The nuclear symmetry energy is fundamental in nuclear astrophysics, influencing phenomena from nuclear structure to gravitational collapse and neutron star formation. Both the symmetry energy and its linear density dependence (L), are critical inputs for numerous nuclear physics and astrophysics applications, as they play a key role in determining properties such as neutron skin thickness (Δrnp) and neutron star radius. Recent results from parity-violating electron scattering experiments on 208Pb (PREX-II: The Lead Radius Experiment)) have offered new insights into these fields. Specifically, the PREX-II experiment has provided a neutron skin thickness for 208Pb of fm. This measurement helps to constrain the nuclear symmetry energy in laboratory environments. In this study, we propose several interactions (SRQs) based on relativistic energy density functionals that correspond to different values of Δrnp for 208Pb, as derived from the PREX-II limits. We observe a correlation between Δrnp of 208Pb and L. We compute the equations of state for nucleonic matter under β - equilibrium conditions for proposed interactions. We also discuss in detail the effects of Δrnp and L on nuclear matter and neutron star properties. Additionally, these interactions are utilized to explore the characteristics of rotating neutron stars.
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