Pairing Correlations: Particle-Particle Excitations in Open-Shell Nuclei

Abstract

Until now we always considered a sharp Fermi level with a very particular distribution of level occupation probabilities. Up to the Fermi level, all levels are fully occupied, while above, all are unoccupied. This conforms with a Hartree-Fock static ground state with 1p – 1h, 2p – 2h, … excitations as elementary modes of excitation (see Sect. 6.2 for a discussion on the TDA approximation). A short range force of sufficient strength is now able to scatter couples of particles across the sharp Fermi level. For nuclei at or near doubly-closed shell configurations, this leads to a “diffuse” ground state with 2p – 2h, 4p – 4h,… correlations, much like the RPA ground state $\left| {\tilde{0}} \right\rangle$ as discussed in Sect. 6.3. When, however, many nucleons outside closed shells are present, this pair can scatter, under certain conditions, lead to a stable, smooth probability distribution for the occupation of the single-particle orbitals. So, the pairing correlations set in and modify the nuclear ground state distribution of nucleons in nuclei in a major way (see Fig. 7.1).