Semi-classical treatment of proton-neutron monopole interaction

We apply a time dependent variational method to a many-body Hamiltonian con sisting of a spherical shelf model term, a proton-proton and neutron-neutro n pairing interaction and a monopole particle-hole and particle-particle pr oton-neutron interaction. The variational state is a generalized BCS state where all T = 1 Cooper pairs with T-z = 0, +/- 1 are included. Stationary s olutions correspond to generalized BCS equations and define the static grou nd state. The linearized equations of motion are of RPA type and describe s mall oscillations of the nuclear system around the static ground state. Num erical application is made for a one level case. In contrast to previous tr eatments, the proton-neutron particle-particle interaction is included firs t in the mean field equations, defining the quasiparticle approximation, an d then the residual interaction is taken into account by the RPA approach. In this way one obtains a noncollapsing RPA ground state. (C) 2000 Elsevier Science B.V. All rights reserved.