Dynamics of nuclear fluid. IV. Some spin and isospin properties in the hydrodynamical model

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Abstract
In the hydrodynamical model, the nuclear spin and isospin symmetry energies and the speeds of spin sound and isospin sound are pertinent to the determination of the static and dynamic properties of finite nuclei. We examine these quantities with a generalized Skyrme interaction. From the explicit expressions we obtain for these quantities, we find an interesting algebraic relation connecting the symmetry energies and likewise the sound speeds. Relevant collective vibrational energies of various types and different multipolarities are evaluated with the known sets of Skyrme interactions, in order to provide information for future amendments or selections among the sets of interactions and for the confrontation of the hydrodynamical model with experiment. We further investigate the dispersion of sound waves due to the range of the nuclear interaction. In particular, the "plasma oscillation" arising from the long-range Coulomb interaction is found to lead to a simple modification of the energies of the isoscalar and isovector collective vibrational states. When applied to the nuclear giant dipole and monopole resonances, the inclusion of the plasma oscillation gives an improved agreement between the hydrodynamical and the experimental giant dipole state energies and modifies the nuclear incompressibility extracted from measured giant monopole energies by as much as 15%.