Difference between revisions of "Limit of Scattering Angle Theta in Lab Frame"

The quantity is known as the

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 at 90 degrees since the incident momentum direction is the same as the scattered momentum direction. However, at a certain angle enough momentum must be transferred to provide the ionization energy to create a Moller electron.

For , by symmetry this implies

This can be rewritten again using the relativistic energy relation

with

and

Minimum Moller Scattering Angle Theta in Lab Frame

Since u is invariant between frames

with for

As found earlier, the Moller electron has a maximum energy possible of:

Using the relativistic energy relation,

for

Rewriting the expression relating the terms

Solving for the angle theta

The Moller electron is traveling near, but not on the beamline.