Correspondence of partial-wave and impact-parameter representations

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Abstract
An alternative but much simpler proof is given that a recently developed high-energy expansion accomplishes the mapping between the partial-wave amplitude and the Fourier-Bessel impact-parameter amplitude. The high-energy expansion is also shown to converge to the exact result for Coulomb scattering at all energies and scattering angles. A Regge pole in the partial-wave amplitude maps to a cut in the Fourier-Bessel impact-parameter amplitude, i.e., the existence of poles in the impact-parameter amplitude is dubious.

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