On the microscopic shell-model version of the Bohr-Mottelson collective model

Abstract

The recently proposed microscopic shell-model version of the Bohr-Mottelson (BM) collective model is considered in more detail in the coordinate representation. The latter possesses a clear and transparent physical meaning, which reveals several features of the new version of the collective model missed in the previous formulation. The relationship to the original BM model is considered, along with the relationships between the different limiting submodels of the microscopic version of the BM model, which closely resemble the relationships of the original Wilets-Jean and rotor models. The kinematically correct many-particle wave functions of the microscopic version of the BM model, conserving the experimentally observed integrals of motion, are shown to consist of collective irrotational-flow and intrinsic components in accordance with the original BM unified model. The general BM Hamiltonian is obtained as a contraction limit of the microscopic many-particle nuclear Hamiltonian, or, alternatively, by restricting the latter to the scalar irreducible collective space.