Tensor parameters in Skyrme and Gogny effective interactions: Trends from a ground-state-focused study

Abstract

Recent ground-state-focused studies of the tensor effects in the mean-field framework are our starting point. On the basis of phenomenological arguments, we indicate regions for acceptable values of the parameters that are associated with the tensor effective forces within both the Skyrme and the Gogny models. We identify acceptable signs and values of the parameters by making an adjustment on the neutron $1f$ spin-orbit splitting for the nuclei ${}^{40}$Ca, ${}^{48}$Ca, and ${}^{56}$Ni. The first nucleus is not used to adjust the tensor parameters because it is spin-saturated, but is employed to tune the spin-orbit strength. One of the main conclusions of this work is that some existing Skyrme parametrizations containing the tensor force should not be employed because the wrong sign of the tensor parameters does not lead to the correct behavior (by comparing with the experimental results). This study also allows us to better constrain the tensor parameters in the Gogny case, where much less work is published and boundaries and signs for the parameters have not been analyzed so far.