# 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.