Semi-classical treatment of proton–neutron monopole interaction Original Research Article

We apply a time dependent variational method to a many-body Hamiltonian consisting of a spherical shell model term, a proton–proton and neutron–neutron pairing interaction and a monopole particle–hole and particle–particle proton–neutron interaction. The variational state is a generalized BCS state where all T=1 Cooper pairs with View the MathML source are included. Stationary solutions correspond to generalized BCS equations and define the static ground state. The linearized equations of motion are of RPA type and describe small oscillations of the nuclear system around the static ground state. Numerical application is made for a one level case. In contrast to previous treatments, the proton–neutron particle–particle interaction is included first in the mean field equations, defining the quasiparticle approximation, and then the residual interaction is taken into account by the RPA approach. In this way one obtains a noncollapsing RPA ground state.