The generator-coordinate-method with conjugate parameters and the unification of microscopic theories for large amplitude collective motion

Abstract

A dynamic theory of large amplitude collective motion of many particle systems is presented which is relevant, for example, to nuclear fission. The theory is microscopic and makes use of a collective path, i.e. a suitably constructed set of distorted nonequilibrium Slater determinants. The approach is a generalization of the generator coordinate method (GCM) and improves its dynamic aspects by extending it to a pair of conjugate generator parameters q and p (DGCM). The problems connected with redundancy and superfluous degrees of freedom are solved by prediagonalizing the local oscillations about each point of the dynamic collective basis | q, p ∼. For adiabatic large amplitude collective motion a Schrödinger equation is derived which appears to be nearly identical to the one obtained by a consistent quantization of semiclassical approaches as e.g. the adiabatic time dependent Hartree-Fock theory (ATDHF). In turn a collective path constructed by ATDHF proves to be particularly suited for being used in the present DGCM formalism. Altogether the formalism unifies two classes of microscopic approaches to collective motion, viz. the quantum mechanical GCM and the classical theories like cranking and ATDHF.