Tensor and isovector–isoscalar terms of relativistic mean field model: Impacts on neutron-skin thickness, charge radius, and nuclear matter

The origin of the neutron skin thickness, measured by the CREX and PREX collaborations as thin for ⁴⁰Ca and thick for ²⁸Pb, remains a mystery. We investigate the effects of tensor and nonlinear isovector–isoscalar terms in a relativistic mean-field model (RMF) on the properties of finite nuclei and nuclear matter. Tensor couplings are crucial for better quality binding energies of finite nuclei and charge radii for relatively heavy nuclei. However, for light nuclei, the tensor terms cannot improve the compatibility of charge radius predictions by the RMF model with experimental data. We find that parameter sets with a larger nonlinear isovector–isoscalar parameter, particularly ${\eta }_{2\rho }$ = 0.028, agree better with experimental data for Δ$r_{np}$ across light, medium, and heavy isotope chains. Using PT28, we calculate Δ$r_{np}$ for ²⁰⁸Pb as 0.214 fm, J as 33.078, and L as 58.426. Δ$r_{np}$ for ²⁰⁸Pb obtained using PT28 is consistent with the PREX-II data. Moreover, the corresponding values of J and L agree with the low L constraints. Meanwhile, the canonical mass radius predicted by PT28 aligns with the mass and radius data from the NICER collaboration. The combination of tensor and nonlinear isovector–isoscalar couplings in the RMF model provides accurate predictions for finite nuclei binding energies and relatively heavy nuclei charge radii, resulting in relatively thick Δ$r_{np}$ values for ²⁰⁸Pb without substantial L values.