AN ASYMPTOTIC THEORY OF REACTION CROSS-SECTIONS FOR ION-ATOM COLLISIONS - SHORT-RANGE FORCES

We investigate an analytical method for calculating a second Born correction for direct reaction cross sections produced by asymptotically fast screened projectiles. We provide a topical proof of the response theorem which leads to a simple formula in terms of an on-shell two-body t-matrix element at an energy determined by a vector form factor. The theory has the advantage that it provides an error estimate. A practical application of the method is presented for the 1s-2s excitation of a hydrogen-like atom. The cross sections are compared to those obtained from an expansion in a finite Hilbert basis set.