Single-particle energies in neutron-rich nuclei by shell model sum rule

Abstract

One of the most striking features in neutron-rich nuclei is the disappearance of magic number $N=8$ or 20, which indicates a change of single-particle energy spectra and the disappearance of a large energy gap at the magic number. A sum-rule method is formulated, based on the shell model, for the evaluation of single-particle energies. It is shown that the triplet-even central component of the $\mathit{NN}$ interaction plays a decisive role through the monopole interaction for a change of single-particle energy spectra, leading to a rapid decrease of the energy gap at $N=8$ and 20. The triplet-even attraction is due partly to the original central interaction and partly to the second-order tensor correlations of the one-pion exchange potential. A multipole expansion analysis of $\mathit{NN}$ interactions shows that the contribution to the single-particle energy from the monopole interactions between two orbits depends on the nodal quantum numbers of the orbits.