Spin-orbit coupling rule in bound fermions systems

TL;DR

This paper derives a universal rule for the magnitude of spin-orbit coupling effects across various quantum systems, explaining differences in shell structure and predicting giant splittings under specific conditions.

Contribution

It introduces a universal rule for spin-orbit effects applicable to diverse systems, linking system parameters to spin-orbit strength and shell structure.

Findings

In nuclei, spin-orbit splittings are comparable to shell spacings due to nucleon mass and potential differences.

A specific mass-to-potential ratio predicts giant spin-orbit splittings.

The rule applies regardless of whether spin-orbit coupling is from strong or electromagnetic interactions.

Abstract

Spin-orbit coupling characterizes quantum systems such as atoms, nuclei, hypernuclei, quarkonia, etc., and is essential for understanding their spectroscopic properties. Depending on the system, the effect of spin-orbit coupling on shell structure is large in nuclei, small in quarkonia, perturbative in atoms. In the standard non-relativistic reduction of the single-particle Dirac equation, we derive a universal rule for the relative magnitude of the spin-orbit effect that applies to very different quantum systems, regardless of whether the spin-orbit coupling originates from the strong or electromagnetic interaction. It is shown that in nuclei the near equality of the mass of the nucleon and the difference between the large repulsive and attractive potentials explains the fact that spin-orbit splittings are comparable to the energy spacing between major shells. For a specific ratio between the particle mass and the effective potential whose gradient determines the spin-orbit force, we predict the occurrence of giant spin-orbit energy splittings that dominate the single-particle excitation spectrum.