Boson expansion techniques, the Pauli principle, and the quasiparticle random phase approximation phase transition

Abstract

The onset of instabilities, in the standard proton-neutron quasiparticle random phase approximation (QRPA), is investigated by using different boson mappings and trial states belonging to a representation of coherent states. The model describes pairing and proton-neutron interactions. It is shown that an exact mapping of the Hamiltonian is needed to describe correctly the QRPA phase transition, i.e., that the algebra of all operators participant in the Hamiltonian should be preserved by the boson mapping. Spurious components of the wave functions, which appear if the Pauli principle is violated, are isolated by construction.