Transition rate and differential cross section

Since the probability of the state is uniform over the whole box, the box normalisation is The properly-normalised wave-packet quantity that is independent of L is 

Next we turn to the normalisation No of the collision amplitude. Introducing the unit operator for the channel space into the definition (6.15) in the wave-packet case we have 

Using (6.27) in (6.30) we find, after some complex-number arithmetic, 

The limit e — 0-1- is kept in the formalism. We introduce a notation for it below. The important quantity in this limit is the T-matrix element 

We continue the formal development in terms of the box-normalised quantities. 

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