Approximations for the rapid evaluation of the Thomas-Fermi equation

The simple Thomas-Fermi model is widely used to give reasonably accurate ap proximations for the electron component of the free energy in the equation of state. The well known atomic scaling means that the model can be used to efficiently cover a wide range of materials. Unfortunately, the limited va lidity of these approximations normally requires a large data table if this approach is used repetitively. In this paper we examine the scope of the a vailable approximations and show how an additional one can be constructed, such that the entire domain of density and temperature is nearly encompasse d.