Estimating the order of magnitude of a ratio of two cross sections

[Chrispy92]

The question is "Make a simple estimate of the order of magnitude of the ratio of the cross sections (electron,positron->2photons) and (electron,positron->3photons)"

Now I know that cross section is proportional to (1/q^4)*(Phase space factor)*(Coupling constant) where q^2 = E^2 - p^2. We are also told that the difference in phase space factors are negligible so will be canceled in the ratio.

I think I can find coupling constant as g^(number of vertices).

My question is; can you actually find the q^2 with the information I've been given? If not am I meant to assume that it's the same for both, but then the ratio would just equal g which makes no sense. Any help would be really appreciated :)

 

[wizwom]

the three-gamma would be a secondary result from the annihilation eigenfunction.
http://www.positronannihilation.net/index_files/positron lifetime.pdf
gives the probability as 99.7% 2, 0.3% 3, so ~300:1

 

[Chrispy92]

Cheers for the reply but that's not really what I was asking. I'm really just looking for HOW an estimate can be made with the information I've been given. It might be too specific a question but I might as well try.

 

[fzero]

The cross section depends on the square of the amplitude. This is why the fine-structure constant, rather than just e turns up in observables.

 

[gareth13479]

I need to know the answer to this exact question too.
It would be really useful if someone could explain how to do it.