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 model. First, an algorithm to solve the nonlinear equation of the 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 Nystr{\"o}m's method. 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.