Relation between the time-dependent Hartree-Fock method and boson expansion methods in a two-level model

Abstract

This paper continues the study of the two-level model utilized in the preceding paper. First the boson expansion method is reformulated from a viewpoint which emphasizes its relationship to the phenomenological description of vibrations. In this version a general method for reaching the limit of large particle numbers is described and carried out, resulting in a complete theory for finding the asymptotic form (semiclassical limit) of any collective parameter. An exact formulation of the theory in terms of single-particle coefficients of fractional parentage is then described. The semiclassical limit of this theory is recognized as a version of a generalized self-consistent cranking model or time dependent Hartree-Fock theory. The two semiclassical limits are shown to be identical. The equivalence of time-dependent Hartree-Fock theory to the asymptotic form of more complete theories of collective motion is argued to be general.