Macroscopic equations of motion and dynamic polarizability in the study of nuclear collective excitations

Time dependent Hartree-Fock equations are derived using a variational principle over a restricted part of the space of the Slater determinants, in the limit of small deformations (RPA). When an external oscillating field interacts with the nucleus, this method leads to an explicit expression of the nuclear response function (dynamic polarizability) as a function of the external frequency and of the deformation field, defining the nuclear deformation induced by the interaction. A linear differential equation for the deformation field is also obtained: in the limit ω → infinity it has analytical solutions which satisfy the energy-weighted sum rule, evaluated in a HF ground state, in both isoscalar and isovector modes. (Auth.)