Abstract
A new technique for the construction of $N$-body Coulomb scattering amplitudes is proposed, suggested by the simplest case of $N=2$: Calculate the scattering amplitude in eikonal approximation, discard the infinite phase factors which appear upon taking the limit of a Coulomb potential, and treat the remainder as an amplitude whose absolute value squared produces the exact, Coulomb differential cross section. The method easily generalizes to the $N$-body Coulomb problem for elastic scattering, and for inelastic rearrangement scattering of Coulomb bound states. We give explicit results for $N=3 \mathrm{and} 4$; in the $N=3$ case we extract amplitudes for the processes (12)+3\ensuremath{\rightarrow}1+2+3 (breakup), (12)+3\ensuremath{\rightarrow}1+(23) (rearrangement), and (12)+3\ensuremath{\rightarrow}(12)\ensuremath{'}+3 (inelastic scattering) as residues at the appropriate poles in the free-free amplitude. The method produces scattering amplitudes ${f}_{N}$ given in terms of explicit quadratures over ${(N\ensuremath{-}2)}^{2}$ distinct integrands.
Published Version
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