Microscopic shell-model counterpart of the Bohr–Mottelson model

In the present paper we demonstrate that there exists a fully microscopic shell-model counterpart of Bohr-Mottelson model by embedding latter in theory atomic nucleus within framework recently proposed proton-neutron symplectic (PNSM). For this purpose, another coupling scheme PNSM is considered which basis states are classified algebraic structure $SU(1,1) \otimes SO(6)$. It shown configuration space contains six-dimensional subspace closely related to generalized quadrupole-monopole and its dynamics splits into radial orbital motions. The group $SO(6)$ acting space, contrast, e.g., popular IBM, an $SU(3)$ subgroup allows introduce counterparts exactly solvable limits parallel relationship original Wilets-Jean rotor models. Wilets-Jean-type approach, contrast collective formulation, governed intrinsic bandhead defines relevant Pauli allowed $SO(6)$, hence $SU(3)$, subrepresentations. recovered for case closed-shell nuclei, trivially reduced scalar or equivalent it irreducible representation.