Microscopic version of the Bohr-Mottelson model and its application

The shell-model coupling scheme of the proton-neutron symplectic model (PNSM), defined by the following dynamical symmetry chain $Sp(12,R) \supset SU(1,1) \otimes SO(6) \supset U(1) \otimes SU_{pn}(3) \otimes SO(2) \supset SO(3)$, 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.