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Differential scattering cross-section

If
$$
\psi\sim e^{ikz}+f(\theta)\frac{e^{ikr}}r,
$$
then the ratio of scattered radial <probability current> through $r^2d\Omega$ to the incident probability flux is
$$
\frac{d\sigma}{d\Omega}=|f(\theta)|^2.
$$

Quantum differential cross-section from a scattering amplitude

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 33B / a / Solution

Quantum differential cross-section from a scattering amplitude

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Quantum differential cross-section from a scattering amplitude

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