Analytical representations of thermodynamic functions of Thomas–Fermi model

The main aim in this paper is to present new analytical representations of the thermodynamic functions of finite-temperature Thomas–Fermi (TF) model. First, an algorithm to solve the nonlinear equation of the TF model, which starts by rewriting it as a Fredholm integral equation, is described. Application of Newton's procedure, then, yields a sequence of linear Fredholm integral equations, which are solved using the standard Nyström's method. The use of Brachman's equation for direct computation of thermal energy of electrons is elaborated. Using extensive tabulations of the thermodynamic functions, over a wide range of scaled temperature and scaled densities, analytical representations of electron energy, pressure, ionization, Fermi-energy, and initial slope of Thomas–Fermi function are developed. Accuracy of these functions is established via computation of electron-Hugoniot and the Hugoniot of Cu and comparison with experimental (or theoretical) data up to about 20.4 TPa.