Variational formulation of nuclear fluid dynamics

A new fluid dynamical description of giant resonances which avoids the scaling approximation and takes into account the interplay between first sound and zero sound is presented. The new method leads to equations satisfying the sum rules $S_{\mathrm{-}1}$, $S_1$, and $S_3$ for the electric modes and the sum rule $S_1$ for the magnetic modes. The model describes surface modes and separates the low lying modes from the giant resonances. Numerical results for the energy spectrum of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are presented.