Starting from the relativistic equation of motion governing quantum collision processes in many-particle systems, we shall formulate the relativistic quantum collision theory in an ab initio manner. Quantum electrodynamic effects are however in corporated perturbatively. Because heavy projectiles or ultra-high incident energies are considered, the recoil of the target is also treated. Electron-impactionization of uraniumion U91+ and proton-impactionization of hydrogen will be given as examples.