Effect of long-range part of the potential on the elastic S-matrix element

Abstract

The quantum mechanical three-body Schrödinger equation can be reduced to a set of coupled differential equations when the projectile is easily breakable into two fragments and when scattering is a heavy stable nucleus. It has been found that the diagonal coupling potentials in this model take the inverse square form at sufficiently large radial distances and non-diagonal part of coupling potentials can be treated as sufficiently short-range to guarantee that numeral calculations are feasible. We will show that this long-range part of the potential has a small contribution to the elastic S-matrix element.