Improved inverse gap equation procedure for quasi-particle calculations

An improvement in the inverse gap equation (IGE) method is proposed in which the fed single-quasi-particle-energies are corrected either by the second-order perturbation theory or by the modified Tamm-Dancoff approximation (MTDA) theory at each iteration. The procedure is fast converging. The behaviour of the extracted quantities for odd Ni isotopes is reasonably close to their expected theoretical behaviour. The extracted Hartree-Fock (HF) energies are highly sensitive to the choice of the effective two-body interaction. These quantities are used in calculating the various quasi-particle quantities for the corresponding even Ni isotopes through the BCS or pairing-model equations. Quasi-particle configuration-mixing calculations are performed for both odd and even Ni isotopes using their respective sets of quasi-particle quantities obtained by (i) the conventional BCS, (ii) IGE and (iii) the improved IGE procedures. These sets of quasi-particle results are compared and their relative merits discussed.