Renormalized Born Approximation

A well-known defect of the Born approximation is that it often yields cross sections correct in shape, but orders of magnitude too large. A method is suggested for renormalizing approximate wave functions so that their amplitude is correct, not asymptotically but at some other more appropriately chosen point. This leads to an expression for the T matrix which is independent of the over-all amplitude of the approximate function. The method is applied to a plane wave Born approximation and a simple distorted-wave Born-approximation calculation of scattering from a square well. The renormalized results are in excellent agreement with exact calculations.