Method of Approximation for the Meson-Nucleon Problem when the Interaction is Fixed and Extended

It is proposed that a consistent and satisfactory method for evaluating the fixed extended source meson problem is: (a) first to renormalize the calculation by the method of the preceding paper; (b) to evaluate the fundamental quantities Lᵣ and Σᵣ by the usual weak coupling method; (c) also to use standard perturbation theory for the irreducible diagrams except when poles occur in integrations over intermediate states. Sums of diagrams in which repeated poles occur should be evaluated exactly.The proposed method is similar to but not identical with the Tamm-Dancoff approximation. The new method is applied to the pion-nucleon scattering problem.