Scattering Theory: Born Series

A 2 Scattering Theory: Born Series

Inverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension.

The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...

Numerical studies of the inverse Born series for diffuse waves

Optical tomography is a recently proposed imaging modality that uses diffuse light to probe structural variations in the optical properties of random media [1–3]. The associated inverse scattering problem for diffuse waves consists of recovering the spatially-varying absorption of the interior of a domain from boundary measurements. The standard approach to this problem is often framed in terms...

Fermion Scattering by a Schwarzschild Black Hole

Abstract We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor part...

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  Replacing the wormhole geometry with an equivalent medium using the perturbation theory of scattering and the Born approximation, we have calculated the differential scattering cross section of electromagnetic waves by a traversable wormhole. It is shown that scattering at long wavelenghts can essentially distinguish wormhole from ordinary scattering object. Some of the zeros of the scatterin...