Electron-proton scattering

[Aki]

How does electron proton scattering work?

[Qfwfq]

In many different ways! Starting from simple Coulomb scattering on to Deep Inelastic Scattering and diffractive DIS.

 

I'm not sure exactly how much detail you're asking for, let's start with the simplest: they have opposite electric charges, so they attract each other, if they fly past each other they are too fast to become a H atom but the force between them will alter their momenta. Hence their velocities will be changed, especially that of the lighter electron and especially in direction.

[Aki]

I mean how would that look like on a Feynman diagram?

[Qfwfq]

The diagrams change, obviously all having the same ingoing lines, e- and proton.

 

In elastic cases the outgoing lines are also those. In the Coulomb case they are connected, at the least, by a gamma line between the two vertices. Diagrams can be more complicated, even in other elastic cases.

 

A good book to look them up, for startsies, might be Bjorken & Drell. I'm quite sure it even includes DIS but perhaps not the more recently investigated diffractive variety of it, I'm less sure of that.

 

:)

[Aki]

Well in electron-electron scattering, one electron releases a photon, and the other electron absorbs it. The absorption causes the second electron to change its direction, to move away from the first electron. Similarly, the first electron moves back as it changes its momentum. So overall the electrons repel.

 

So I'd like to know why/how does an electron get attract to a proton.

[Qfwfq]

Ah, yes. Now I see what the problem is. Oh dear... it's not a simple matter, actually. Relativistic Quantum Field Theory isn't a simple matter at all!!!

 

The Feynman diagrams are instrumental to RQFT and they are a depiction of a whole mathematical apparatus that's very complicated indeed, I could never go into it in detail here. It has several mysteries, including the one you point out. Don't take the diagrams quite tooooooo literally, despite their great descriptive value. They are really just a trick that helps in calculating the cross sections which can then be measured. For one, even to describe the one single process, the simplest diagram gives the main contribution, quite often compatible with the final value, but formally the amplitude would be given by an infinite number of them. This has to do with Fock space.

 

First of all, the exchanged photon is called a virtual photon, it is somewhat different from a free one that is propagating through space. You can even boil it down to the fact that it represents the EM field between the two charges. Any EM field, as described classically by the Maxwell equations, can in principle be represented in this manner but it would be complicated to have the whole picture exactly. The is a calculation of RQFT, somewhat complicated, which derives the Coulomb potential between two charges quite exactly and even without the difficulties of UV or IR divergences, renormalization or whatnot. This is highly comforting to RQFT as a description of interactions.

 

A simple figure of speech, often mentioned in courses, is to think that the photon leaves one of the two charges with a momentum pointing away from the other and then, virtually, arrives at the other charge and is absorbed. A bit counter-intuitive, just like many other things that work fine all the same. A virtual particle can do some quite odd things......... virtually. :)

 

The book I mentioned yesterday, although not the only one, is perhaps the best guide through the most basic part of the whole matter but it requires some background. BTW yesterday I was actually thinking of two books but made a muddle, the one I had in mind for DIS is Perkins, "Quarks and Leptons" I think. More experimental and less formal, and less complete on RQFT, but perhaps slightly easier to go through.

 

Don't let it keep you awake at night! :)

[Bo]

as said by qfwqf: you shouldn't take feynman diagrams to literally, and you shouldnt consider virtual photons as real photons (however, we (i at least) can't picture ourselves virtual photons, so there is a problem :))

but for one difference in e-e or e-p diagrams, is that the arrows of feynmann diagrams follow the charges, so the oppoisite charge, moves in feynmann diagrams the opposite way.

 

Bo

[Qfwfq]

the arrows of feynmann diagrams follow the charges

Hmmm... as far as I remember Bo, there is no such convention for the arrows of fermionic lines. Indeed, not all fermions are charged! The neutron, the neutrino, just for example.

 

You can always choose which particle is the anti- as long as you do so coherently. If you are working on a process with ingoing positron(s) and no ingoing electron, you might well choose the arrow to go along with the positive charge, for that pair. Suppose you are studying proton-positron collisions:

 

e+ p+ --> whatever

 

you could draw both of the ingoing lines with ingoing arrows, just for clarity. The line for an outgoing e+ would have its arrow also outgoing, while the line for an outgoing e- would have its arrow pointing back inward. An electron is an antipositron! :)

[Bo]

hmm i think your absolutely right :)

 

i shall kick my QFT teacher for teaching me wrong things :)

 

Bo

[Aki]

Well that answers my question:)

Thanks Qfwfq and Bo!

[Qfwfq]

You're welcome, Aki!

 

Bo! Don't be too harsh on your teacher! It's only a slight mistake, many could make it, easily! :)