Algebraic solutions for q − sdl- and q − sdll′-boson systems in the transitional region

Abstract

Exact eigenenergies and the corresponding wave functions of the interacting boson system in transitional region are obtained by using the Bethe ansatz within an infinite-dimensional Lie algebra. In this paper, a transitional interacting boson model (IBM) Hamiltonian in both sdl and sdll′ versions based on affine SU(1,1) Lie algebra is proposed for transitional nuclei showing transitional behavior from spherical to gamma-unstable quantum shape phase transitions. Also, a deformed version of sdl- and sdll′-boson models is produced. In this method, complicated Hamiltonian can be easily determined via the exactly solvable method. Some observables such as the energy levels and energy differences are calculated and examined for Ba isotopes. The calculations confirm a good agreement for the energy spectra and quantum phase transitions.