Scattering is a phenomenon where a particle or wave is deviated from its trajectory due to the presence of an obstacle or force in the medium through which it travels. It represents the common ideas of "collision", "deflection" and "interaction".
Scattering phenomena are exceptionally varied and present in most if not all branches of physics. Examples include the bouncing of sound off of walls, billiard balls bouncing off of one another, light being reflected by a mirror or any other surface, electrons being deflected by atoms, sunlight diffusing in the atmosphere to give the sky its color, and high-energy collisions inside of a particle accelerator.
The obstacle deflecting the incident particle or wave can be of any nature. Often, it's another particle or some other highly-localized object. Other times, it's an idealized limitation, such as a perfectly flat surface, which is represented by a boundary condition.
Mathematically, scattering is expressed through the aptly named scattering theory, which studies how the differential equations of motion or propagation interact to form these deviations or collisions. It attempts to predict how a particle or wave will scatter off of an object or force that we understand (a direct scattering problem) and tries to reverse-engineer what the object or force is when we don't understand it, but can see how particles and waves scatter off of it (an inverse scattering problem).
In quantum physics in particular, wave-particle duality unifies particle and wave scattering phenomena. Quantum scattering is much more complex, in large part due to quantum uncertainty making it impossible to rigidly define concepts such as "trajectory" and "size", which are fundamental in classical scattering.
Elastic and inelastic#
Scattering phenomena are divided in two big categories.
In elastic scattering, all participants of the scattering are left unchanged or largely unchanged by the scattering. The namesake example is an elastic ball bouncing off a wall which, in the ideal case of perfect elasticity, retains all of its kinetic energy; the ball that bounces back to you is identical to the one you threw save for its trajectory.
In inelastic scattering, the participants are left changed by the scattering. What "changed" means depends on the the scattering phenomenon. For instance, a partially elastic ball would dissipate kinetic energy into heat when bouncing, losing it to the environment, before bouncing back with reduced strength. The ball lost energy and the system ended up with less total energy than it started. In fact, inelastic scattering is often associated with irreversibility or a permanent change in the state of the system. In many cases, elastic scattering is just the idealized limit of inelastic scattering in which one property is pushed to its theoretical limit.