Equation of state to compact objects with ion crystal lattice

Crystal lattice structure is present in stellar compact objects, such as white dwarf stars and in the crust of neutron stars. These structures can be described by a body-centered cubic crystal, which is formed by ions due to Coulombian interactions in presence of stellar electron plasma. The electron-electron interaction is currently described in the electrodynamics context by a quantum homogeneous plasma. Particularly, we investigate the changes in the medium Equations of State (EoS), improving results presented in the literature. The main purpose of this work is to analyse the distribution of electrons in the stellar medium considering their interaction with ions in the crystal lattice. The electric field produced by the presence of crystal lattice is obtained using linear response theory in the context of finite temperature field theory. The screening and distribution of electrons are corrected by an arbitrary number of neighbor ions, which is a novelty in the literature and significantly impact the EoS. Numerical results are presented for a completely degenerate electron plasma and for different species of ions that make up the lattice. These EoS can be applied to determine the structure of the aforementioned compact stellar objects.