Rutherford scattering

This is a placeholder entry. Rutherford scattering is the classical elastic scattering of a charged particle off a fixed target charge via the Coulomb interaction, following the hyperbolic trajectory of inverse-square central-force motion. The differential scattering cross-section worked out by Ernest Rutherford in 1911 to fit his gold-foil alpha-scattering data was dσ/dΩ = (zZe²/4E)²/sin⁴(θ/2), where z and Z are the projectile and target charges and E is the projectile kinetic energy. The sin⁻⁴(θ/2) small-angle divergence is characteristic of the long-range Coulomb potential and distinguishes it from short-ranged nuclear-force scattering.

In §10.5 bremsstrahlung, Rutherford scattering provides the classical trajectory of the electron passing through the Coulomb field of a tungsten nucleus: the sharp transverse acceleration at the hyperbola's perihelion produces the bremsstrahlung radiation pulse. The full quantitative treatment of Rutherford scattering — including the relativistic Mott and Dirac extensions, the screening of the Coulomb potential by atomic electrons at large impact parameters, and the breakdown of classical scattering when the de Broglie wavelength becomes comparable to the impact parameter — belongs to a later branch (quantum mechanics or nuclear physics).