Regularities of proton-neutron interactions for nuclei in thesdshell

Abstract

In this paper we study the proton-neutron interaction of nuclei in the $sd$ shell by using the shell model. The isoscalar proton-neutron interactions of the shell model results are found to be consistent with those empirically extracted by the double difference of binding energies. We point out that there exists an additional binding energy for both even-even and odd-odd nuclei, and both these energies lead to the odd-even staggering for $\ensuremath{\delta}{V}_{1\mathrm{p}\ensuremath{-}1\mathrm{n}}$. We also study the possible origin of the anomaly of proton-neutron interactions.