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 $2\ensuremath{\Elzxh}\ensuremath{\omega}$ 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) $\ensuremath{\Elzxh}\ensuremath{\omega}$ 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 ${d}_{3/2}\ensuremath{-}{d}_{5/2}$ splitting in $A=17.$