A Relation between the Electric and Diamagnetic Susceptibilities of Monatomic Gases

A relation is derived by quantum-mechanical perturbation theory, using a center of gravity argument and the Kuhn-Reiche sum rule, between the polarizability and diamagnetic susceptibility of monatomic gases. On comparison with a similar paper by Kirkwood, who uses a variational method, a criterion is derived for the validity of a perturbed wave function of the form ψ₀(1+λv), where ψ₀ is the unperturbed wave function of the normal state and v the perturbing potential energy of a uniform electric field. It is also pointed out that inclusion of an electronic interaction term σ neglected by Kirkwood removes a difficulty appearing in his paper.