Absorptive Peripheral Model for Three-Body Final States:NN→NNϱ

Abstract

An absorptive peripheral model for production processes involving three-body final states is developed. Motivated by the success of the absorptive peripheral model for the two-body reactions ($\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\rho}N$), the same Born approximation is incorporated as a subprocess into a double peripheral Born approximation for production of mesonic resonances in nucleon-nucleon collisions ($\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}\ensuremath{\rho}$). Absorptive effects of interactions in the three-body final states are taken into account by the method of the high-energy distorted-wave Born approximation applied successively to two-body subsystems ($\ensuremath{\rho},N$) that are then recoupled: ($N(\ensuremath{\rho},N)$). An approximation scheme for very-low-momentum-transfer events is developed from which curves predicting the characteristic shapes and magnitudes of the differential cross sections are calculated. The general formalism developed is sufficient for more detailed calculations at almost any degree of complexity in case the basic foundations of the model are found to be justified.