Random-PhaseK-Matrix Approach to Absorption in Peripheral Interactions

Initial- and final-state corrections to single-particle exchange amplitudes are studied. Two multichannel $K$-matrix formalisms, which are expected to be valid for different energy regions, are developed by means of a random-phase approximation, and two similar absorption formulas are derived. Both reduce to the Gottfried-Jackson form for weak absorption, but give more absorption in the lower partial waves. The models are applied to the reactions ${\pi }^{\pm }p\to {\pi }^{\pm }p$ for scattering angles near 180°, and to the reaction ${\pi }^{-}p\to {\pi }^{0}n$ for small momentum transfer. It is found that the improved absorption models do not solve the problem found in earlier work of failing to fit the energy dependence of the cross sections. However, the increased absorption makes it possible to fit the data in the 4-10 BeV/c region by an arbitrary choice of absorption parameters.