Take the differential cross-section and integrate over &phgr; which is either the azimuthal angle n about n' or the azimuthal angle of n' about n.
To get we must multiply by &egr;(1-&bgr; &mgr;e) and a &dgr;-function with the following argument:; and then integrate over &mgr;e'
Integrating through the &dgr;-function eliminates with the folloing replacement
and one picks up a factor ofrom the integration over the &dgr;-function:
we have added the extra factor -1 since it is the absolute value which is required
It is sort of obvious that this is just (1-&bgr; )dSigmadDelta[&dgr;,&bgr;,] which we now verify:
To get we instead integrate through the &dgr;-function which eliminates with the following replacement
and one picks up a different factor from the integration over the &dgr;-function:
(no -1 required here).
It is not so obvious why this is just (1+&Dgr;)(1-&bgr; )dSigmadDelta , but it is true:
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