Relativistic Effects in First Order Three-Body Calculations

The Faddeev equation for three-body scattering including relativistic features is directly formulated in momentum space without employing the partial wave decomposition. Based on a Malfliet-Tjon-type potential, the observables of three-body scattering are calculated in first order. The relativistic features considered are kinematics and boost effects, and are examined within the frame work of Poincar\'{e} invariant quantum mechanics. Differential cross sections for elastic and break-up scattering are calculated at selected energies up the GeV scale and compared to the corresponding nonrelativistic cross sections.