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Atomic form factor

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data
    1. Let -Q charge be uniformly distributed over a sphere radius R. Find [itex]f(|\vec{G}|)[/itex], the atomic form factor.
    2. Let the incident xrays have wavelength [itex]\lambda[/itex], determine the dependence of [itex]f(|\vec{G}|)[/itex] on [itex]\theta[/itex], the scattering angle.

    2. Relevant equations

    [tex]f(|\vec{G}|)=\int_0^{\infty} \rho(r) e^{i \vec{G} \cdot \vec{r}} dr [/tex]

    3. The attempt at a solution

    [tex] \rho(r) = -Q \delta (r-R) [/tex]

    [tex]\vec{G} \cdot \vec{r} =\vec{G} \cdot r \hat{r} = |G||r| cos(\theta) [/tex]

    [tex]f(|\vec{G}|)=\int_0^{\infty} -Q \delta (r-R) e^{i |G|r cos(\theta)} dr [/tex]

    My instinct would be just to say:

    [tex]f(|\vec{G}|)=-Q e^{i |G|R cos(\theta)} [/tex]

    But this leaves the term to be imaginary. Any ideas?
  2. jcsd
  3. Jan 29, 2010 #2
    anyone have any thoughts?
  4. Jan 30, 2010 #3
    Well, your calculation is correct from what I can see. What is the problem with an complex form factor?

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