Minimum energy of a free electron in inert gases

The properties of the minimum energy W of a low-energy free electron in an inert gas are discussed. This quantity is one of the basic characteristics of the electron in problems of the formation of various charged clusters (bubbles or compacts) in low-dimensional electronic states along interfaces. A relation between the energy W and a similar energy W ₀ determined in the so-called optical approximation, where the energy W ₀ is proportional to the gas density n _g, has been obtained. Comparison makes it possible to determine the n _g dependence of the scattering length a ₀ introduced in the “optical” description of the gaseous medium and to reveal the conditions under which a ₀(n _g) may change sign, which behavior, by definition, is beyond the framework of the optical approximation and is observed experimentally.