The possibility of a 4He2 bound state, effective range theory, and very low energy He–He scattering

Abstract

The best available intermolecular potential for helium by Aziz, Nain, Carley, Taylor, and McConville is shown here for the first time to have a ⁴He₂ bound state. Two numerical analyses, namely, eigenvalue solution and effective range theory, are used to support this conclusion. Unlike usual chemically bound species, the binding energy of this very weakly bound level is found to be only 8.3×10⁻⁴ K, which is four orders of magnitude smaller than the potential well depth ε = 10.8 K. The scattering length for He+He collisions, determined from effective range theory, is used to calculate the elastic cross section in the very low energy limit. The results (1.878×10⁵ Ų for ⁴He+⁴He and 6.035×10² Å for ³He+³He) are consistent with measurements at the lowest velocities yet attained. In terms of the estimated uncertainties of the parameters of the potential of Aziz and co‐workers, it is shown that it is very likely that a bound state of the ⁴He₂ molecule does in fact exist.