In
mathematics and
physics,
scattering theory is a framework for studying and understanding the
scattering of
waves and
particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance
sunlight scattered by
rain drops to form a
rainbow. Scattering also includes the interaction of
billiard balls on a table, the
Rutherford scattering (or angle change) of
alpha particles by
gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the
inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of
partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a
boundary condition, and then propagate away "to the distant future". The
direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the
scatterer. The
inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.