Energy dependence of pion double charge exchange

Pion double charge exchange ~DCX! on nuclear targets has been extensively studied, both experimentally and theoretically, throughout the last two decades. Because at least two nucleons must be involved in the process, the study of DCX is a natural tool for exploring nucleon-nucleon correlations. In the course of these studies at low energies, a prominent peak in the (p,p) cross section in the neighborhood of Tp540 MeV was observed by a number of experimental groups @1–3#. The peak occurs for a variety of nuclear targets and seemingly independent of the final state. It has been claimed @3# that this peak provides evidence for the existence of a dibaryon at this energy. Before accepting such an interpretation, it is important to consider the more conventional ones. In this paper we will show ~as has been previously suggested @4–8#! that such a peak arises naturally because of the pion propagation in the conventional ‘‘sequential process,’’ in which DCX occurs through two successive pN charge exchange reactions on two neutrons @9–11#. Our calculation is based on the conventional distorted-wave impulse approximation ~DWIA!, which we briefly outline. Calculations of the reaction leading to both the double isobaric analog state ~DIAS! and the ground state are made. While other reaction mechanisms have been studied @7,12–15#, we treat DCX as a two-step sequential process. It is generally accepted now that this is likely to be the dominant mechanism for the types of transitions treated here although the other mechanisms could alter the picture somewhat. In contrast to most nuclear reaction calculations, the DCX amplitude must be evaluated in second order so that we will need to compute, not only the distorted incoming (p) and outgoing (p) pion wave functions, but also the distorted p Green function, which describes the propagation of the pion between two nucleons. The distorted pion wave functions and Green’s functions