Impact of tensor forces on spin-orbit splittings in neutron-proton drops

Abstract

A systematic study of the tensor-force impact in neutron-proton drops has been reported using the relativistic Hartree-Fock (RHF) theory with the $\ensuremath{\pi}\text{\ensuremath{-}}N$ coupling strength optimized to the relativistic Brueckner-Hartree-Fock (RBHF) results for neutron drops. The evolutions of the neutron spin-orbit splittings as a function of the neutron number for neutron-proton drops with one proton behave similarly to the pure neutron drops, which show the tensor-force effect. By adding one more proton or neutron in the neutron drop with $N=20$, it is found that the tensor-force effect is more prominent between neutrons and protons than between neutrons. This can be attributed to the isospin factor in the tensor term of the $\ensuremath{\pi}\text{\ensuremath{-}}N$ interaction in the RHF density functional theory, which reflects the fact that the neutron-proton tensor force is stronger than the neutron-neutron one. Similar behavior for the spin-orbit splitting evolutions has also been found for the neutron-proton drops with 20 protons, where the tensor-force strength $\ensuremath{\lambda}$ is redetermined according to the RBHF results due to the large central densities of the systems.