In the framework of a chiral hadronic model it has been numerically proven that the parabolic expansion with respect to δ^2 at finite density and temperature is a good approximation in the relativistic mean field theory,It is also shown that the proton fraction in the modified Urca process is considerably restrained in comparison with that of the direct Urca process.Then,we discuss the influences of the density-dependent and temperature-dependent asymmetry energy on the proton fraction in hot neutron star matter.
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