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 TMF, 1999, Volume 118, Number 1, Pages 74–94 (Mi tmf687)

Extension theory approach to scattering and annihilation in the $\bar pd$ system

Yu. A. Kuperin, S. B. Levin

Saint-Petersburg State University

Abstract: We consider the problems of three-particle scattering and annihilation in a system of three strongly interacting charged particles $(\bar ppn)$. We propose a model for the elastic scattering and the breakup process in the nucleon channel as well as for the annihilation into mesons. The mathematical foundation of the model is the extension theory of symmetrical operators. In the framework of this model, we construct the modified integral Faddeev equations with energy-dependent interactions taking the annihilation processes into account. These equations are uniquely resolvable for suitable classes of functions. On this basis, we deduce the corresponding differential Faddeev equations, construct asymptotic boundary conditions for wave function components, and formulate boundary problems for a system composed of nucleonic and mesonic channels. The results obtained are applied to scattering and annihilation processes in the three-particle system $\bar pd$.

DOI: https://doi.org/10.4213/tmf687

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English version:
Theoretical and Mathematical Physics, 1999, 118:1, 60–76

Bibliographic databases:

Citation: Yu. A. Kuperin, S. B. Levin, “Extension theory approach to scattering and annihilation in the $\bar pd$ system”, TMF, 118:1 (1999), 74–94; Theoret. and Math. Phys., 118:1 (1999), 60–76

Citation in format AMSBIB
\Bibitem{KupLev99} \by Yu.~A.~Kuperin, S.~B.~Levin \paper Extension theory approach to scattering and annihilation in the $\bar pd$ system \jour TMF \yr 1999 \vol 118 \issue 1 \pages 74--94 \mathnet{http://mi.mathnet.ru/tmf687} \crossref{https://doi.org/10.4213/tmf687} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702840} \zmath{https://zbmath.org/?q=an:0991.81135} \elib{http://elibrary.ru/item.asp?id=13324500} \transl \jour Theoret. and Math. Phys. \yr 1999 \vol 118 \issue 1 \pages 60--76 \crossref{https://doi.org/10.1007/BF02557196} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079262300006} 

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• https://doi.org/10.4213/tmf687
• http://mi.mathnet.ru/eng/tmf/v118/i1/p74

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This publication is cited in the following articles:
1. Pomerantsev V.N. Kukulin V.I. Rubtsova O.A., “Model With Coupled Internal and External Channels For <Bold>2N</Bold> and <Bold>3N</Bold> Systems”, Few-Body Syst., 60:3 (2019), UNSP 48
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