How Do You Calculate Compton Scattering and Pair Production Cross-Sections?

[Eryndel]

First time visitor to this cool little forum we have here.

So I'm trying to figure out how to determine the cross-section of Compton Scattering and Pair Production when a high energy photon interacting with the Coulomb field of an atomic nucleus. I see a lot of pretty charts and/or values showing Compton slowly going down as energy increases, while pair production rises rapidly and then levels out. Usually these charts are for Al or Fe. How do they come up with these?

Specifically I'm looking on how to do this on my own, looking for sigma[Compton] and sigma[PP] as a function of E[gamma] and Z. I have a hunch that this would best be done using QED, but I might be mistaken.

As for my background, I've take a few courses in QM using Cohen-Tannoudji (sp?) and a brief survey course in particle physics using Griffiths. I've been seriously eyeing Zee's QFT in a Nutshell, and will definitely pick this up in the near future.

Any pointers on how to best solve this problem?

[This isn't a homework problem, I'm out of school and trying to keep my tools sharp. But if this is better in the Homework section of this forum, feel free to move this. My apologies, I'm new here.]

Thanks in advance.

 

[samalkhaiat]

First time visitor to this cool little forum we have here.

I wish you good luck.

Specifically I'm looking on how to do this on my own, looking for sigma[Compton] and sigma[PP] as a function of E[gamma] and Z. I have a hunch that this would best be done using QED, but I might be mistaken

Your "hunch" is right. Scattering processes are QED problems. The 8 rules menu of Feynman QED shows you how to calculate the total amplitude for any scattering process. Griffiths does that for you in Ch7, check the examples: 7.1 to 7.4



regards

sam