Semi-classical description of a system with proton–neutron interaction Original Research Article

A solvable many-body Hamiltonian, written in the quasiparticle representation, is treated semiclassically using a time-dependent variational principle formalism with four different variational states. One of the description is equivalent to the standard pnQRPA approach, while another one is valid for 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 corresponds to a phase transition. The classical equations of motion were quantized and several boson representations for bi-fermionic operators have been obtained. For the quantized ground and first excited states, the quasiparticle correlations, the β− and β+ transition amplitude and the Ikeda sum rule have been calculated. The energies of the second excited states of the model Hamiltonian are also treated semiclassically. Although a harmonic 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.