Low-energy He-He interactions with phenomenological potentials

The low-energy atom-atom scattering properties are studied for various combinations of He isotopes interacting via a family of semiphenomenological potentials. Some of the potentials bind the (⁴He)₂ molecule and some do not, and it is observed that molecular beam scattering measurements at energies currently accessible cannot resolve the difference between the two types of potentials. Our results are discussed within the framework of possible measurements to resolve this discrepancy. We present a method for solving the Schrödinger equation which is uniformly applicable for both bound and scattering state solutions and which is particularly suited to the types of potentials describing interactions for the rare gas atoms.