Document Type

Article

Publication Date

2004

Abstract

The stationary linear transport equation models the scattering and absorption of a low-density beam of neutrons as it passes through a body. In Euclidean space, to a first approximation, particles travel in straight lines. Here we study the analogous transport equation for particles in an ambient field described by a Riemannian metric where, again to first approximation, particles follow geodesics of the metric. We consider the problem of determining the scattering and absorption coefficients from knowledge of the albedo operator on the boundary of the domain. Under certain restrictions, the albedo operator is shown to determine the geodesic ray transform of the absorption coefficient; for “simple” manifolds this transform is invertible and so the coefficient itself is determined. In dimensions 3 or greater, we show that one may then obtain the collision (or scattering) kernel.

Publication Title

Pacific Journal of Mathematics

Volume

216

Issue

2

First Page

303

Last Page

326

Required Publisher's Statement

Mathematical Sciences Publishers

DOI: 10.2140/pjm.2004.216.303

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Analysis Commons

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