# Relativistic Differential Cross-section

dQ is the invariant Lorentz phase space factor

and F is the flux of incoming particles

where is the relative velocity between the particles in the frame where particle 1 is at rest

Using the relativistic definition of energy

Letting be the energy of particle 2 wiith respect to particle 1, the relativistic energy equation can be rewritten such that

where similarly is defined as the momentum of particle 2 with respect to particle 1.

The relative velocity can be expressed as

The invariant form of F is

where in the center of mass frame

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In the center of mass frame