= Differential cross-section for scalar wave scattering
{title2=$d\sigma/d\Omega=|f_\infty|^2$}
If a unit incident <plane wave> has scattered field $\psi_s=e^{ikR}f_\infty(\widehat{\mathbf r},\widehat{\mathbf r}_0)/R+O(R^{-2})$, the differential wave scattering cross-section is
$$
\frac{d\sigma}{d\Omega}=|f_\infty(\widehat{\mathbf r},\widehat{\mathbf r}_0)|^2.
$$
It is the far-field limit of $R^2$ times the scattered-to-incident <energy flux> ratio. The common physical amplitude normalization cancels when the incident and scattered waves are in the same background medium. The formula assumes that the $1/(4\pi)$ Green-function factor, if present, is already included in the <far-field pattern>.
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