An effective nonlocal potential is constructed by requiring that its Born expansion give the same amplitude as the peripheral-interaction expansion of Cutkosky. The latter is a modified perturbation expansion based on dispersion theory in which each line of a Feynman graph represents not only discrete states, but also all states lying in the continuum which have a limited angular momentum; in higher order diagrams one also has to subtract out certain contributions which are already included in lower order diagrams, so as to avoid double counting. It can then be argued that, at least if we go up to fourth order, there should be a repulsive core in the potential. The Schrödinger equation is thus solvable without cutoff in configuration space. Because of the difficulties of such a program, only a rough momentum-space calculation was carried out for $\pi \pi$ scattering with $\rho$ exchange.

• Received 8 September 1965

DOI:https://doi.org/10.1103/PhysRev.141.1532