Pairing and quadrupole forces in a two-dimensional soluble model

Abstract

The model treated is a system of particles moving in a two-dimensional harmonic oscillator potential with two-body pairing and quadrupole forces mixing states within a single major shell. A simple representation is found in which the Hamiltonian is exactly diagonal. An “energy gap” is obtained in the limit of pure pairing forces and rotational spectra in the limit of pure quadrupole forces. In the intermediate region the spectrum varies from energy gap to rotational as the number of particles is increased. The effective moment of inertia of the rotational band is unaffected by the pairing force, remaining constant at the value for a pure quadrupole force. The model is also treated by replacing the quadrupole force by a self-consistent deformed field and the moment of inertia is calculated using the cranking model. The results agree with the exact solution. Implications of the model for more realistic cases are discussed.