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Homework Help: Determine scattering amplitude for atomic charge which is spread as wavefunction

  1. Oct 23, 2012 #1
    Determine scattering amplitude for atomic charge which is "spread" as wavefunction

    1. The problem statement, all variables and given/known data
    Derive the scattering amplitude and differential cross section for Rutherford scattering (done this). Now rederive the same quantities for the atomic charge which is "spread" with the wavefunction proportional to exp[-r/b] (don't forget to normalize the wavefunction). Compare the results.

    2. The attempt at a solution
    So I completed the first part with determining the amplitude and cross section for Rutherford scattering. However, I don't exactly understand the part about the spread atomic charge, especially when it says to normalize the wavefunction. Because the integral will not converge, isn't this wavefunction not able to be normalized? Also, how exactly would you go about incorporating the wavefunction into the Born approximation? I'm assuming it would just create a different type of potential.

    I really just don't understand the second part of the question. I should be able to carry it out once it's clarified a bit.


    *EDIT Had my limits wrong for integration, changed from 0 to infinity and it works out. Still unclear about how to use this though!
  2. jcsd
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