The effect of electron screening on the structure of crystals in degenerate stars

The neutron stars crust and white dwarfs consist of a degenerate relativistic electron gas and atomic nuclei arranged into a crystal lattice. The type of lattice that ions form may depend on many parameters, for example, on the external magnetic field, temperature (T), and ion number density (n). In this paper, we consider the effect of electron background polarization on the type of lattice at T = 0. Two approximations are used to describe this background. If it is described by the Thomas-Fermi model, the influence of polarization is determined only by the parameter κ_TFa, where κ_TF is the Thomas-Fermi wave number, a = (4πn/3)^−1/3 is the radius of the ion sphere and at κ_TFa ⋦ 1 the bcc lattice has the lowest energy. On the other hand, if we use the random-phase approximation for the electron dielectric function, the energy of the static lattice will be a function of κ_TF and the relativistic electron parameter x_r. In this case, the bcc lattice possesses the lowest energy at κ_TFa < 0.28 and any x_r, while at higher κ_TFa the formation of other lattice in consideration (fcc and hcp) is possible.