Bosonic Treatment of Pairing Correlations in a Solvable Many-Level Model

摘要

We discuss two extensions of RPA based on a boson formalism and report on some applications within an exactly solvable many-level pairing model. By making use of a Marumori-type mapping procedure, we preliminary define the boson image of the fermion operators of interest and, in particular, of the model Hamiltonian. This includes two and four-boson terms. We therefore construct renormalized RPA-type equations in correspondence with different expansions of the boson operators. The approximate calculations are compared with the exact ones and with those obtained within RPA and Self Consistent RPA. We find that it is possible to improve considerably upon RPA by still keeping the formalism simple enough to be applied in more realistic cases without a too serious computational effort.