Kinetic equation for collective modes of a Fermi system with free surface

A semiclassical approach for studying collective modes of finite Fermi systems is proposed on the basis of the Landau-Vlasov kinetic equation. In the theory the effective surface is explicitly used. The surface-motion equation is deduced. The problem is reduced to solving a linearized kinetic equation with mirror-reflection conditions at the free-moving effective surface. An equation for eigenfrequencies is obtained when the collision integral and the residual quasiparticle interaction in the bulk of the system are neglected. The eigenfrequencies for oscillations with multipolarities L>0 are complex. A simple analytical solution is found for monopole eigenfrequencies. The properties of the first monopole mode agree with the ones derived in the corresponding RPA approximation. (orig.)