Spin-orbit interaction in relativistic nuclear structure models

TL;DR

This paper investigates how exchange terms influence the isovector properties of the spin-orbit interaction in relativistic nuclear models, connecting theoretical predictions with experimental data on nuclear structure and isotope shifts.

Contribution

It demonstrates that including exchange contributions in relativistic models yields an isovector spin-orbit potential similar to non-relativistic approaches, aiding interpretation of experimental data.

Findings

Exchange terms induce an isovector structure in relativistic models.

Data on spin-orbit splittings can constrain the isovector-scalar channel.

Relativistic models reproduce the isotope shift kink in Pb nuclei.

Abstract

Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas non-relativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data, however standard relativistic mean-field and non-relativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analysed, and it is shown that it leads to an isovector structure similar to the one used in standard non-relativistic Hartree-Fock. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.