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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 2, Pages 273–287
DOI: https://doi.org/10.4213/tmf9093 (Mi tmf9093) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Approximate formulas for moderately small eikonal amplitudes

A. V. Kisselev

Institute for High Energy Physics, National Research University "Kurchatov Institute,", Protvino, Moscow Oblast, Russia
Full-text PDF (467 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9093
Abstract: We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jν(az) to the case with noninteger ν and complex a.
Keywords: scattering amplitude, eikonal approximation, improper integral, Bessel function.
Received: 06.11.2015
Revised: 26.12.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 2, Pages 1197–1209
DOI: https://doi.org/10.1134/S0040577916080055
Bibliographic databases:
PACS: 11.80.Fv
MSC: 81Uxx
Language: Russian
Citation: A. V. Kisselev, “Approximate formulas for moderately small eikonal amplitudes”, TMF, 188:2 (2016), 273–287; Theoret. and Math. Phys., 188:2 (2016), 1197–1209
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9093
  • https://doi.org/10.4213/tmf9093
  • https://www.mathnet.ru/eng/tmf/v188/i2/p273
    • This publication is cited in the following 2 articles:
    1. O. H. E. Philcox, Z. Slepian, “An exact integral-to-sum relation for products of Bessel functions”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2253 (2021), 20210376  crossref  mathscinet  isi
    2. A. V. Kisselev, “Approximate formula for the total cross section for a moderately small eikonal function”, Theoret. and Math. Phys., 201:1 (2019), 1484–1502  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:81
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