Exactly solvable model in quadrupole-octupole coupled states

Abstract

Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear structure phenomenon. For example, several transitions of the electric dipole and quadrupole (E1 and E2) values are indicative of QOC states. Various collective models as three-level and four-level pairing models were employed in order to account for the observed properties of the QOC states. We suggest a simultaneous description of low-lying collective positive and negative-parity states to use the spdf and sdf interacting boson model to reproduce the general characteristics of the QOC states. Also, quantum phase transitions are investigated based on dual algebraic structures for the sd, sdf and spdf-IBM. The low lying positive and negative parity states and the QOC properties of the stable even–even Cd isotopes are calculated in solvable extended transitional Hamiltonian of the IBM-spdf and IBM-sdf models based on the affine SU(1,1)ˆ Lie algebra. Some observables such as energy levels, transition rates, expectation value of boson number operators, energy differences and staggering pattern are calculated and examined for Cd isotopes. The IBM calculations indicate a nuclear structure of the electric E1, E2 and E3 strength and energy spectra in the low-lying, thus confirming the experimental results for transition region. The calculations confirm a good agreement for the energy spectra, quantum phase transitions and fragmentation of the E1, E2 and E3 strengths.