Theory of multiple scattering

Abstract

The rigorous theory of multiple scattering is developed for monoergic particles incident normally on a plane parallel, homogeneous, amorphous foil. All formulae are given in terms of the single-scattering function, the collision frequency per unit path, and the foil thickness. The underlying random flight problem is formally solved by a set of interlocking recurrence relations. The multiple scattering function is found to depend upon solution of a complicated integral equation, which is discussed in particular for the case of forward scattering. A first forward approximation leads to the general formula of Goudsmith & Saunderson (1940) which, like the equivalent theory of Molière, is therefore valid up to about 10° only. In a second approximation, valid up to about 35°, the basic integral equation must be iterated; the first iterate of the multiple scattering function is obtained explicitly in terms of the simpler first approximation.