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Form Factor - Simply take the real part?

  1. Apr 22, 2015 #1
    1. The problem statement, all variables and given/known data

    Show that the Form factor is ##\frac{3(sin x - x cos x)}{x^3}##.

    2013_B4_Q4.png
    2. Relevant equations


    3. The attempt at a solution

    I know that the form factor is simply the fourier transform of the normalized charge density:
    [tex]F(q) = \int \frac{\rho}{Z} e^{-i (\Delta \vec k) \cdot \vec r} d^3 r [/tex]
    [tex]= \int_0^R \left( \frac{\rho_0}{\frac{4}{3} \pi R^3 \rho_0} \right) e^{i \left( \frac{ q}{\hbar}\right) r} \cdot 4 \pi r^2 dr [/tex]
    [tex] = \frac{3}{R^3} \int_0^R r^2 e^{-i \left( \frac{q}{\hbar} \right) r} dr [/tex]

    Do I simply take the real part of this integral? Or do I have to do some form of complex/contour integration?

    I tried taking only the real part, which gave the wrong asnwer: ## F(q) = \frac{3\left(x^2 sin (x) - 2x cos(x) - 2 sin (x) \right)}{x^3}##.
     
  2. jcsd
  3. Apr 24, 2015 #2
    Solved it.
     
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