Difference between revisions of "Limit of Energy in Lab Frame"

The t quantity is known as the square of the 4-momentum transfer

In the CM Frame

where and is the angle between the before and after momentum in the CM frame

Using the relativistic relation this reduces to

There is no scattering, or no momentum transfer since the incident momentum direction is the same as the scattered momentum direction

The maximum momentum is transfered at 90 degrees, i.e.

This can be rewritten again using the relativistic energy relation

The maximum momentum is transfered at 180 degrees, i.e.

This can be rewritten again using the relativistic energy relation

with

and

Maximum Moller Energy in Lab Frame

Since t is invariant between frames

with for

The Moller electron has a maximum energy possible of:

Minimum Moller Energy in Lab Frame

Since t is invariant between frames