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Zapiski Nauchnykh Seminarov LOMI, 1985, Volume 147, Pages 155–178 (Mi znsl5346)  

This article is cited in 1 scientific paper (total in 1 paper)

Phase analysis in the problem of scattering by a radial potential

A. V. Sobolev, D. R. Yafaev
Abstract: Let $\sigma(k,g)$ be the total cross-section for scattering of a three-dimensional quantum particle of energy $k^2$ by a radial potential $gV(r)$, $r=|x|$. Under the assumption $V(r)\sim v_0|r|^{-\alpha}$, $\alpha>2$, $r\to\infty$ it is shown that in the region $gk^{-1}\to\infty$, $g^{3-\alpha}k^{2(\alpha-2)}\to\infty$ the asymptotics $\sigma(k,g)\sim\varkappa_\alpha(|v_0|gk^{-1})^{2\lambda_\alpha}$, $\lambda_\alpha=(\alpha-1)^{-1}$ is valid; the coefficient $\varkappa_\alpha$ is expressed explicitly in terms of the $\Gamma$-function. For nonnegative potentials this asymptotics holds even in the broader region. For potentials with a strong positive singularity $V(r)\sim v_0r^{-\beta}$, $v_0>0$, $\beta>2$, $r\to0$ the asymptotics $\sigma(r,g)\sim\varkappa_\beta(v_0gk^{-1})^{2\lambda_\beta}$ as $gk^{-1}\to0$, $gk^{\beta-2}\to\infty$ is established. Similar results are obtained for the forward scattering amplitude.
Bibliographic databases:
Document Type: Article
UDC: 539.101
Language: Russian
Citation: A. V. Sobolev, D. R. Yafaev, “Phase analysis in the problem of scattering by a radial potential”, Boundary-value problems of mathematical physics and related problems of function theory. Part 17, Zap. Nauchn. Sem. LOMI, 147, "Nauka", Leningrad. Otdel., Leningrad, 1985, 155–178
Citation in format AMSBIB
\Bibitem{SobYaf85}
\by A.~V.~Sobolev, D.~R.~Yafaev
\paper Phase analysis in the problem of scattering by a radial potential
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~17
\serial Zap. Nauchn. Sem. LOMI
\yr 1985
\vol 147
\pages 155--178
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl5346}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=821483}
\zmath{https://zbmath.org/?q=an:0588.47011}
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  • https://www.mathnet.ru/eng/znsl/v147/p155
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Записки научных семинаров ПОМИ
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