= Right-angle Compton scattering in the centre-of-momentum frame
For a <photon> and a massive particle with zero total <momentum>, their momenta are opposite and equal. Conservation of total <energy> fixes the same <momentum> magnitude before and after elastic scattering, independently of direction. A right-angle <photon> turn therefore makes the recoiling particle move perpendicular to the original <photon> direction in that frame. Transform both <velocity> components, or the complete <four-momentum>, to obtain the laboratory recoil; a transverse component is reduced by the boost <Lorentz factor> when the particle has zero longitudinal <velocity> in the zero-momentum frame.
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