A Simple Absorption Model for High-Energyπ−N,K−N, andN−NScattering: Application to Charge-Exchange Reactions

A simple parametrization of the high-energy $\pi -N$, $K-N$, and $N-N$ scattering phase shifts is obtained. The partial-wave amplitudes are assumed to be purely imaginary. This representation is used to discuss the absorption in a peripheral-model description of charge-exchange reactions with incident pions, kaons, and nucleons. The Jacob-Wick helicity amplitudes are used to treat the spin dependence. The $n-p$ charge-exchange differential cross section is found to be narrow, primarily because, in the presence of absorption, the pion-exchange contribution is not zero in the forward direction. In addition the angular distribution exhibits a secondary maximum at a small angle due to one of the helicity-flip amplitudes. In contrast, the $\pi -N$ and $K-N$ charge-exchange angular distributions, determined by $\rho$ exchange, are relatively wide.