Diffuse approximation to the kinetic theory in a Fermi system

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 Dp(p) has a maximum at Fermi momentum p = pF whereas the drift coefficient Kp(p) is negative and reaches a minimum at p ≈ pF. For a cold Fermi system the diffusion coefficient takes the nonzero 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 τr ≈ 8.3 ⋅ 10-23 s is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.