DWBA

The Distorted Wave Born Approximation (DWBA) is a theoretical approach in scattering theory (or, more generally, in quantum mechanics). In the Born approximation (BA), when calculating the interaction between matter and incident radiation ('scattering'), the total field inside the material is assumed to simply be the incident field. In other words, the modification of the field due to scattering events is assumed to be negligible; this is valid in the limit of weak scattering. Every particle simply sees the incident field, and scatters independently (though these scattered fields interfere with one another, giving rise to the usual appearance of scattering features in the far-field).

The Born approximation is not valid in all cases; in particular, when scattering becomes very strong, the approximation is no longer valid. As one example, at some point one must consider multiple scattering: the scattered rays can, themselves, become sources of scattering. GISAXS and other grazing-incidence techniques typically probe regimes where the Born approximation is not valid. For instance, in GISAXS, the x-ray beam will be reflected by the film-substrate and film-ambient interfaces; and may in fact undergo multiple reflections (waveguiding). This, and other dynamical scattering effects need to be accounted for in order to understand GISAXS data.

The DWBA is an extension to the BA, which accounts for higher-order multiple scattering effects. Conceptually, it accounts for the fact that the radiation field in the material should be solved under the condition that the scattering entities introduce substantial perturbations to the field. Mathematically, DWBA uses the BA as an idealized case, to which successive perturbation terms are introduced.

Mathematical Form

TBD

See Also

• Wikipedia:DWBA
• GISAXS.de Theory