Diffuse approximation to the kinetic theory in a Fermi system

TL;DR

This paper introduces a diffuse approach to kinetic theory in Fermi systems, evaluating diffusion and drift coefficients considering interparticle collisions, and applies it to nuclear particle-hole excitations, showing results consistent with Fermi-liquid theory.

Contribution

It develops a diffuse approximation method for relaxation processes in Fermi systems, incorporating interparticle collisions and applying it to nuclear excitations with numerical validation.

Findings

Diffusion coefficient peaks at Fermi momentum $p_{F}$.

Drift coefficient is negative and minimized near $p_{F}$.

Relaxation time in a nucleus is approximately $8.3 imes 10^{-23}$ seconds.

Abstract

We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the distorted Fermi surface. Using the finite range interaction, we show that the momentum dependence of the diffuse coefficient $D_{p}(p)$ has a maximum at Fermi momentum $p=p_{F}$ whereas the drift coefficient $K_{p}(p)$ is negative and reaches a minimum at $p\approx p_{F}$. For a cold Fermi system the diffusion coefficient takes the non-zero value which is caused by the relaxation on the distorted Fermi-surface at temperature $T=0$. The numerical solution of the diffusion equation was performed for the particle-hole excitation in a nucleus with $A=16$. The evaluated relaxation time $\tau_{r}\approx 8.3\cdot 10^{-23}\mathrm{s}$ is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.