# Atomic form factor

1. Jan 24, 2010

### anon134

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

$$f(|\vec{G}|)=\int_0^{\infty} \rho(r) e^{i \vec{G} \cdot \vec{r}} dr$$

3. 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?

2. Jan 29, 2010

### anon134

anyone have any thoughts?

3. Jan 30, 2010

### torquil

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

Torquil