Electrostatic Energy of Multicomponent Crystal Mixtures in the Interiors of Degenerate Stars

Abstract

A new approach to calculating the electrostatic energy of solid interiors of degenerate stars has been developed. It is applicable to systems with any ionic composition. The proposed method is used to study ordered Coulomb crystals formed by two types of ions with charge numbers \(Z_{1}\) and \(Z_{2}\). Eight different body-centered cubic lattices are considered at \(x_{1}\geq 1/2\), where \(x_{1}\) is the relative number of ions with charge number \(Z_{1}\). Six of them are new, while for \(x_{1}=1/2\) and \(1/4\) the results for electrostatic energy coincide with those known earlier. All obtained results are approximated by an expression convenient for practical use.