427 0.484 0.528 0.532

-0.32 -0.36 -0.42 -0.38 -0.42

1.7 1.5 0.5 0.7 1.7

11 11 13 11 11

n°Cd

ll2cd ll4cd ll6Cd

-+0.004 +- 0.004 +- 0.004 +-0.004 -+0.004

The B ( E 2 : 0 +-+ 2 +) and Q2 ÷ values deduced from the 4He and 160 data using the W]nther-de Boer Coulomb excitation code are given in table t. The quoted errors arise from the quadratic combination o f the errors due to beam energy and target thickness uncertainties and statistical and systematic errors in intensity extraction. The E2 matrix elements for higher levels are required in the analysis and were obtained largely from ref. [12]. In table t only solutions corresponding to constructive interference from all higher 2 + states are included; for destructive interference the B(E2) values are virtually unchanged, but the Q2 ÷ values are reduced in magnitude by about 0.2 eb. Small ( ~ 1%) corrections to the experimental excitation probabilities have been applied for virtual excitation o f the giant dipole resonance, quantum mechanical effects, atomic screening and vacuum polarization [ 13]. In the present experiment only the giant dipole resonance correction significantly effects Q2 ÷, reducing IQ2+I by about 0.05 eb. Our results for ll4Cd are in encouraging agreement with well-established values [1 ]. This suggests that, in addition to giving reliable relative values for quadrupole moments and B(E2)'s of the cadmium isotopes, our results are also accurate in absolute magnitude. For 106Cd our value for Q2 ÷ is in fair agreement with Hall et al. [3] and in disagreement with refs. [2, 14]. For 116Cd tile previously adopted values [15] for B(E2; 0 + ~ 2 +) and Q2 ÷ are 0.65-+0.04 e2b 2 and -0.88-+ 0.25 eb, respectively. The 20% disagreement in the B ( E 2 ) value is surprising; however our relative B(E2)'s are similar to those of Milner et al. [12] for all isotopes studied. Our value for l l 6 C d is also in good agreement with a preliminary result, B(E2) 0.52 e2b 2, o f Werdecker et al. [16]. It is apparent from fig. 1 that our quadrupole mo-

244

+- 0.08 • 0.08 +-0.08 +-0.08 +- 0.08

ment values are in poor agreement with the theoretical predictions of Sips [4] and Sorensen [5]. The lack o f any significant variation in the quadrupole moments with mass number supports the basic postulate o f the particle-vibration coupling model of Alaga [ 17], that the effects o f neutron shell structure are small and the neutrons can be treated as a collective core. A re-calculation of Q2 ÷ for all the cadmium isotopes using the Alaga model therefore appears desirable.

References [1] A. Christy and O. Hausser, Nucl. Data Tables 11 (1972) 281. [2] S.G. Steadman et al., Nucl. Phys. A155 (1970) 1. [3] I. Hal, M.F. Nolan, D.J. Thomas and M.J. Throop, J. of Phys. A7 (1974) 50. [4] L. Sips, Phys. Lett. 36B (1971) 193. [5] B. Sorensen, Nucl. Phys. A217 (1973) 505. [6] L. Hasselgren et al., Uppsala University Institute of Physics Report UUIP-897 (1975) (unpublished). [7] R.D. Larsen et al., Nucl. Phys. A195 (1972) 119. [8] R.A. Broglia, R. Liotta and V. Paar, Phys. Lett. 38B (1972) 480. [9] Supplied by ORTEC Inc. [10] J.X. Saladin, J.E. Glenn and R.J. Pryor, Phys. Rev. 186 (1969) 1241. [11] Z. Berant et al., Phys. Rev. Lett. 27 (1971) 110. [12] W.T. Milner et al., Nucl. Phys. A129 (1969) 687. [13] O. Hausser, in Nuclear spectroscopy and reactions, Part C., ed. J. Cerny (Academic Press, New York, 1974) p. 55. [14] A.M. Kleinfeld et al., Nucl. Phys. A158 (1970) 81. [15] G.H. Carlson, W.L. Talbert and S. Ramon, Nucl. Data Sheets 14 (1975) 247. [16] D. Werdecker, A.M. Kleinfeld and J.S. Greenberg, J. Phys. Soc. Japan 34 Supplement (1973) 195, and University of K61n Annual Report 1972/73 (unpublished). [17] C. Alaga, F. Krmpotic and V. Lopac, Phys. Lett. 24B (1967) 537.