A non-local model t-matrix in a quasi-three-body reaction

Abstract

The (p, 2p) cross section is calculated using local and non-local p-p effective interactions in order to distinguish off-energy-shell effects between the interactions. The quasi-three-body assumption is used in which the effects of other channels are taken into account with a complex potential. The formalism used is the distorted wave t-matrix approximation in the static limit. The distorted waves are approximated by fairly simple but realistic optical wave functions. The parameters involved in these approximate optical waves are determined using a local t-matrix and a good fit to the more complicated DWTA theory is obtained. The effects of these parameters on the (p, 2p) cross sections are indicated. Then three values for the non-local range parameter R are chosen, one of which is zero and the parameters in all the t-matrices are adjusted to fit p-p scattering as closely as possible. The theoretical calculations fit the experimental p-p energy distribution at 90° in the centre-of-mass system over a wide range of energies. Then the (p, 2p) angular distributions are calculated using the non-local t-matrices, and the local and non-local (p, 2p) cross sections are compared to experiment. It is seen that the off-energy-shell effects associated with each t-matrix are discernible and a fairly good fit to experiment is obtained with R = 0.5 fm.