Photon - Matter Interactions

[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

 

[sir-pinski]

Hello and welcome to our forum! I'm glad you're finding our discussions interesting and informative.

To answer your question, the cross-section of Compton scattering and pair production can be determined through theoretical calculations using quantum electrodynamics (QED) and also through experimental measurements. The values you see in the charts are likely a combination of both.

In QED, the cross-section can be calculated using Feynman diagrams, which represent the interactions between particles. In the case of Compton scattering, the diagram would involve an electron and a photon exchanging energy. For pair production, the diagram would involve a high energy photon creating an electron-positron pair.

The values in the charts may also include experimental measurements, which involve shooting high energy photons at a target and measuring the resulting particles. These experiments can be done using particle accelerators or other high energy sources.

As for determining the cross-section on your own, it would require a solid understanding of QED and the relevant equations. Zee's QFT in a Nutshell is a great resource to learn more about this topic. You can also check out other textbooks or online resources on QED to deepen your understanding.

I hope this helps and good luck with your studies! Don't hesitate to ask any further questions or share your findings with us on the forum.