The angle by which a particle is deflected from its original trajectory after a collision.The scattering angle is the angle between a particle's initial direction of motion and its direction after a collision with another particle or a potential field. It is a fundamental observable in physics, encoding information about the forces and structure of the scattering target. In particle physics, measuring scattering angles reveals the internal structure of protons and nuclei; in astrophysics, it helps trace the paths of cosmic rays; and in materials science, it is used to probe crystal lattices.
The concept dates back to Ernest Rutherford's 1911 gold foil experiment, where the scattering angles of alpha particles revealed the existence of a tiny, dense nucleus. The theoretical framework was later formalized in quantum mechanics by Max Born and others.
When a projectile approaches a target, the interaction potential deflects it. The scattering angle depends on the impact parameter (how 'off-center' the collision is), the energy of the projectile, and the shape of the potential. By measuring the distribution of scattering angles (the differential cross-section), physicists can infer the potential and the target's properties. For quantum scattering, the angle distribution also shows interference patterns due to wave nature.
Scattering angles are used in medical imaging (e.g., X-ray diffraction), in particle accelerators to identify new particles, and in neutron scattering to study the structure of materials.
In Rutherford's experiment, most alpha particles passed straight through with zero scattering angle, but a tiny fraction bounced back at angles greater than 90 degrees—a result that was 'as surprising as if a cannonball rebounded from a sheet of paper.'



