Abstract
It is shown, with some restrictions, that on-shell two-cluster partial-wave scattering amplitudes for atomic systems whose particles interact via two-body Coulomb potentials have analytic continuations in the complex energy plane below the physical part of the real axis. The result is proved only for energies lower than any three (or more) cluster threshold. Poles of the amplitudes can occur only at discrete eigenvalues of the rotated Hamiltonian which may be reached by continuation along the same path. The method of proof uses analyticity related to a generalized scaling transformation and the boost transformation.
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References
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Communicated by J. Ginibre
Supported in part by the National Research Council of Canada
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Nuttall, J., Singh, S.R. Continuation of partial-wave two-cluster atomic scattering amplitudes. Commun.Math. Phys. 72, 1–13 (1980). https://doi.org/10.1007/BF01200107
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DOI: https://doi.org/10.1007/BF01200107