Spin-orbit interaction in relativistic nuclear structure models

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 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 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.

Laser and decay spectroscopy of the short-lived isotope Fr214 in the vicinity of the N=126 shell closure

“…However, in contrast, ν1i 11/2 configuration mixing accounts for 33.5% of the 214 Fr ground state assignment when I = (2 − ), with g( 214g Fr I=(2 − ) ) = +0.144 (10). In either case, evidence of a contribution from the ν1i 11/2 orbital supports previous theoretical studies that require this in order to reproduce the kink in the mean square charge-radii values at the N = 126 shell closure [14,15,17]. For the ν2g 7/2 orbital, mixing calculations have been performed using the same empirical values as mentioned above for the π 1h 9/2 , ν2g 9/2 , and ν2g 7/2 orbitals, as well as the calculated B(M1) value connecting the ν2g 9/2 and ν2g 7/2 orbitals [49].…”

“…Modifications to the spin-orbit interaction in mean-field calculations have successfully reproduced the kink in the Pb and Po isotope chains [14,15,17]. Other studies suggest the inclusion of a density-dependent term to the spin-orbit term [13,16], with the latter also proposing the inclusion of three-nucleon (3N ) interactions in mean-field calculations.…”

“…Many groups have investigated this region with mean-field calculations [13][14][15][16][17] but no general consensus exists on how to reproduce the correct magnitudes. Until now, limited experimental input has been available regarding the gradient of the kink at this particular shell closure.…”

Spin-orbit splittings of neutron states inN=20isotones from covariant density functionals and their extensions

“…In the relativistic models the value of this ratio depends on the density and can take different values for various nuclei, especially for functionals where the coupling constants are also density dependent, as explained in Ref. [72]. In that reference there is a calculation of this ratio for several nuclei, including 34 Si, as a function of the nuclear radius.…”

Isovector Properties Of The Nuclear Equation Of State from The Quark-Meson Coupling Model

“…Covariant energy density functionals offer another interesting approach to the nuclear many-body problem [11]. Being fully relativistic, they naturally generate a spin-orbit interaction and, if exchange terms are properly included, some isovector dependence [12]. However, as in the Skyrme EDF, the density dependence of the coupling constants requires some phenomenology, leading to a relatively large number of parameters needed to fit experimental data or pseudodata.…”