Collective motion in finite fermi systems within Vlasov dynamics

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 such as (heavy) nuclei in regimes for which the finite size of the system is more important than the collisions between constituents. Such an approach requires solving the linearized Vlasov equation for finite systems; however, in this case, the problem of choosing appropriate boundary conditions for fluctuations in the phase-space density is nontrivial. Calculations of isoscalar response functions using different boundary conditions, corresponding to a 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 the experimental data. 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 similarity is attained because of the well-known close relation between classical trajectories and shell structure.