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We study the diversities in the properties of the neutron stars arising dueto the different choices for the cross-coupling between various mesons whichgoverns the density dependence of the nuclear symmetry energy in the extendedrelativistic mean-field(RMF) model. For this purpose, we obtain two differentfamilies of the extended RMF model corresponding to different non-linearcross-coupling term in the isovector part of the effective Lagrangian density.The lowest order contributions for the $\delta$ mesons are also included. Thedifferent models within the same family are so obtained that they yield widevariation in the value of neutron-skin thickness in the $^{208}$Pb nucleus.These models are employed to compute the neutron star properties such as,core-crust transition density, radius and red shift at canonical mass($1.4M_{\odot}$), tidal polarizability parameter, and threshold mass requiredfor the enhanced cooling through direct Urca process. Most of the neutron starproperties considered are significantly different(10\%-40\%) for the differentfamilies of models at a smaller neutron-skin thickness ($\sim 0.15$ fm) in the$^{208}$Pb nucleus.

Diversities in the properties of neutron stars at a fixed neutron-skin thickness in $^{208}$Pb nucleus