Use of Born Approximations inNDCalculations

Abstract

The $\frac{N}{D}$ equations have been solved with the first, second, and third Born approximations to the left-hand cut, for nonrelativistic, single-channel potential scattering, with potentials involving combinations of attraction and repulsion of different ranges, and the results are compared with the exact solution of the Schrödinger equation. It is found that for the sort of potential strengths which occur in strong-interaction dynamics, the third Born approximation is satisfactory. It is known that the first Born approximation, which is commonly used, suffers from several defects in that long-range repulsions can produce attractive effects, and "ghosts" appear on the physical sheet, and we explore the way in which the approximation breaks down. It is concluded that in dynamical calculations, such as those involving the strip approximation, much more satisfactory results are likely to be obtained if the left-hand cut is calculated from a few iterations of the potential.