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Problems with intuition for scattering / xsections 
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#1
Jun1514, 06:44 AM

P: 11

Dear PF,
although I've gone through many particle phyics lectures and text books, I still have problems with wrap my mind around the whole scattering theory and cross section topics. 1. Is there a deep reason why cross sections for charged, pointlike particles decrease with the centerofmass energy (the Mandelstam s) as [itex]\frac{1}{s}[/itex]? I read that it can be explained with the Heisenberg uncertainty principle, but I don't really see the connection. 2. Moving on to the differential cross section with respect to momentum transfer, I guess that the factor [itex]q^{2}[/itex] is due to the Fourier transform of the Coulomb potential. In the space picture I understand that it's less likely for a particle to interact with a Coulomb potential if it's further away from it. What is the corresponding intuition in momentum space? 3. Fermi's Golden rule tells us that the interaction rate scales with the phase space, i.e., with the number of possible final states. How can I understand this intuitively? How does an electron know before annihilating with a positron to a photon how many possibilities of decay the photon will have? Similarly, why should the electron care about the fact that quarks have colors so that the cross section for the [itex]q\bar{q}[/itex] final state is three times higher than for muons? Thanks so much in advance! 


#2
Jun1514, 07:31 AM

Sci Advisor
Thanks
P: 4,160




#3
Jun1514, 07:39 AM

P: 519

It's worth remembering too that the electron and positron don't annihilate with 100% certainty.



#4
Jun1514, 07:43 AM

P: 11

Problems with intuition for scattering / xsections
I still don't understand. So if my projectile has low momentum and the spatial resolution is low, the particle doesn't look pointlike but like a disc and I have to fold the potential with this disk? If I increase the momentum, the particle will approach its pointlike nature and the potential is folded with a delta function? In my intuition, the interaction between two particles determines how often they interact and just after this interaction I need to care about how I distribute this interaction rate among the possible final states. I'm sure I'm missing something... 


#5
Jun1514, 08:20 AM

P: 519

Yes, you are missing the idea that the number of possible final states actually determines the interaction rate in the first place.



#6
Jun1514, 09:21 AM

P: 11




#7
Jun1514, 09:53 AM

P: 883




#8
Jun1514, 05:56 PM

P: 370

As for this bit: 


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