On the Thomas–Fermi model: Gabor J. Kalman's contribution and numerical approximations

In this article, we would like to pay tribute to Gabor Kalman, outlining his contribution to a model widely used in dense plasma physics: the high-temperature Thomas–Fermi model. The approach of Ruoxian Ying and Kalman relies on the separation of the bound and free electrons, a physically reasonable definition of the bound electrons, a description of the source density in the Poisson equation through the electron–ion and ion–ion pair correlation functions and a determination of the degree of ionization from the minimization of the total free energy. We also report on different approximations of the function $\Phi$, which is a cornerstone of the original Thomas-Femi model.