Dielectric Constant of Simple Gases

A general expression for the second dielectric virial coefficient for a rare gas is derived by a simple cluster method. The resulting formula requires for its evaluation a knowledge of the exact form of the polarizability of a pair of interacting atoms as a function of their separation. Previous analyses have replaced this exact form by its asymptotic long‐range limit. To explore the validity of this approximation, we use metallic spheres as a model of atoms. For this model, it is possible to determine the polarizability exactly by solving Laplace's equation in bispherical coordinates. It is found that the exact expression is sharply peaked at contact, which suggests that for real atoms overlap effects are of paramount importance. Comparison of the exact and asymptotic forms shows the latter to lead to a second dielectric virial coefficient which is too small by a factor of about 2.

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