Phase space Limiting Particles
4.1.2 Phase space Limiting Particles
Since the angle phi has been constrained to remain constant, the x and y components of the momentum will increase in the positive first quadrant. This implies that the z component of the momentum must decrease by the relation:
In the Center of Mass frame, this becomes:
Since the momentum in the CM frame is a constant, this implies that pz must decrease. We can use the variable rapidity:
this implies that as
For forward travel in the light cone:
This corresponds to the scattered electron proven earlier.
For backward travel in the light cone:
Similarly, this corresponds to the Moller electron.
For a particle that transforms from the Lab frame to the CM frame where the particle is not within the light cone:
These particles are outside the light cone and are more timelike, thus not visible in normal space. This will reduce the range in theta that Moller electrons will be detected.