Exact boson mappings for the proton-neutron nuclear p-shell with the symmetry Sp(12)⊃U(6)

Abstract

The closed set of commutation relations obeyed by the fermion pair and multipole operators for a major shell of protons and neutrons in LST coupling is found. The case of a p-shell of protons and neutrons coupled to S=0 is studied in detail. The associated Lie algebra is the compact unitary symplectic algebra Sp(12). The corresponding multipole subalgebra is the unitary algebra U(6), which has an SU(3)⊗ U(1)⊗SU T (2) subalgebra. Number conserving exact boson mappings of both the Dyson and hermitian form are constructed and their group theoretical structure is emphasized. The method is directly generalizable to the case of an sd-shell of protons and neutrons and can lead to a link between the isospin invariant versions of the interacting boson model (IBM-3 and IBM-4) and the shell model. In addition it provides a bosonized version of the k-active limit of the isospin invariant form of the fermion dynamical symmetry model (FDSM).