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, $\sigma^{2}\bm{\delta}^{2}$ and $\omega_{\mu}\omega^{\mu}\bm{\rho}_{\nu}\bm{\rho}^{\nu}$. 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, $R_{\rm skin}^{208}=0.243$~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.