Recoil and correlations in pion double scattering

The contribution to the optical potential due to double scattering of a pion by a pair of correlated nucleons has been calculated for nuclear matter taking account of nucleon and delta kinetic energies. The calculation includes a variety of field theoretical effects due to crossed processes and all possible time sequences of the two scattering events including overlap in time. For sequential processes, where the first scattering is complete before the second starts, it is found that inclusion of kinetic energies of the nucleon and delta reduces the contribution drastically. The contribution of these sequential processes is about 2% of the first-order optical potential as contrasted with about 50% at $T_{\pi }=140\mathrm{}$ MeV when the fixed scatterer approximation is employed. The most important correlated double scattering contributions arise from the field theoretical effects which yield about 8% of the first-order optical potential at $T_{\pi }=0\mathrm{} \mathrm{and} 140$ MeV. Thus, the net contribution of correlated double scattering processes is about 10% of the first-order optical potential. Since the double scattering of the pion by a correlated nucleon pair is a major contributor to the Ericson-Ericson effect, the present work suggests reduced importance of the effect.