Shell-model-based deformation analysis of light cadmium isotopes

Abstract

Large-scale shell-model calculations for the even-even Cadmium isotopes 98 Cd -108 Cd have been performed with the ANTOINE code in the π(2p 1/2 ; 1g 9/2 ) ν(2d 5/2 ; 3s 1/2 ; 2d 3/2 ; 1g 7/2 ; 1h 11/2 ) model space without further truncation. Known experimental energy levels and B(E2) values could be well reproduced. Taking these calculations as a starting ground we analyze the deformation parameters predicted for the Cd isotopes as a function of neutron number N and spin J using the methods of model independent invariants introduced by K. Kumar and D. Cline.

The neutron-rich edge of the nuclear landscape: Experiment and theory.

“…The calculation of β and γ requires knowledge of the expectation values of the second-and third-order invariants defined, respectively, byQ 2 =Q •Q and Q 3 = (Q ×Q) •Q (whereQ ×Q is the coupling ofQ with itself to a second-rank operator). These invariants were recently applied to describe the evolution of collectivity in cadmium isotopes [177]. However, it is not meaningful to assign effective values to β and γ without also studying their fluctuations, and this task requires to calculate all the moments up to the sixth.…”

Statistical theory of deformation distributions in nuclear spectra

“…The use of quadrupole invariants [13,14], which in turn can be related to lab-frame moments ofQ 20 (up to fifth order in deformation), allowed the extraction of effective intrinsic deformation parameters β, γ. Quadrupole invariants have been used in the context of the CI shell model for lighter nuclei; see Refs. [15,16] and references cited therein. Here we introduce a novel method to calculate the complete intrinsic-frame quadrupole distribution using a Landaulike expansion of its logarithm.…”

E2 collectivity in shell-model calculations for odd-mass nuclei near 132Sn

“…Details of the effective charges adopted and relevant experimental data are shown in Table 1. Literature choices for the effective proton charge for the In isotopes range between e p = 1.35 [13] to e p = 1.7 [14][15][16]. A value of e p = 1.34 has been chosen for the present work based on the known lifetime of the I π = 8 + , E x = 2130 keV isomer in 130 Cd.…”