Scattering by potentials with an inverse-square attraction

Abstract

A solution is proposed for the scattering problem with an attractive inverse-square potential function. As this solution involves absorption, potentials including an inverse-square attraction may have physical applications in the description of particle absorption. The cross sections for a square well plus inverse-square attraction are calculated. Such potentials giving S and P wave resonances near zero energy, or giving minimum cross sections at zero energy, are shown by a graph specifying the potential parameters. These results show that the optical model potential is not of this form.