Derivation of a fluid-dynamical lagrangian and electric giant resonances

Abstract

Starting from the TDHF equations and a schematic interaction of the Skyrme type we have derived an approach to nuclear vibrations in which only macroscopic densities and velocity fields appear. The specific role of the momentum-dependent terms which closely imitate the usual charge exchange forces is discussed. It is shown how a hamiltonian density that includes these exchange effects can be constructed. The method presented is applied to the description of nuclear electric monopole and dipole vibrations. The role of surface effects in determining the eigenfrequencies is emphasized. It is shown how an effective dipole mass introduced previously phenomenologically in the framework of the dynamical liquid droplet model comes out naturally from our approach. The expressions giving the collective energies are simple enough to relate the final results to the various parameters characterizing the effective interaction. The constraints that the present experimental information put on the effective interaction are discussed. Finally comparison is made of our results in the limit of a large system with the ones obtained in the framework of the Landau theory.