Microscopic theory of dissipation for slowly time-dependent mean field potentials

We study the dissipation rate Q˙ in systems of nucleons bound by a slowly time-dependent mean-field potential and slightly interacting between themselves. Starting from the many-body linear response formula we evaluate an expression for Q˙ in terms of the pure shell-model quantities and the nucleon-nucleon collision rate Γ. The application of the classical sum rule leads then to an expression for Q˙ in terms of the classical-path integral with the weighting function including Γ. For vanishing Γ this expression reduces to the Koonin-Randrup Knudsen-gas formula. For simplified Skyrme interactions the classical approximation for the Γ itself is obtained. In leptodermous systems the classical-path expression for Q˙ decomposes into the wall formula and the multiple-reflection term owing to incomplete randomization of particle motion between consecutive encounters with the boundary. The mean-free path and temperature dependence of dissipation is analyzed for small-amplitude distortions of spherical cavities.