Free paths and transport phenomena in gases and the quantum theory of collisions. II.—The determination of the laws of force between atoms and molecules

Abstract

The quantum theory has provided a means of calculating the interaction energies of two atoms by a perturbation method. It appears that, the short range interaction forces are due mainly to electron exchange phenomena between the two atoms, while the van der Waals forces arise from mutual polarization effects. The theory gives the first of these forces in the first approximation, while the van der Waals forces appear only in the second approximation, At large distances, where the interaction is small, it is somewhat surprising that the first approximation is not sufficient, and one is led to doubt the accuracy of the method when applied at distances at which the first and second approximations give comparable results. At these distances the mutual potential energy is comparable with the mean kinetic energy of a gas atom at ordinary temperatures, and it is therefore clear that a study of gas-kinetic collision phenomena should provide a satisfactory test of the validity of the perturbation method in this region. It is the object of this paper to carry out a number of calculations with this aim in view. In a previous paper the quantum theory of collisions was applied to gas-kinetic collisions, and it was shown that, although the classical theory can be used with accuracy to determine the law of force from viscosity and diffusion phenomena associated with heavy gases, it cannot he applied with safety to hydrogen and helium. The method to he used in such cases was given, and it was also shown that the existence of a definite total collision area—a feature of the quantum theory of scattering by a centre of force, the potential of which falls of more rapidly than r -2 at large distances—provides a further means of determining the law of force. As this collision area can now be directly measured with accuracy by molecular ray experiments, the range of applicability of tins method is considerably greater than that of methods based on transport phenomena.