We study the diversities in the properties of the neutron stars arising due to the different choices for the cross-coupling between various mesons which governs the density dependence of the nuclear symmetry energy in the extended relativistic mean-field ( RMF ) model .
For this purpose , we obtain two different families of the extended RMF model corresponding to different non-linear cross-coupling term in the isovector part of the effective Lagrangian density .
The lowest order contributions for the \delta mesons are also included .
The different models within the same family are so obtained that they yield wide variation 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 ( 1.4 M _ { \odot } ) , tidal polarizability parameter , and threshold mass required for the enhanced cooling through direct Urca process .
Most of the neutron star properties considered are significantly different ( 10 % -40 % ) for the different families of models at a smaller neutron-skin thickness ( \sim 0.15 fm ) in the ^ { 208 } Pb nucleus .