Role of the tensor interaction in He isotopes with a tensor-optimized shell model

Abstract

We studied the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8${}^{\ensuremath{'}}$ obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the $LS$ splitting energy observed in ${}^{5}$He, in which the ${p}_{1/2}$ and ${p}_{3/2}$ orbits play different roles on the tensor correlation. In ${}^{6,7,8}$He, the low-lying states containing extra neutrons in the ${p}_{3/2}$ orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the ${p}_{1/2}$ orbit lose the tensor contribution due to the Pauli-blocking effect with the $2p2h$ states in the ${}^{4}$He core configuration.