Abstract
The propagator matrix is one ingredient in exact theories of multiple scattering. It occurs in the addition theorem (or translation formula) for expanding a spherical outgoing multipole, singular at one point, in terms of regular spherical solutions about another point. It also occurs in the two-centre expansion of the free-space Green's function (or free-particle propagator). Many methods have been devised for computing the propagator matrix, but one of the most efficient, numerically, is based on a formula obtained in 1990 by Rehr and Albers and by Fritzsche. A clear derivation of this formula is given. The formula is also simplified, leading to an expansion in inverse powers of kb, where k is the wavenumber and b is the spacing. This leads to consistent approximations, which are asymptotic as .
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