Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential cross-section divergence

  1. Jul 24, 2008 #1
    Hello, I was wondering if anyone could explain the troubling divergence here of the differential cross-section for rutherford scattering for [tex]\theta = 0[/tex]. I know it must have something to do with the fact that the em force extends to infinity, which makes sense to me for the [tex]total[/tex] cross section.. Why would the differential be 0 for [tex]\theta = 0[/tex] and not over all angles?

    [tex]\frac{d\sigma}{d\Omega} \theta = -\frac{b}{\sin \theta}\frac{db}{d\theta}[/tex]

    Thanks..
    Anna
     
  2. jcsd
  3. Jul 24, 2008 #2
    Hi, and welcome on PF,

    the formula
    [tex]\frac{d\sigma}{d\Omega} = \left|\frac{b}{\sin \theta}\left(\frac{db}{d\theta}\right)\right|[/tex]
    is not the Rutherford formula. It is hard sphere scattering, and is merely geometrical.

    Rutherford formula is
    [tex]\frac{d\sigma}{d\Omega} = \left(\frac{q_1q_2}{4E\sin^2 (\theta/2)}\right)^2[/tex]

    I have no clue whether you are refering to the optical theorem which relates the total cross section to the forward amplitude.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Differential cross-section divergence
Loading...