Microscopic version of the Bohr-Mottelson model and its application

Abstract

The shell-model coupling scheme of the proton-neutron symplectic model (PNSM), defined by the following dynamical symmetry chain $Sp(12,R)\supset SU(1,1)\otimes SO(6)\supset U(1)\otimes S{U}_{pn}(3)\otimes SO(2)\supset SO(3)$, is considered. It is shown that it corresponds to a microscopic version of the Bohr-Mottelson collective model which captures the original relationships between its exactly solvable submodel limits. This variant of the PNSM provides an interesting and relevant shell-model symplectic-based framework for exploring the nuclear collective dynamics. Some simple applications of the present theory to different nuclei with various collective properties are given.

Comments: 11 pages, 2 figures, to appear in the Proceedings of the international workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA21), Sofia, Bulgaria, 16-18 September 2021, ed. N. Minkov