Role of tensor terms of the Skyrme energy-density functional on neutron deformed magic numbers in the rare-earth region

Abstract

The role of the tensor part of the nuclear interaction is actively investigated in recent years due to experimental advancement yielding new data in nuclei far from the $\beta$-stability line. In this article we study the effect of this part of the nuclear interaction on deformed neutron magic numbers in the rare-earth region within the Skyrme energy-density functional for various TIJ \cite{lesinski:2007} parametrizations. Two quantities signaling magic numbers are considered: two-neutron separation energies and single-particle energies. They are calculated in isotopic series involving well-deformed rare-earth nuclei ranging from $Z=64$ to $Z=72$ in the $N=100$ region. Obtained results show that, whereas the neutron-proton tensor contribution to binding energies is important to reproduce neutron sub-shell closure at $N = 104$ in heavier rare earths Yb ($Z=70$) and Hf ($Z=72$) isotopes, like-particle tensor also plays a role in the single-particle spectrum around Fermi level and is even favored in lighter Gd ($Z=64$) and Dy ($Z=66$) rare-earth isotopes.