Complete set of states for microscopic nuclear collective models

Abstract

For several years the authors have been interested in determining complete sets of states for macroscopic nuclear collective models, such as the Bohr–Mottelson one (BM) and the interacting boson approximation (IBA), as well as in their use in nuclear structure calculations. In the present paper we obtain a complete set of states for microscopic nuclear collective models such as those of Vanagas and of Filippov and Smirnov. For calculations in these models, one requires a set of states for the A nucleon system, in appropriate coordinates which include the ones related with collective degrees of freedom. As is customary in nuclear physics, the complete set of states is derived more conveniently if one assumes an oscillator interaction between the nucleons. We obtain explicitly this set of states when A≫1, showing that it can be expressed in terms of wavefunctions whose dependence on the collective coordinates is similar to those appearing in the BM model and in the IBA. We briefly indicate how this set of states can be used in microscopic collective model calculations.