Exact boson mapping of the nuclear pairing Hamiltonian

Abstract

An exact boson mapping of the deformed mean-field plus equal strength pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The mapping occurs at the level of the Richardson–Gaudin equations. The image of the mapping results is a Bose–Hubbard model with level-dependent hopping. Although the resultant Bose–Hubbard Hamiltonian is non-Hermitian, a part of spectrum of the Bose–Hubbard Hamiltonian with U/t = 1 determined by the corresponding Richardson–Gaudin (Bethe ansatz) equations corresponds exactly to the whole spectrum of the pairing Hamiltonian.