A theoretical study on the effective quadrupole deformations of 100−128Cd isotopic chain

Abstract

In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the [Formula: see text]Cd, [Formula: see text]Cd and [Formula: see text]Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of different energy levels indicates that there is a close relationship between ground and excited-state quantum phase transitions (ESQPTs).

Origin of regularity in different nuclei from the viewpoint of the effective quadrupole deformation and triaxiality

“…Equation ( 5) is obtained by the effect of the creation and annihilation operators on the U(5) limit eigenfunction [11,22,23]. To calculate the q , 2 we use the Wigner-Eckart theorem and the Clebsch-Gordan coefficients [22]:…”

“…Similarly with equations (5), ( 7) is obtained by the effect of the creation and annihilation operators on the SU(3) limit eigenfunction [11,22,23]. To know how to determine quantum numbers K, l and L, refer to [30][31][32][33].…”

“…Also, D. Cline et al studied this issue more widely in their articles [20,21]. Using the IBM, we calculated the effective quadrupole deformation of different levels (for the respective isotopes) in [22,23].…”