Abstract
The quantum theory of the third virial coefficient is discussed. Three types of intermolecular pair forces must be distinguished. (1) No bound or low-lying two- and/or three-body states exist. The first four terms of the low-temperature expansion of are obtained. They depend on the scattering length, the effective range, and a third length which cannot be inferred from scattering data. The limitations of the applicability of such expansions are discussed, both for and , by means of a comparison of the corresponding expansion for the second virial coefficient with detailed numerical results known for specific potentials. (2) Existence of a near zero energy level both for the two- and the three-body system. It is shown how in this case the actual potentials may be replaced by suitably matched boundary conditions on the two- and the three-body wave functions near the respective coordinate origins. It is first explained how the method applies to . Then the leading term of is explicitly determined. (3) Existence of strongly bound two- and three-body states. An approximate expression for is given by treating the single atoms and the binary and ternary compounds as a system of three ideal gases in chemical equilibrium.
- Received 20 May 1959
DOI:https://doi.org/10.1103/PhysRev.116.250
©1959 American Physical Society