The origin of the spin-orbit and pseudospin-orbit splittings' evolution in neutron drop

TL;DR

This paper investigates the evolution of spin-orbit and pseudospin-orbit splittings in neutron drops, revealing that their staggering pattern mainly results from density changes and the SO potential, rather than tensor forces.

Contribution

It provides an intuitive explanation for the staggering evolution of SO and PSO splittings in neutron drops within Skyrme EDF theory, emphasizing the role of density and SO potential terms.

Findings

Staggering pattern observed in both EDF and RBHF theories.

Density changes primarily cause the staggering evolution.

SO potential, not tensor force, determines the pattern.

Abstract

We found the same staggering pattern in the evolution of the spin-orbit (SO) and pseudospin-orbit (PSO) splittings in neutron drops obtained by the energy-density functional (EDF) theory using SAMi-T and SLy5 parameterizations, with and without the tensor terms respectively. This staggering evolution is similar to the results recently obtained by the relativistic Brueckner-Hartree-Fock (RBHF) theory with Bonn A potential, which was claimed to be a tensor effect. In this work, we present an intuitive but essential explanation on the origin of this staggering evolution in the Skyrme EDF theory. We found that for both the SO and PSO partners, the energy splittings mainly originate from the SO potential. The staggering evolution of both the SO and PSO splittings is mainly due to the drastic change of density while neutrons filling different single-particle orbits. The key to determine the specific staggering pattern is the strength of the neutron density gradient term and the SO density term in the SO potential, not necessarily the tensor force.