Inverse problem for multiple scattering of fast charged particles in a mesoscopic medium

We consider an inverse problem of multiple scattering for fast charged particles propagating in an inhomogeneous medium. The scattering processes are described by the diffusion-type equation in the small-angle approximation. It is shown that by using the scattering data given on some small interval, it is possible to recover the spatial dependence of the density of the medium. This inverse problem is ill posed in the sense that small noise in the data may lead to large perturbations in ε(z) if no a priori assumptions are made about ε(z). This is clear from our presentation, since an analytic continuation of ε(z) is involved. One hopes that the proposed method can be applied to thin foils and to mesoscopic systems