Towards a Better Understanding of Nuclear Pairing and Its Interplay with Other Residual Interactions

Abstract

Experimental evidence indicates that pairing interaction often plays a major role in determining physics of nuclear many-body systems. The goal of this work is to discuss properties of pairing in a mesoscopic nuclear environment, study the interplay of pairing and other residual interactions and develop new practical approaches. We use Sn isotopes as a testing arena. We utilize the exact solution of pairing problem based on quasispin formalism. 1), 2) This treatment of pairing (EP algorithm) is free of well-known BCS shortcomings and enables one to address fluctuating pair vibrations and chaotic effects of other residual interactions which significantly change the usual macroscopic BCS picture, 3) furthermore it provides a basis, with classification by seniority quantum numbers, that can be used for perturbatively accounting for other interactions. We demonstrate in a simple model that although in general twobody interactions do not preserve seniority, kinematics still often favors seniority conservation. The lowest seniority subspace can serve as a good starting truncation. Interactions of a non-pairing nature have only diagonal monopole contributions in this subspace. We show that this technique of exact pairing plus monopole 2) can be successful in the analysis of ground state properties of nuclei, furthermore being a well formulated variational method and part of a more general seniority truncation technique it is perfect for adjusting shell model parameters. Pairing and approximate treatment of other residual interactions can be combined through the Hartree-Fock (HF) and exact pairing (EP) technique. In Fig. 1 one-neutron separation energies are calculated for the Sn isotopes, including those beyond 132Sn. These energies were obtained from the fully self-consistent spherically symmetric solution of HF equations, using the SKX interaction, 4) with the EP solution based on renormalized G-matrix interactions from Ref. 5). The HF+EP approach can be considered as a variant of the density functional method. In this method we make an initial guess for the spherical HF potential from which the single particle energies are determined. In the valence subspace the pairing problem is solved using a fixed set of two-body matrix elements. This determines the particle distribution and pairing correlation energy. With new occupation numbers a new HF potential can be calculated. This procedure is repeated iteratively until convergence. The total energy is the sum of the Skyrme HF energy and the pairing correlation energy. Figure 1 shows an example of such calculations and exhibits an