A phenomenological test of the independent quasi-particle model

Abstract

The analysis of the experimental low-lying spectra of single-closed shell nuclei by means of the inverse gap equations method yields uniquely in the pairing model the effective nucleon-nucleon force strength, the Hartree-Fock single-particle energies and the BCS wave functions. The results are free from any adjustable parameter. The constancy in a given nuclear region of the force strength and of the HF energies thus provides an unambiguous test of the pure one-quasi-particle description for such nuclei. The analysis is carried out with a central, finite-range force for all spherical single-closed shell nuclei for which enough data are available (i.e. the isotones N = 28 and 50, and the isotopes Z = 28, 50 and 82). The results show the importance of including more than one major shell for the pairing effects. Inclusion of remote shells renormalizes the force strength appreciably. However, it does not affect the wave functions of quasi-particle states near the Fermi level. When the number of nucleons is varied, the extracted force strength and the Hartree-Fock energies remain nearly constant (within±1 MeV and ±0.5 MeV, respectively), which is close to their average value in most of the studied nuclear regions.