Fluid-dynamical description of nuclear collective excitations

Fluid-dynamic models are derived in the framework of the time-dependent Hartree--Fock theory. The generalized scaling (GS) and the hydrodynamic (HD) models are discussed in detail and their applicability to nuclear giant resonances is explicitly investigated. The response function of the system (dynamic polarizability) and its connections to sum rules are analyzed in the framework of the fluid--dynamic approach. It is shown that the GS model correctly reproduces the high-frequency limit of the response function, while the HD model is more suited to investigate its static limit. In terms of sum rules, this means that the two models are expected to reproduce the cubic energy-weighted and inverse energy-weighted sum rules, respectively. Arguments based on sum rules and on the form of the boundary conditions suggest that the HD model provides a useful tool to investigate isoscalar compression excitations and, in general, isovector modes, while it dramatically fails in the description of divergency free motions, where the GS model results are much more successful. The role of surface effects on the nuclear motion is also discussed. It is shown that the effect of the surface symmetry energy term on isovector excitations can be taken into account by means of a suitable choice of the boundary conditions