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