We consider a relativistic elastic collision between a projectile of momentum p with a target atom of momentum k in a general inertial frame. We employ one space plus one time Minkowski geometry and calculate the momentum transfer vector qμ suffered by the projectile calculated via a Lorentz transformation to the barycentric frame and then eliminate k. The resulting expression for qμ reproduces several known cases, its algebraic behavior can be interpreted physically, and it leads to a simple understanding of the relativistic equipartition law.
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