I am going to embark on a project involving deep-inelastic scattering but first I am trying to do some really basic background reading to get me up to task. My only background in particle physics is Griffiths chapters 1-5, and most papers I find on the topic are really advanced (I don't expect papers to be expository in nature anyway).

I kept seeing the following terms pop-up but I can't find any "beginners" explanation for them on the web. I was wondering if someone could give me an expository explanation on the following section found on pages 7-8 of this document. In particular:

In summary: I have managed to read up on the layman explanation of deep-inelastic scattering and what it is supposed to do. But upon venturing further (i.e. once symbols and jargons appear), I can't find any explanation for the symbols and jargons which they use, or how I should understand the subject. Any exposition/references would be greatly appreciated!

  • 1
    $\begingroup$ Could you separate this into three separate questions? I'd say edit the last two questions out of this post, and post them separately, so you make three posts in all. We prefer to have one question per post. $\endgroup$
    – David Z
    Jun 11, 2014 at 7:05
  • $\begingroup$ What if I edit this question to make it more coherent? These are all mentioned under a single section of "scaling and the parton model" in the document I raised, and I'm really looking for a coherent (and layman) explanation of that section. $\endgroup$
    – suncup224
    Jun 11, 2014 at 7:09
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    $\begingroup$ No, they are three completely separate questions. Just because they happen to be mentioned in the same section of the document doesn't make them the same question. Though I guess you could kind of combine the first two by asking "What is Bjorken scaling?" and mentioning that you don't know what the structure function $F_2$ is. $\endgroup$
    – David Z
    Jun 11, 2014 at 13:13
  • $\begingroup$ David is right about this. They are distinct questions, and while you are seeing them come up together that is down to the nature of the system you are reading about: in other systems they can come up separately. $\endgroup$ Jun 11, 2014 at 20:13
  • $\begingroup$ Okay, I have removed the other two questions. Will post them separately $\endgroup$
    – suncup224
    Jun 12, 2014 at 3:04

1 Answer 1


Maybe I am oversimplifying but these answers are read also by others with similar concerns so I will start simply.

In classical physics it is easy to measure the cross section of a target. We take a tape measure and get its cross section from the geometry. For objects at a distance we use light intelligently and with corresponding geometrical formulas get the cross section.

We could get it by shooting at a small inaccessible target and counting the hits from the miss and the geometry of bullets and space arrive at a cross section of the target in a messy way ( light is much better).

When we reach the elementary particle sizes of nanometers and less, we enter the quantum mechanical regime and the only tools we have really are in shooting particles against each other and looking at the outgoing particles. Given the quantum mechanical probability formulation the counting of hits and misses gave a "cross section" in centimeters-squared, the same concept as in classical mechanics, but this time dominated by the probabilistic nature of the beast. The formulae used were solutions of quantum mechanical equations and these lead to a formula given in your link as formula 1) . Quantum mechanics said that the scattering could be described in this functional form, where the functions W1 and W2 would be checked by measuring them in scattering experiments. As electrons were the smallest in mass particle that one could manipulate in the lab, electrons were used as beams and protons as targets.

This blog entry might help you, it goes through the history of the terminology.


In the picture above, on the left, experimental data show the form factors (extracted from the scattering rate) as a function of the square of the momentum transfer, q^2. The factors behave according to a simple "dipole formula", which implies that the proton looks like a rather simple object, with a distribution of charge and magnetic moment following an exponential distribution. Note that the dependence on momentum transfer of the form factors implies that the electron is seeing an object with an extended structure, with a well-defined characteristic size.

In this way using the cross section formula we can get a size for the proton which is dependent on the four momentum transfer of the incoming electron, the higher the Q**2 the smaller the proton.

These form factors were tabulated and used to confirm the simple model, that the proton behaves as a type of uniform distribution of matter.

So the data conforms to a simple model, but this does not yet explain much of what the proton and the neutron actually contain. In order to gather more information, higher-energy interactions are required.

This simple picture was modified once higher energies were reached, because it became apparent that, (as in the Rutherford experiment), the electrons were hitting a hard core , a second level of scattering from charges within the proton.

In general, structure functions are mathematical functions entering the cross section calculations which can be measured and tabulated and tested against models.

  • $\begingroup$ anna v: "[...] the counting of hits and misses gave a "cross section" in centimeters" -- Not rather "square centimeters", for instance? "In classical physics it is easy to measure the cross section of a target. We take a tape measure and get its cross section from the geometry." -- More specificly, this may only apply to the cross section if the projectile(s) and/or the target are neutral. $\endgroup$
    – user12262
    Jun 13, 2014 at 5:48
  • $\begingroup$ @user12262 corrected the cm to cm**2 of course. tape measures have no problem. If one would try to measure a crossection classically of charged targets and projectiles one would again have to use the concept of form factors, a modification to get the geometrical crossection. $\endgroup$
    – anna v
    Jun 13, 2014 at 5:56

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