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Sensitivity of neutron radii in the $"" sup 208_Pb nucleus and a neutron star to nucleon-$ sigma_-$ rho_ coupling corrections in relativistic mean field theory

We study the sensitivity of the neutron skin thickness, $S$, in a $^{208}$Pb nucleus to the addition of nucleon-sigma-rho coupling corrections to a selection (PK1, NL3, S271, Z271) of interactions in relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of $S$ = 0.16 fm in comparison with the original value of $S$ = 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of $S$ = 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore $S$, in $^{208}$Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4 solar-mass neutron star and $S$.