= Symmetric equal-mass relativistic elastic scattering
A particle of total incident <energy> $E$ and <rest energy> $E_0$ strikes an identical stationary particle. If the two outgoing paths make equal and opposite nonzero angles $\theta$ to the incoming direction in the <laboratory frame>, transverse <conservation of momentum> makes their outgoing <energies> equal to $(E+E_0)/2$. Longitudinal <conservation of momentum> and the <mass shell> relation imply $\tan^2\theta=2E_0/(E+E_0)$. The nonrelativistic limit is $\theta=45^\circ$; at large incident <energy> both paths become forward directed.
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