EFFECTIVE OPERATOR-THEORY IN BOSON MAPPINGS

The convenience of a boson basis used in conjunction with a boson mapp ed hamiltonian may sometimes be complicated by the appearance of spuri ous states in the spectrum. Under ideal circumstances where either no truncation of the boson Fock space is introduced, or where truncation involves a set of completely decoupled collective degrees of freedom o nly, the identification and role of such spurious states are well unde rstood and analysed. However, for situations where truncation involves degrees of freedom which are not completely decoupled, no analogous s ystematic analysis has yet been given. A formalism which suggests itse lf for such an analysis, is effective operator theory. The energy-inde pendent effective interaction approach of Suzuki and Lee seems to be w ell suited for this purpose. We first extend this approach beyond inte ractions only, and construct the effective operator corresponding to a n arbitrary operator. We then show how the formalism is applied in the present context of identifying spurious states. In particular, we app ly the extended procedure to the generalized SO(5) model, to a single- j proton-neutron model, and also to the multi-j similarity-transformed Dyson mapping. We also compare the present approach to an alternative energy-independent effective-operator approach which is based on the use of a Majorana-like operator in conjunction with the SO(2n) Dyson b oson mapping. The present application is also linked to applications i n the derivation of effective shell-model interactions.