Temperature Behavior of the Thomas-Fermi Statistical Model for Atoms

The usual theoretical calculations of equations of state and specific heats, particularly at high temperatures and pressures, are dependent on the Thomas-Fermi statistical model of the atom. The mathematical description of this model involves complicated nonlinear differential equations, for which there have been an inadequate number of solutions available in the past. A number of solutions sufficiently extensive to determine the thermodynamic properties of all elements over an exceedingly wide range of temperatures and densities have been obtained with the aid of an IBM 701 Defense Calculator. The results are presented in graphical form.In addition, some of the analytic properties of the Thomas-Fermi equations have been investigated and certain approximate analytic solutions have been derived for limiting cases.