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The reciprocity equation for reaction cross section reads

$$ka^{2}\sigma_{ab}=kb^{2}\sigma_{ba}$$ or $$pa^{2}\sigma_{ab}=pb^{2}\sigma_{ba}$$

Here

$\sigma_{ab}$ is the total reaction cross section for the incoming channel a to outgoing channel b. ka and pa are the wave number and momentum for channel a respectively. Similarly for channel b.

My question is how can one justify the multiplication by momentum square on physical grounds. That is what exactly are these quantities, Number of scattered particles per second etc.

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  • $\begingroup$ Number of detected not scattered particles. $\endgroup$
    – SAKhan
    Commented Apr 21 at 6:23
  • $\begingroup$ Thanks @Qmechanic $\endgroup$
    – SAKhan
    Commented Apr 21 at 7:18

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