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 Jυ (az) to the case with noninteger υ and complex a.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 188, No. 2, pp. 273–287, August, 2016.
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Kisselev, A.V. Approximate formulas for moderately small eikonal amplitudes. Theor Math Phys 188, 1197–1209 (2016). https://doi.org/10.1134/S0040577916080055
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DOI: https://doi.org/10.1134/S0040577916080055