Hydrodynamical Model of the Nucleus with Surface Effects

An attempt is made to improve the predictions of the $A$ dependence of giant dipole energies of the two-fluid hydrodynamical models by the introduction of a more realistic surface behavior of the ground-state densities. The Euler-Lagrange equations of motion for the dipole oscillation are obtained by the expansion of the energy functional $\epsilon [\rho , {\left(\overrightarrow{\nabla }\rho \right)}^2, \alpha (\overrightarrow{\mathrm{r}}\left)\right]$, where minimization yields acceptable neutron and proton densities, in quadratic powers of the densities and their derivatives. The equations are solved under certain limiting conditions, but within these limitations a much better $A$ dependence is obtained.