  Atomic and molecular breakup reactions, such as multiple-ionisation, are
described by a driven Schr\"odinger equation. This equation is equivalent to a
high-dimensional Helmholtz equation and it has solutions that are outgoing
waves, emerging from the target. We show that these waves can be described by a
low-rank approximation. For 2D problems this it a matrix product of two
low-rank matrices, for 3D problems it is a low-rank tensor decomposition. We
propose an iterative method that solves, in an alternating way, for these
low-rank components of the scattered wave. We illustrate the method with
examples in 2D and 3D.
