Semi-classical description of a system with proton-neutron interaction

A solvable many-body Hamiltonian, written in the quasiparticle representati on, is treated semiclassically using a time-dependent variational principle formalism with four different variational states. One of the description i s equivalent to the standard pnQRPA approach, while another one is valid fo r a strength of the particle-particle two-body interaction lying in a range where the former approximation is not valid, although it describes a small amplitude harmonic motion. The transition from one solution to the other c orresponds to a phase transition. The classical equations of motion were qu antized and several boson representations for bi-fermionic operators have b een obtained. For the quantized ground and first excited states, the quasip article correlations, the beta(-) and beta(+) transition amplitude and the Ikeda sum rule have been calculated. The energies of the second excited sta tes of the model Hamiltonian are also treated semiclassically. Although a h armonic representation is adopted, some anharmonic effects are included, as one sees, if one compares the results with the two-phonon states obtained within the former approaches. (C) 2000 Elsevier Science B.V. All rights res erved.