Modified Two-Pion-Exchange Model for Double-Charge-Exchange Processes

The eikonal method, applied to the problem of coupled channels of different mass in potential theory, is used to derive an expansion for the scattering amplitudes in powers of the potentials between different channels. Just as single-exchange processes are given approximately by the first-order term in the Born series with absorptive modifications, double-exchange processes are given approximately by the modified imaginary part of the second-order term. This result is taken over to a relativistic theory, with one-pion-exchange "potentials" connecting different channels, and used to estimate the differential cross section for the double-charge-exchange process ${\pi }^{-}+p\to {\pi }^{+}+{\Delta }^{-}$.