Collective motion in finite Fermi systems within Vlasov dynamics

TL;DR

This paper reviews a semiclassical Vlasov equation approach to study isoscalar vibrations in finite nuclei, demonstrating its effectiveness and comparing boundary conditions, with results aligning well with quantum calculations despite neglecting shell effects.

Contribution

It introduces a semiclassical Vlasov-based method for analyzing finite Fermi systems' response, emphasizing boundary condition choices and their impact on agreement with experimental data.

Findings

Moving-surface boundary conditions improve experimental agreement.

Semiclassical strength functions closely match quantum results.

The approach effectively captures finite size effects without shell corrections.

Abstract

A semiclassical theory of linear response in finite Fermi systems, based on the Vlasov equation, and its applications to the study of isoscalar vibrations in heavy nuclei are reviewed. It is argued that the Vlasov equation can be used to study the response of small quantum systems like (heavy) nuclei in regimes for which the finite size of the system is more important than the collisions between constituents. This requires solving the linearized Vlasov equation for finite systems, however, in this case the problem of choosing appropriate boundary conditions for the fluctuations of the phase-space-density is non-trivial. Calculations of the isoscalar response functions performed by using different boundary conditions, corresponding to fixed and moving nuclear surface, are compared for different multipoles and it is found that, in a sharp-surface model, the moving-surface boundary conditions give better agreement with experiment. The semiclassical strength functions given by this theory are strikingly similar to the results of analogous quantum calculations, in spite of the fact that shell effects are not included in the theory, this happens because of a well known close relation between classical trajectories and shell structure.