Differential cross-section for Coulomb scattering. The classic formula from Rutherford's gold foil experiment.
Rutherford scattering describes the elastic scattering of charged particles by the Coulomb field of a nucleus. The differential cross-section goes as 1/sin⁴(θ/2), meaning most particles scatter at small angles while very few are deflected backward. This was the basis of Rutherford's famous 1911 experiment that proved the existence of the atomic nucleus — the fact that some alpha particles bounced back from gold foil could only be explained by a small, dense, positively charged core.
The formula works well for energies below the Coulomb barrier, where nuclear forces don't play a significant role. At higher energies, deviations from the Rutherford formula reveal information about nuclear structure and the strong force.