1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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}##.

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted