A Discussion and Generalization of Bethe's Second‐Order Approximation

Using the Howie and Whelan system a perturbation technique is presented, based on the Löwdin partioning technique, to take into account the effect of weak beams in contrast calculations. This method is a generalization of the well known Bethe second order correction method. The usual Bethe method is found in the limit of very small weak beam interaction. Some explicit situations are discussed which show the limitations of the usual Bethe method for practical calculations.