# Form Factor - Simply take the real part?

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1. Apr 22, 2015

### unscientific

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

Show that the Form factor is $\frac{3(sin x - x cos x)}{x^3}$.

2. Relevant equations

3. The attempt at a solution

I know that the form factor is simply the fourier transform of the normalized charge density:
$$F(q) = \int \frac{\rho}{Z} e^{-i (\Delta \vec k) \cdot \vec r} d^3 r$$
$$= \int_0^R \left( \frac{\rho_0}{\frac{4}{3} \pi R^3 \rho_0} \right) e^{i \left( \frac{ q}{\hbar}\right) r} \cdot 4 \pi r^2 dr$$
$$= \frac{3}{R^3} \int_0^R r^2 e^{-i \left( \frac{q}{\hbar} \right) r} dr$$

Do I simply take the real part of this integral? Or do I have to do some form of complex/contour integration?

I tried taking only the real part, which gave the wrong asnwer: $F(q) = \frac{3\left(x^2 sin (x) - 2x cos(x) - 2 sin (x) \right)}{x^3}$.

2. Apr 24, 2015

Solved it.