The continuum limit Lippmann—Schwinger equation

The number of final states in the range d kfid kt about k, k, is 

The differential cross section is again obtained from the expression (6.40) for the transition rate w,o. However, in the case of ionisation the continuum limit of j) in the definition (6.28) of is (6.8), which has two plane waves. The analogue of (6.29,6.33) for the limit as e — 0-1- of the properly-normalised quantity independent of L is 

We therefore have the following expression for the differential cross section 

Accounting for degeneracies in the initial and final states the differential cross section becomes 

In this section we first summarise the meaning of the notation for the channel and collision states with box normalisation and in the continuum limit L — 00. We then define notation for the limit 6 — 0-1- and write the corresponding integral equations. 

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