Model for Quantum Scattering of Rotons. I. Hard-Sphere Interaction

A new model is proposed for the behavior of rotons. We postulate a linear Schrodinger equation with a hypothetical Hamiltonian fit to the dispersion relation and treat the three-dimensional scattering problem. All calculations are done in closed form. As an example, we study scattering by a hard sphere, which yields the same result as that obtained in the high-energy limit of the usual Schrodinger equation. The calculated mobility gives a reasonable fit to the radii of both positive and negative ions.