PREX and CREX: Evidence for Strong Isovector Spin-Orbit Interaction

Abstract: The recent PREX-2 and CREX data on the model-independent extraction of the charge-weak form factor difference $\Delta F_{\rm CW}$ in $^{208}$Pb and $^{48}$Ca challenge modern nuclear energy density functionals (EDFs) as well as our present understanding on the neutron skin and nuclear symmetry energy. Within the Skyrme-like EDFs, we demonstrate that the isovector spin-orbit interaction can strongly change the $\Delta F_{\rm CW}$ in $^{48}$Ca while it has essentially no influence on the $\Delta F_{\rm CW}$ in $^{208}$Pb, mainly due to the eight spin-orbit unpaired $1f_{7/2}$ neutrons in $^{48}$Ca. To simultaneously describe PREX-2 and CREX data in $1\sigma$ error, we find the strength of isovector spin-orbit interaction should be larger than about four times of that in the conventional Skyrme-like EDFs, implying the neutrons and protons have significantly different spin-orbit interaction. To further reconcile the data on electric dipole polarizability in $^{208}$Pb and $^{48}$Ca, we obtain $L \approx 55$ MeV for the slope parameter of the symmetry energy, $\Delta r_{\rm np}(^{208}\rm{Pb}) \approx 0.19$ fm and $\Delta r_{\rm np}(^{48}\rm{Ca}) \approx 0.12$ fm for the neutron skin thickness. The implications of the strong isovector spin-orbit interaction are discussed.