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anon134
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Homework Statement
1. Let -Q charge be uniformly distributed over a sphere radius R. Find f(|\vec{G}|), the atomic form factor.
2. Let the incident xrays have wavelength \lambda, determine the dependence of f(|\vec{G}|) on \theta, the scattering angle.
Homework Equations
f(|\vec{G}|)=\int_0^{\infty} \rho(r) e^{i \vec{G} \cdot \vec{r}} dr
The Attempt at a Solution
\rho(r) = -Q \delta (r-R)
\vec{G} \cdot \vec{r} =\vec{G} \cdot r \hat{r} = |G||r| cos(\theta)
f(|\vec{G}|)=\int_0^{\infty} -Q \delta (r-R) e^{i |G|r cos(\theta)} dr
My instinct would be just to say:
f(|\vec{G}|)=-Q e^{i |G|R cos(\theta)}
But this leaves the term to be imaginary. Any ideas?