Connecting neutron skin thickness and neutron star observables through isovector scalar delta meson in relativistic framework

Recent developments in the parity-violating electron scattering experiments on ⁴⁸Ca (CREX) and for ²⁰⁸Pb (PREX-II) has provided new insight on the neutron skin thickness. These findings reveal several viewpoints on nuclear matter parameters (NMPs) such as symmetry energy (J) and its linear density dependency (L), which are directly related to the equation of state (EoS) of asymmetric dense matter. While PREX results lead to stiffer L and hence necessitate a stiffer EoS, the CREX experiments favor softer L and hence a softer EoS. Therefore, it is challenging to produce neutron skin of both (⁴⁸Ca and ²⁰⁸Pb) in relativistic mean field (RMF) models simultaneously. To address this issue, we propose relativistic interactions based on RMF model comprising of self and cross interactions of σ, ω, ρ and δ mesons. These interactions are consistent with the results of both experiments, and they accurately replicate experimental data related to the ground state properties, such as binding energies (BE) and charge radii ($r_{ch}$), of both closed and open shell nuclei. We also compute the EoSs comprising of npeμ matter under β-equilibrium condition for the proposed interactions and hence calculate neutron star observables.