Time-independent multichannel scattering theory for charged particles

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Abstract
Rigorous derivations are given of two time-independent formulas for the multichannel scattering operator for nonrelativistic charged particle systems. The derivations are based on Dollard's time-dependent theory and use techniques of spectral integration. The formulas involve a complex power of the resolvent operator, in contrast to short-range formulas. Bilateral Laplace transforms are used to derive a generalized multichannel resolvent equation and to prove existence and uniqueness of the solution. The formulas are applied to recover the well-known two-body Coulomb scattering amplitude.