A kink in the trial nucleon density at the center of cylindrical or plane-parallel Wigner-Seitz cells makes the fourth-order extended Thomas-Fermi energy divergent; only spherical-cell kinks are harmless.
Liquid-gas coexistence vs. energy minimization with respect to the density profile in the inhomogeneous inner crust of neutron stars
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abstract
We compare two approaches to describe the inner crust of neutron stars: on the one hand, the simple coexistence of a liquid (clusters) and a gas phase, and on the other hand, the energy minimization with respect to the density profile, including Coulomb and surface effects. We find that the phase-coexistence model gives a reasonable description of the densities in the clusters and in the gas, but the precision is not high enough to obtain the correct proton fraction at low baryon densities. We also discuss the surface tension and neutron skin obtained within the energy minimization.
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On variational trial functions in the extended Thomas-Fermi method
A kink in the trial nucleon density at the center of cylindrical or plane-parallel Wigner-Seitz cells makes the fourth-order extended Thomas-Fermi energy divergent; only spherical-cell kinks are harmless.