Why 2 photons are formed from positron-electron annihilation at rest

[phosgene]

This isn't a homework question, though it kind of relates to a practical I did recently. Sorry if it's posted in the wrong section!

So, why are only 2 photons formed from positron-electron annihilation at rest? I understand why you can't have just one, as then you won't get conservation of momentum. But why do you only get 2 photons instead of say, 10 or 1000? I've looked up various particle physics textbooks and one on radiation detection, but they only explain that you can't get a single photon.

 

[mfb]

As far as I know, you can get any number of photons except 1, but the reaction to two photons is really dominating, as it just needs [strike]one[/strike] two vertices ("interaction points") (edit: fixed) in the Feynman graph. In addition, the photons always have the same energy, so it is easy to detect.

3-photon annihilation, suppressed by a factor of 370.

Positronium is interesting, as it has one short-living state (which decays to two photons) and one long-living state (which cannot do this, and has to decay to three photons)

 

[phosgene]

Thanks for the reply. I don't quite understand, though. I thought that positron-electron annihilation always occurs when a positron captures an electron to form positronium, which then decays. If positronium can only decay into 2 and 3 photons, doesn't this rule out the decay into other numbers of photons?

 

[mfb]

Those numbers for positronium are just the most likely numbers (as all lower numbers are forbidden), and a positron/electron pair does not have to form positronium to annihilate.

 

[andrien]

but the reaction to two photons is really dominating, as it just needs 1 vertex ("interaction point") in the Feynman graph

there are two vertex in annihilation.There is a electron or/and positron internal line between the two photons.

 

[mfb]

Oops, thanks. I imagined two and wrote one.

 

[phosgene]

Ah, I see. I guess the other mechanism is a plan old collision? The wording of Das and Ferbel's intro to nuclear and particle physics seemed to imply that positronium always formed before an annihilation, so I just assumed that it formed in a collision.

 

[snorkack]

This:
http://arxiv.org/pdf/hep-ph/0310099v1.pdf
gives the theoretic ratios of 4 photon annihilation to 2, and 5 photon annihilation to 3, in the region of 1/1 000 000. Experiments are similar, though they have measurement errors.