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The cross section within the small angle approximation for particles in a solution reads

$\frac{d \Sigma}{d \Omega} \equiv n \Delta \rho^2 V_p^2 \left| S(\mathbf{q})\right|^2 P(\mathbf{q})$

where the particle density is given by

$n = \frac{N}{V}$

The scattering length density contrast between the particles and the solvent reads

$\Delta \rho(\mathbf{r}) = \rho_b(\mathbf{r}) - \rho_s$

$P(\mathbf{q}) = \left| \frac{1}{V} \int dV e^{-i \mathbf{q} \cdot \mathbf{r}} \right|^2$