Relaxation of a single-particle excitation in a Fermi system within the diffusion approximation of kinetic theory

TL;DR

This paper investigates how single-particle excitations relax in a Fermi system using a diffusion approximation, introducing a method to distinguish different relaxation processes and analyzing their characteristic times.

Contribution

It proposes a new method to separate dissipative processes and introduces distinct relaxation times for excitation and core relaxation within kinetic theory.

Findings

Relaxation times differ from previous kinetic coefficient estimates.

Diffusion and drift coefficients significantly influence relaxation times.

A numerical approach to solving nonlinear diffusion equations was developed.

Abstract

The time evolution of the Wigner distribution function for a single-particle excitation in a Fermi system was studied within the framework of the diffusion approximation of kinetic theory by numerically solving a nonlinear diffusion equation with constant kinetic coefficients. A method was proposed to separate the dissipative processes into contributions from the relaxation of the single-particle excitation and from the relaxation of the nuclear core, with a distinct relaxation time introduced for each process. The influence of the diffusion and drift coefficients on the characteristic relaxation time scale was analyzed. It was found that the resulting relaxation times exhibit a discrepancy relative to the kinetic coefficient estimates known from previous studies.