Theory of meson exchange potentials for nuclear physics

Abstract

A diagrammatic technique for relating the nucleon-nucleon potential description to an underlying meson exchange description is explained. Because potentials are instantaneous interactions and meson exchange interactions time delayed a special type of diagram, the folded diagram, is needed. We illustrate the general rules by calculating some one- and two-meson exchange contributions to the potential, and some one-meson exchange contributions to the effective operator for proton-proton bremsstrahlung. The potential is Hermitian and defined so that the solution of Schrödinger's equation gives correctly the phase shifts for energies below the first inelastic threshold. The effective operator, when used in conjunction with these solutions, permits calculation of other observables. The well-known off-energy-shell ambiguity for elastically equivalent potentials corresponds to our discovery of a class of such diagrammatic expansions. We are able to find one that is much simpler than any other, and hence, preferred for practical calculations. The two-meson exchange contribution to the potential, using this prescription, is examined in the case of spinless “nucleons” exchanging scalar, isoscalar mesons, and in the case of nucleons exchanging pions. In the former case we find a substantial cancellation; we use the latter calculation to compare our method to that of Partovi and Lomon. The one-meson exchange terms of the effective operator are shown to contain terms that are “potential-dependent;” these terms have the important role of correcting the theory so that off-shell ambiguities of the potential will not affect physical observables.