Exact boson mappings for nuclear neutron (proton) shell-model algebras having SU(3) subalgebras

Abstract

In this paper the commutation relations of the fermion pair operators of identical nucleons coupled to spin zero are given for the general nuclear major shell in LST coupling. The associated Lie algebras are the unitary symplectic algebras Sp(2 M). The corresponding multipole subalgebras are the unitary algebras U( M), which possess SU(3) subalgebras. Number conserving exact boson mappings of both the Dyson and hermitian form are given for the nuclear neutron (proton) s− d, p− f, s− d− g, and p− f− h shells, and their group theoretical structure is emphasized. The results are directly applicable in the case of the s− d shell, while in higher shells the experimentally plausible pseudo- SU(3) symmetry makes them applicable. The final purpose of this work is to provide a link between the shell model and the Interacting Boson Model (IBM) in the deformed limit. As already implied in the work of Draayer and Hecht, it is difficult to associate the boson model developed here with the conventional IBM model. The differences between the two approaches (due mainly to the effects of the Pauli principle) as well as their physical implications are extensively discussed.