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I Evaluating Scattering Integral

  1. Apr 1, 2016 #1
    Hi,

    I really don't have a clue to solve this.

    1SR45bL.png


    I tried something like the dirac function identity:

    utoxnMx.png

    But then I saw it's dk' not dk' and couldn't got it straight.

    Can someone help me with this?
     
  2. jcsd
  3. Apr 1, 2016 #2

    DrClaude

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    Staff: Mentor

    As it is said, you have to change to spherical coordinates. The Dirac delta will then only affect the integral over r.
     
  4. Apr 1, 2016 #3
    I don't see it. dk' is not a volume element?
     
  5. Apr 1, 2016 #4
    1a83c429226b2c6a2da143ae35a00751.png

    dk' is a vector. Then I have an integral comprising of 3 terms each involving unit vectors.

    I really don't have a clue.
     
  6. Apr 1, 2016 #5
    Wait wait, I am extremely confused.

    I just have to integrate over the k' first?
     
  7. Apr 1, 2016 #6
    Mr
    6 hours and I still have no clue, can you please hold my hand and solve it with me. I mean, just say what I have to do, I will solve it, but give me instructions.

    I mean what's the deal with the dirac function and the dk', it's supposed to be a volume element and the dirac term, why isnt it delta(k-k')
     
  8. Apr 1, 2016 #7

    blue_leaf77

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    Science Advisor
    Homework Helper

    ##d\vec{k}## is a volume element. Write it as a volume element in spherical coordinate. To make the integrand even more transparent, use the cosine law to express ##|\vec{k}-\vec{k'}|^2## in terms of ##k##, ##k'##, and ##\theta##.
     
  9. Apr 1, 2016 #8
    mW21BmR.png

    How come dk' is a volume element, it's the derivative of a vector. Most textbooks, the volume element is called a d tau or a dV

    My head is a mess. It's like I completely forgot how to calculus.

    Good news: I know I'm wrong.

    Really don't see it
     
  10. Apr 1, 2016 #9

    DrClaude

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    What happened to the Dirac delta? You should do the integral over k' first.
     
  11. Apr 1, 2016 #10

    DrClaude

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    Staff: Mentor

    It's not a derivative, it is an infinitesimal vector element.
     
  12. Apr 1, 2016 #11
    It's been this the whole time?, with r being k'

    eqn_vol_e.gif

    Ps: After this I'm going to finally learn LaTeX
     
  13. Apr 1, 2016 #12

    blue_leaf77

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    Why did the Dirac delta disappear in the second equation from the last one?
     
  14. Apr 1, 2016 #13
    TEAEU8n.png


    sv97Qux.png

    This is what I got uptil now, but I have to leave.

    Thanks for help, give me feedback if you want to, and I will post update when I'm back, probably tomorrow. Thanks for the patience anyway!!
     
  15. Apr 18, 2016 #14
    Hi,

    Sorry for the late reply.

    Hope this is somewhat more clear, because last post was a bit messy. Still haven't learned LaTex.

    34XvfUc.png

    Is this valid?

    I couldn't evaluatie the last integral, because of the square.

    Do I need to use partial fractions?

    Thanks
     
  16. Apr 18, 2016 #15
    Hi myself,

    I found out I need to include something like 1- ( stuff going in the z direction after k scattering) / (stuff that would go in z direction if there was no scattering at all), so 1 - k' projected on z axis /k = 1 - (k cos theta) / k

    Yes, I'm a noob.

    So I'll start over. :')
     
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