Long-Range Interactions in Atoms and Diatomic Molecules

Abstract

It is now many years since Castillejo, Percival, and Seaton(1) published a paper on the theory of elastic collisions between electrons and hydrogen atoms. The Schrodinger equation for the whole system was expressed in terms of the usual infinite set of coupled equations by expanding the total wave function in terms of a complete set of unperturbed states of the hydrogen atom. They then used these equations to show that the leading term in the interaction between the electron and the hydrogen atom at large separations r was — α d /(2r 4), where here α d is the static dipole polarizability of hydrogen. Throughout this article atomic units are used, so that all distances are expressed in units of the Bohr radius a 0, and one atomic unit of energy is equal to e 2/a 0. Much more recently, Seaton and Steenman-Clark(2) again used the coupled equations that represent the electron—hydrogen system to show that the next long-range term in the interaction is — α’/(2r 6), where α’ is linearly dependent upon the energy of the elastically scattered electron and can be determined analytically. Thus Professor Seaton’s interest in the derivation of the form of the long-range potentials spans a period of over 20 years, and I have great pleasure in contributing a chapter on this topic to this special volume in honor of Professor Seaton’s 60th birthday. I am indebted to him for originally stimulating my own interest in the electron—atom problem; subsequently I also became interested in two-center problems, and therefore this chapter represents a synthesis of the interests of us both.