Generalized Holstein-Primakoff images of fermion operators

Abstract

The generalized Holstein-Primakoff (GHP) boson expansion is used to derive the images of single-fermion creation and annihilation operators in terms of collective bosons and ideal fermions for the case of well-deformed nuclei. The boson-fermion image of the quadrupole operator is then obtained, and is found to include a pure boson term, a pure fermion term, a boson-fermion exchange term and a further exchange term that mixes bosons with two quasifermions. We apply this method to a single- j model and show that in the deformed limit, the GHP expansion for the quadrupole operator gives a more appropriate description of quasiparticle energy systematics than does the corresponding operator obtained from a generalized seniority mapping. Finally, we consider the term that mixes bosons and quasifermion pairs within the context of the single- j model and show that it has precisely the form proposed phenomenologically in an extension of the IBM to high-spin states.