Pairing effects in nuclei described by the Hartree-Fock theory

Abstract

The amount of energy gap between occupied and unoccupied single-particle states determines the reliability of a Hartree-Fock (HF) calculation. If the gap is comparable to the residual pairing interaction, the sharp Fermi surface corresponding to the HF state is meared out through mixing with pair-excited configurations. In heavy and medium-heavy nuclei, it is believed that such mixing with configurations having several pairs are important. In the light 2s, 1d shell nuclei, where the energy gap is 6–8 MeV, it is a fairly good approximation to calculate the correction to the HF state by mixing only the two hole (h)-two particle (p) type excited configurations. Such corrections represent a genuine pairing correlation present in the intrinsic state. Formulae have been worked out for diagonalizing the residual interaction between the HF state and the 2h-2p states. Explicit numerical results are presented for ²⁰Ne using the two-body, effective matrix elements of the Yale potential. The corrected ground state is found to contain about 8% admixture of excited configurations, thus showing that the pairing corrections are not very important in 2s, 1d shell nuclei. The reason for this finding is analysed.