Transport theory for inclusive pion reactions and mean proton momentum for (. pi. ,p)

The inclusive pion inelastic scattering and absorption for energies around the (3,3) resonance region are studied in a unified way using statistical transport models. A statistical expression is derived for the mean momentum of the protons in the (..pi..,p) reaction, allowing comparison with recent rapidity measurements. Two one-dimensional models, one with ..pi.. and one with ..pi.. and ..delta.. channels, are developed, which show the target mass and beam energy dependence of the inclusive cross sections with reasonable values for the input absorption parameters. The mean momentum calculated in the two models reproduces the (..pi../sup +/,p) rapidity data with a 2N absorption process, but not with larger clusters.