Spin-orbit interaction in relativistic nuclear structure models

Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas nonrelativistic 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 nonrelativistic 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 analyzed, and it is shown that it leads to an isovector structure similar to the one used in standard nonrelativistic Hartree-Fock models. 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.

Figure 1

Radial dependence of the proton (solid) and neutron (dashed) ratio $\left(\frac{W_1}{W_2}\right)$ of parameters of the spin-orbit potential [Eq. (17)], for the ground states of ${}^{16}\mathrm{O}, {}^{34}\mathrm{Si}$, and ${}^{208}\mathrm{Pb}$, calculated with the RMF effective interactions DD-ME2 (left) and DD-PC1 (right).

Figure 2

Same as Fig. 1, but the ratio of the parameters is given by Eq. (30) for the case of the relativistic Hartree-Fock effective interaction PKO2.

Figure 3

Isotope shifts for even-$A$ Pb nuclei with respect to the reference nucleus ${}^{208}\mathrm{Pb}$. Experimental values [29, 30] are shown in comparison with theoretical results obtained in the RMF calculation with the effective interaction DD-PC1, using the relativistic Hartree-Fock effective interaction PKO2, and with the RMF model obtained by performing the Fierz transformation of the point-coupling approximation of PKO2.