An algorithm for ab initio computation of small-angle multiple scattering angular distributions

Abstract

Small-angle multiple scattering is a venerable problem in nuclear and particle-solid interaction physics and has received extensive theoretical treatment. In this paper, motivated by the need to establish the efficiency of time-of-flight spectrometers which employ thin foils to generate “start” signals, we revisit this problem. Our objective is to develop an efficient, general computational procedure which is not tied to the current state of computing machinery or specific cross sections, but which takes advantage of significant numerical-algorithmic advances which have occurred since the multiple-scattering problem was originally formulated. By introducing a new approach for dealing with the azimuthal symmetry of the problem, we avoid Hankel transforms which have been used in all previous treatments and, in so doing, make it possible to apply the fast Fourier transform algorithm in one dimension. The resulting computation can be carried out to arbitrary accuracy with sufficiently dense sampling of the cross section and is very fast when compared with numerically computed Hankel transforms. Angular distributions for several scattering potentials and a compound target are compared.