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A proton with momentum 3 GeV in LAB frame of reference is difussed elastically by a stationary proton. The angle of diffusion of one of the protons, in the CM system is 10º, corresponding to a moment fo 2.982GeV in LAB.

This is part of an exam problem, it then goes on to ask about energy, momentum and angle in both frames.

The doubt I have is conceptual: ¿How can there be an angle of diffusion in the CM frame? naively, I guess, one would expect the collision to be heads on in the CM frame, why is this not the case?

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Before the shock, the two particles get closer from the CM (and closer to each other) on a common line L1. After the shock, the two particles are moving away from the CM (and away from each other) on a common line L2. The angle of diffusion is the angle between the two lines L1 and L2. Chances are very low that the two lines are the same and the angle is null. Think about the movement of two balls on a pool : except if the first ball strikes the second ball exactly in the center, there will be a deviation of the trajectory.

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