How Can We Derive the Wavelength Sum Formula in Electron/Positron Annihilation?

[Feynmanfan]

Well, I've been trying to figure out how to prove that when a positron and an electron annihilate and two photons are produced, the addition of their wavelengths equals

L1+L2=Lcompton(1-cos(theta)) where theta is the angle that separates both photons.

It's a relativity problem I guess. I keep trying E^2=Eo^2+c^2p^2 and other formulae but get no result.

Thanks for your help

 

[vincentchan]

What is L?

 

[Nylex]

I think he means lambda.

 

[dextercioby]

Who's wavelengths are u referring to...?Draw a diagram (not the Feynman diagram,it's useless) and use conservation of 4 momentum...

Daniel.

 

[vincentchan]

Draw a diagram (not the Feynman diagram,it's useless) and use conservation of 4 momentum...

Just in case the Original poster hasn't learned 4 vactor yet...

here is another way to approach this problem:
Use conservation of energy and momentum...
the algebra might be a little bit messy, this is college level problem, don't expect you can finish it in 10 minutes

 

[dextercioby]

He's Feynmanfan,he SHOULD know everything about Feynman diagrams & 4momentum conservation.



Daniel.