Evaluation of Some Integrals Arising in the Theory of Ionized Gases

In some recent theories of the equation of state of classical ionized systems, the free energy depends on integrals of the form {integral}{sub 0}{sup {infinity}}[e{sup -{beta}V{sub s}}-1+{beta}V{sub s}-{beta}{sup 2}V{sub s}{sup 2}/2]r{sup 2}dr, where V{sub s} is a "screened" potential obtained from the real potential by summing certain infinite series of diagrams. This integral has been tabulated for V{sub s} appropriate to a potential {+-}(e{sup 2}/ r)(1 - e{sup -{gamma}r}). The equation of state is also given for a one-component electron gas in a uniform background of positive charge (limit{gamma}{approaches}{infinity})