Number-Conserving Treatment of Pairing Correlations in Even-Even Nuclei

A simple method is proposed for treating pairing correlations in even-even nuclei without violating the particle-number conservation. A dispersion formula is derived which makes it possible to calculate the eigenenergies for a system with $A$ particles, once the occupation numbers for the ($A-2\mathrm{}$)-particle system are known. This formula is used to calculate the ground-state energies for the even Ni isotopes; the results turn out to be much better than those obtained by the standard BCS method. The ground-state wave function is discussed and compared with the $A$-particle component of the BCS wave function. The possibility of treating neutron-proton correlations by the same method is also considered, and the general formulation is given for the case of a charge-independent pairing interaction between particles in nondegenerate orbitals. The degenerate model is studied in detail, and the approximate ground-state energy is compared with the exact one. The results obtained suggest that the present method may be usefully applied in the general case of nondegenerate levels.