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 TMF, 2003, Volume 134, Number 3, Pages 341–352 (Mi tmf159)

Fermi Rule and Scattering Amplitude Resonances

A. A. Arsen'ev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: The behavior of the scattering amplitude near a resonance with a small imaginary part is investigated. We prove that the scattering amplitude as an energy function suffers a jump near the real part of the resonance and the jump is independent of the interaction details. In terms of the problem data, we derive an estimate for the imaginary part of the resonance.

Keywords: scattering, pole, resonance

DOI: https://doi.org/10.4213/tmf159

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English version:
Theoretical and Mathematical Physics, 2003, 134:3, 296–307

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Revised: 12.09.2002

Citation: A. A. Arsen'ev, “Fermi Rule and Scattering Amplitude Resonances”, TMF, 134:3 (2003), 341–352; Theoret. and Math. Phys., 134:3 (2003), 296–307

Citation in format AMSBIB
\Bibitem{Ars03} \by A.~A.~Arsen'ev \paper Fermi Rule and Scattering Amplitude Resonances \jour TMF \yr 2003 \vol 134 \issue 3 \pages 341--352 \mathnet{http://mi.mathnet.ru/tmf159} \crossref{https://doi.org/10.4213/tmf159} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2001812} \zmath{https://zbmath.org/?q=an:1178.81269} \elib{http://elibrary.ru/item.asp?id=13428352} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 134 \issue 3 \pages 296--307 \crossref{https://doi.org/10.1023/A:1022689119601} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182047100001} 

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• https://doi.org/10.4213/tmf159
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. A. Arsen'ev, “Mathematical Model of Resonances and Tunneling in a System with a Bound State”, Theoret. and Math. Phys., 136:3 (2003), 1336–1345
2. A. A. Arsen'ev, “Relation Between a Pole of the Scattering Matrix and the Transmission and Reflection Coefficients in Scattering in a Quantum Waveguide”, Theoret. and Math. Phys., 140:2 (2004), 1151–1156
3. A. A. Arsen'ev, “Resonances and Tunneling in the Tight-Binding Approximation to Scattering in a Quantum Billiard”, Theoret. and Math. Phys., 141:1 (2004), 1415–1426
4. A. A. Arsen'ev, “Resonances and trapped modes in a quantum waveguide”, Comput. Math. Math. Phys., 45:9 (2005), 1573–1581
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