Can the PREX-2 and CREX results be understood by relativistic mean-field models with the astrophysical constraints?

We construct new effective interactions using the relativistic mean-field models with the isoscalar- and isovector-meson mixing, ${\sigma }^2{\mathit{\delta }}^2$ and ${\omega }_{\mu }{\omega }^{\mu }{\mathit{\rho }}_{\nu }{\mathit{\rho }}^{\nu }$. Taking into account the particle flow data in heavy-ion collisions, the observed mass of PSR J0740$+$6620, and the tidal deformability of a neutron star from binary merger events, GW170817 and GW190814, we study the ground-state properties of finite, closed-shell nuclei, and try to explain the recent results from the PREX-2 and CREX experiments. It is found that the $\sigma$–$\delta$ mixing is very powerful to understand the terrestrial experiments and astrophysical observations of neutron stars self-consistently. We can predict the large neutron skin thickness of ${}^{208}$Pb, $R_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}^{208}=0.243$~fm, using the slope parameter of nuclear symmetry energy, $L=70$~MeV, which is consistent with the PREX-2 result. However, to explain the CREX data, it is preferable to adopt the small value of $L=20$~MeV. It is very difficult to understand the PREX-2 and CREX results simultaneously within relativistic mean-field models.