Particles enter on the left with impact parameter b and azimuthal angle φ. They scatter off a hard sphere and emerge in directions (θ, φ) on the detection sphere at infinity.
The annular incoming area equals the differential cross section: dσ = b db dφ (an area). It maps to the solid-angle patch dΩ = sinθ dθ dφ on the sphere; their ratio is dσ/dΩ.
dσ/dΩ = (b / sinθ) · |db/dθ|
For hard sphere: b = R cos(θ/2)
⟹ dσ/dΩ = R²/4 (isotropic in θ)
Drag to rotate · scroll to zoom · right-drag to pan