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Equation of state and thickness of the inner crust of neutron stars

The cell structure of $β$-stable clusters in the inner crust of cold and warm neutron stars is studied within the Thomas-Fermi approach using relativistic mean field nuclear models. The relative size of the inner crust and the pasta phase of neutron stars is calculated, and the effect of the symmetry energy slope parameter, $L$, on the profile of the neutron star crust is discussed. It is shown that while the size of the total crust is mainly determined by the incompressibility modulus, the relative size of the inner crust depends on $L$. It is found that the inner crust represents a larger fraction of the total crust for smaller values of $L$. Finally, it is shown that at finite temperature the pasta phase in $β$-equilibrium matter essentially melts above $5-6$ MeV, and that the onset density of the rodlike and slablike structures does not depend on the temperature.