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# Scattering Theory

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Version 25

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

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

where the particle density is given by

$n = \frac Unknown macro: {N} Unknown macro: {V}$

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

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

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