On classical hydrodynamics and collective motion as approximation to the nuclear many-body problem

Using time-dependent unitary transformations, one can cast a one-body equation of the time-dependent Hartree-Fock type into a form which is closely related to equations for a classical irrotational fluid. The hydrodynamic equation of state finds its counterpart in a stationary constrained field equation. The hydrodynamic equations in turn can be translated into a classical Hamiltonian formalism with an infinite number of generalised coordinates, which are given as all possible spatial moments of the density. The reduction to a few ones, the 'natural collective coordinates' is possible by the choice of appropriate initial conditions. The lowest of the hydrodynamical frequencies can be calculated in closed form by harmonic approximations. For the quadrupole frequency a value of ω = 31 Asup(-1/3) MeV/h is obtained. As expected, the value does not agree with the experiment, but rather is in between the characteristic frequency for the β-vibration and the isoscalar giant quadrupole vibration. (orig.)