The interplay between first sound and zero sound in a finite Fermi system

A derivation of nuclear fluid dynamics for finite Fermi systems based on the time dependent variational principle is presented. As variational function a Slater determinant /phi >= exp(iF/(h/2π)/phisub(f)> is considered where /phisub(f)> is a Slater determinant which includes local equilibrium deformations and F is an hermitian time dependent generator of the form F = chi + s.p. + 1/2PαPβPHIsub(αβ). This fluid dynamical scheme provides a simultaneous description of low lying states and giant resonances in atomic nuclei. Assuming density dependent delta forces it is shown that in the classical limit the ground state density is rho0(r) = rho0(0) theta(R-r) where rho0(0) is the nuclear matter equilibrium density