Dependence of the Shell-Model Single-Particle Energies on Different Components of the Nucleon-Nucleon Interaction

Abstract

The spin-orbit splittings in the spectra of nuclei with mass numbers 5, 15 and 17 are studied within the framework of shell-model configuration mixing calculations including 2$\hbar ω$ excitations. The contributions of the two-body spin-orbit and tensor components of the nucleon-nucleon interaction are studied in various model spaces. It is found that the effects of the two-body spin-orbit interaction are dominant and quite sensitive to the size of the model-space considered. The effects of the tensor interaction are weaker. The correlations effects which are included in the larger (0+2) $\hbar ω$ shell-model space reduce the spin-orbit splitting in the case of A=5 by 20%, and enhance it for A=15 by about the same 20%. However, it is found that the correlations have a very small effect on the $d_{3/2} - d_{5/2}$ splitting in A=17.