Tensor and tensor-isospin terms in the effective Gogny interaction

Abstract

We discuss the need of including tensor terms in the effective Gogny interaction used in mean-field calculations. We show in one illustrative case that, with the usual tensor term that is employed in the Skyrme interaction (and that allows us to separate the like--nucleon and the neutron-proton tensor contributions), we can describe the evolution of the $N=28$ neutron gap in calcium isotopes. We propose to include a tensor and a tensor-isospin term in finite-range interactions of Gogny type. The parameters of the two tensor terms allow us to treat separately the like-nucleon and the neutron-proton contributions. Two parametrizations of the tensor terms have been chosen to reproduce different neutron single-particle properties in the ${}^{48}$Ca nucleus and the energy of the first ${0}^{\ensuremath{-}}$ state in the ${}^{16}$O nucleus. By employing these two parametrizations we analyze the evolution of the $N=14$, 28, and 90 neutron energy gaps in oxygen, calcium, and tin isotopes, respectively. We show that the combination of the parameters governing the like-nucleon contribution is crucial to correctly reproduce the experimental (where available) or shell-model trends for the evolution of the three neutron gaps under study.