Application of thomas fermi model on the study of the transition phase from the inner crust to the core of neutron star

Abstract

The study of the Thomas Fermi model and its application on the study of the inner crust of neutron star has been done in order to explain pasta phase (the geometric structure changing of atomic nuclei from spherical ones to homogenous liquid) on the transition area from the inner crust to the core of neutron star. The study was carried out by the Wigner Seitz approach on the inner crust that is obtaining the total energy equation as a function of the density of the system, as a Thomas Fermi’s model. In this study Thomas Fermi’s model explains atomic nuclei that consist of Fermion gas in a system of functional total energy to density by taking into account the contribution of kinetic energy, potential energy and the contribution of interactions between particles. The energy state equation obtained was used to explain the effect of increasing density on the inner crust energy and explain the pasta phase through the interpretation of the graph of Thomas Fermi energy per baryon as a function of baryon density for every geometric structure of atomic nuclei.