Microscopic approach to the interacting boson model

Abstract

A method is outlined for analyzing the interacting boson model microscopically in terms of S- and D-fermion pairs. We derive the number operator approximation (NOA) of Otsuka and Arima by considering functions that generate normalizations and matrix elements of states built of S-pairs. An extension of the formalism leads to a generalization of the NOA including both S and D. This approximation is suggested as a starting point for determining the collective SD subspace in a dynamical way. The simplified fermion problem that results from restriction of the hamiltonian to the SD subspace can be mapped onto a corresponding sd boson problem. Due to the finiteness of the fermion space, and the non-orthogonality of the collective SD basis, the boson hamiltonian obtained is non-hermitian.