- #1
anon134
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Homework Statement
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.
Homework Equations
[tex]f(|\vec{G}|)=\int_0^{\infty} \rho(r) e^{i \vec{G} \cdot \vec{r}} dr [/tex]
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?