Nonsingular integral equation for two-body scattering and applications in two and three dimensions

Abstract

We introduce a new nonsingular scattering integral equation, which is suitable for the investigation of the total (also off-shell) transition matrix in arbitrary dimension n≥2. In particular, the low-energy properties are derived and lead, in connection with spin-polarized atomic hydrogen H↓, to the low-temperature behavior of two- and three-body surface processes. In addition, for three dimensions the method leads in a natural way to a separable approximation to the T matrix for all energies, with the possibility of formulating a procedure for optimizing this approximation. To show the practicability of the equation we also present numerical results for both n=2 and n=3.