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Isotropic material fitted by Ornstein-Zernike form

  1. Mar 21, 2017 #1
    I have known what Ornstein-Zernike equation is. I try to plug in the form as follow to the isotropic materials:
    Still, I cannot show the pair correlation function as follow.

    Can anyone know what I have missed?
  2. jcsd
  3. Mar 22, 2017 #2
    I don't know if this will help but I get the result you are looking for by evaluating the integral,$$\frac{N_c}{4\pi^3r}\int_{-\infty}^{\infty}dk\frac{e^{-ikr}}{1+k^2l_c^2}$$
    by closing the infinite semi-circle in the lower half of the complex plane and using the residue theorem.
    Last edited: Mar 22, 2017
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