Microscopic Transport Theory of Nuclear Processes

TL;DR

This paper develops a microscopic theoretical framework for nuclear fission decay, combining the Hartree-Fock-Bogoliubov method and Generator Coordinate Method, to explicitly treat slow shape evolution and intrinsic excitations.

Contribution

It introduces a novel microscopic approach that models nuclear shape dynamics explicitly using a reduced density matrix and statistical approximations for intrinsic excitations.

Findings

Derived a rigorous equation of motion for the nuclear shape density matrix.

Simplified the equation using the Markov approximation.

Established a method to determine local temperature based on excitation energy.

Abstract

We formulate a microscopic theory of the decay of a compound nucleus through fission which generalizes earlier microscopic approaches of fission dynamics performed in the framework of the adiabatic hypothesis. It is based on the constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate Method, and requires an effective nucleon-nucleon interaction as the only input quantity. The basic assumption is that the slow evolution of the nuclear shape must be treated explicitely, whereas the rapidly time-dependent intrinsic excitations can be treated by statistical approximations. More precisely, we introduce a reference density which represents the slow evolution of the nuclear shape by a reduced density matrix and the state of intrinsic excitations by a canonical distribution at each given shape of the nucleus. The shape of the nuclear density distribution is described by parameters ("generator coordinates"), not by "superabundant" degrees of freedom introduced in addition to the complete set of nucleonic degrees of freedom. We first derive a rigorous equation of motion for the reference density and, subsequently, simplify this equation on the basis of the Markov approximation. The temperature which appears in the canonical distribution is determined by the requirement that, at each time t, the reference density should correctly reproduce the mean excitation energy at given values of the shape parameters. The resulting equation for the "local" temperature must be solved together with the equations of motion obtained for the reduced density matrix.