Atomic Form Factor: Finding f(|G|) with λ & θ

[anon134]

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?

 

[anon134]

anyone have any thoughts?

 

[torquil]

Well, your calculation is correct from what I can see. What is the problem with an complex form factor?

Torquil