distorted-wave Born approximation (DWBA), the incident waves are solutions to a part of the problem that is treated by some other method, either analytical or numerical. The interaction of interest is treated as a perturbation to some system that can be solved by some other method. For nuclear reactions, numerical optical model waves are used. For scattering of charged particles by charged particles, analytic solutions for coulomb scattering are used. This gives the non-Born preliminary equation and the Born approximation Other applications include bremsstrahlung and the photoelectric effect. For a charged-particle-induced direct nuclear reaction, the procedure is used twice. There are similar methods that do not use the Born approximations. In condensed-matter research, DWBA is used to analyze grazing-incidence small-angle scattering. See also Born series Lippmann–Schwinger equation Dyson series Electromagnetic modeling Rayleigh–Gans approximation References Wu and Ohmura, Quantum Theory of Scattering, Prentice Hall, 1962 Scattering theory Max Born