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Phase analysis in the problem of scattering by a radial potential

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Abstract

Let б(k,g) be the total scattering cross section of a three-dimensional quantum particle of energy K2 by a radial potential

. Under the assumption

it is shown that in the domain

one has the asymptotics

where the coefficient

is is expressed explicitly in terms of the Gamma function. For nonnegative potentials, the domain of validity of this asymptotic is even larger. For potentials with a strong positive singularity

, it is established that

as

. Similar results are obtained for the forward scattering amplitude.

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Authors
  1. A. V. Sobolev
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  2. D. R. Yafaev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 155–178, 1985.

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Sobolev, A.V., Yafaev, D.R. Phase analysis in the problem of scattering by a radial potential. J Math Sci 37, 888–902 (1987). https://doi.org/10.1007/BF01387729

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  • DOI: https://doi.org/10.1007/BF01387729

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