Macroscopic structure of giant multipole resonance states

With use of Skyrme forces, macroscopic structure of giant resonance states is discussed on isoscalar quadrupole and isovector dipole and quadrupole modes. On the basis of the sum rules for the nuclear four-current we construct the semiclassical model, where the time-dependent wave functions are obtained by the scale and the gauge transformation of the ground state wave functions as introduced by Bertsch et al. Whereas the restoring force for isoscalar modes stems mainly from volume terms of the energy density, in isovector modes, besides the volume terms, surface terms not only from the symmetry potential energy, but also from isoscalar potential energy play a crucial role. The dependence of the frequencies on the mass number (A), the effective mass (m*) and the exchange effect (kappa) is shown to be mode-dependent. The effects of Nnot equalZ and the nuclear deformation are also discussed. The useful relationship between frequencies of the three modes is derived, being in good agreement with experiment. (author)