Scattering theory

Scattering theory describes how incident particles or waves change direction, energy, or state through interaction with a target or potential.

Scattering amplitude: A complex quantity whose magnitude and phase encode the probability and phase shift of a scattering outcome. It translates a scattering calculation into the angular distribution measured in experiments.
Wave packet: A localized superposition of waves with different frequencies or momenta. It models an incident state with finite spatial extent and momentum spread.
Rutherford scattering: The deflection of charged particles by atomic nuclei through Coulomb interactions. Its angular pattern provided evidence for a compact, positively charged atomic nucleus.
Absorption: The transfer of incident wave or particle energy into a material or another physical channel. Scattering redirects incident energy, whereas absorption removes it from the outgoing beam.
Differential cross section: A measure of scattering probability per unit solid angle, often expressed as a function of outgoing direction. It is the principal observable predicted by the scattering amplitude.
Green's function: A function describing the response of a linear differential operator to a localized source. It encodes propagation between the interaction region and distant observation points.
Neutron diffraction: A method that uses neutron scattering to infer the structure and dynamics of matter. Neutrons reveal atomic positions and magnetic order through their scattering.
Reflection: The return of a wave from an interface into the medium from which it arrived. Reflection is a boundary response; scattering also includes redistribution into other directions and channels.
S-matrix: An operator relating incoming states to outgoing states in a scattering process. It packages all transition amplitudes between possible incoming and outgoing channels.
Boundary condition: A constraint on a solution at the boundary of a domain or at infinity. Outgoing-wave conditions distinguish physical scattering states from other solutions.

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