Analytic solutions of the Schrödinger equation are presented for a repulsive ${1/r}^3$ potential. They lead to an in-depth understanding of scattering by a pure repulsive ${1/r}^3$ interaction including exact cross sections and phase shifts. Scattering by any potential which is asymptotically a repulsive ${1/r}^3$ is also discussed.

• Received 3 November 1998

DOI:https://doi.org/10.1103/PhysRevA.59.2778