Accurate Low-Energy Atom-Atom Scattering

Abstract

Measurements of low-temperature thermodynamic properties of gases yield information concerning the pairwise scattering parameters of the atoms of the gas. For recent helium-gas experiments, the He-He scattering potential has been determined with a high degree of accuracy. This necessitates a reanalysis of low-energy He-He scattering theory with inclusion of previously neglected effects of order $\frac{m}{M}$. The formulation requires a nonlinear transformation of coordinates to ensure the correct form of the incident wave, and a novel definition of the adiabatic Hamiltonian to ensure the dissociation of the "molecular" states into correct atomic states. In addition to the usual nonadiabatic terms, we find additional terms of the same order not usually encountered. They are necessary to make the potentials vanish at infinity. It is shown that the procedure of determining a potential interaction from the second virial coefficient (scattering data) and then predicting bound-state properties (if any) is a correct one.