Algebraic solutions for two-level pairing model in IBM-2 and IVBM

Abstract

In this paper the affine $ SU(1,1)$ approach is applied to numerically solve two pairing problems. A dynamical symmetry limit of the two-fluid interacting boson model-2 (IBM-2) and of the interacting vector boson model (IVBM) defined through the chains $ U_{\pi}(6) \otimes U_{\nu}(6) \supset SO_{\pi}(5)\otimes SO_{\nu}(5) \supset SO_{\pi}(3) \otimes SO_{\nu}(3) \supset SO(3)$ and $ U(6) \supset U_{\pi}(3) \otimes U_{\nu}(3) \supset SO_{\pi}(3) \otimes SO_{\nu}(3) \supset SO(3)$ are introduced, respectively. The quantum phase transition between spherical and $ \gamma$ -soft shapes in medium-mass nuclei is analyzed using $ U(5) \leftrightarrow SO(6)$ transitional nuclei in IBM-2 and one case $ U_{\pi}(3) \otimes U_{\nu}(3) \leftrightarrow SO(6)$ transitional nuclei in IVBM found by using an infinite dimensional algebraic method based on affine $ SU(1,1)$ Lie algebra. The calculated energy spectra, energy ratio and energy staggering of Mo isotopes are compared with experimental results. The interplay between phase transitions and configuration mixing of intruder excitations between spherical vibrations and the $ \gamma$ -soft shapes in Mo isotopes is succinctly addressed and displays fingerprints of the transitional dynamical symmetry E(5).