Open AccessEvaluation of Some Integrals Arising in the Theory of Ionized Gases
Author(s) -
John G. Trulio,
Stephen G. Brush
Publication year - 1961
Language(s) - English
Resource type - Reports
DOI - 10.2172/1122804
Subject(s) - limit (mathematics) , component (thermodynamics) , ionization , series (stratigraphy) , physics , charge (physics) , real gas , equation of state , state (computer science) , integral equation , mathematics , electron , mathematical physics , statistical physics , atomic physics , quantum electrodynamics , mathematical analysis , quantum mechanics , ion , paleontology , algorithm , biology
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})