Exact solutions and constrained Hartree-Fock spectra in a soluble triaxial quasispin model

It is shown that in a soluble triaxial quasispin model the good quasispin states {vert_bar}{ital JK}{r_angle} and {vert_bar}{ital J}{r_angle} can be established on basis SU(2){times}SU(2) by means of the diagonalization method. The energy eigenstate {vert_bar}{ital J}{r_angle} has an approximate good quantum number {ital K} which can be determined through the procedure proposed here. The triaxiality of the exact solutions of the model Hamiltonian and the characteristics of the energy spectra are discussed. Two new constrained Hartree-Fock (CHF) methods are proposed and solved. The comparisons of calculated CHF spectra with exact solutions show that the new CHF prescriptions proposed in this paper are the effective methods for producing states having good quasispin quantum numbers and the spectra with multiband structure.