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We construct new effective interactions using the relativistic mean-fieldmodels 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 accountthe particle flow data in heavy-ion collisions, the observed mass of PSRJ0740$+$6620, and the tidal deformability of a neutron star from binary mergerevents, 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 andCREX experiments. It is found that the $\sigma$--$\delta$ mixing is verypowerful to understand the terrestrial experiments and astrophysicalobservations of neutron stars self-consistently. We can predict the largeneutron skin thickness of $^{208}$Pb, $R_{\rm skin}^{208}=0.243$~fm, using theslope parameter of nuclear symmetry energy, $L=70$~MeV, which is consistentwith the PREX-2 result. However, to explain the CREX data, it is preferable toadopt the small value of $L=20$~MeV. It is very difficult to understand thePREX-2 and CREX results simultaneously within relativistic mean-field models.

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