Eikonal Approximation for Three-Particle Scattering

R. L. Kelly

doi:10.1103/PhysRevD.4.1755

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Eikonal Approximation for Three-Particle Scattering

R. L. Kelly

Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213

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Phys. Rev. D 4, 1755 – Published 15 September, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.1755

Abstract

The behavior of the $3 \to 3$ amplitude in nonrelativistic potential scattering is investigated at high energies and small momentum transfers. An approximation scheme is proposed which involves only on-shell two-body amplitudes. The single- and double-scattering terms are obtained from the Watson-Faddeev equations. An eikonal approximation for the triple-scattering term is developed, and the result is expressed as a one-dimensional integral over the product of the three two-body amplitudes.

References (5)

Arnold Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), p. 233
R. L. Sugar and R. Blankenbecler, Phys. Rev. 183, 1387 (1969)
R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Brittin and L. G. Dunham (Interscience, New York, 1959), Vol. I, p. 315
Omitted endnote
K. M. Watson, Phys. Rev. 89, 575 (1953) L. D. Faddeev, Zh. Eksperim. i Teor. Fiz. 39, 1459 (1960) [Soviet Phys. JETP 12, 1014 (1961)]

[c1] Arnold Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), p. 233

[c2] R. L. Sugar and R. Blankenbecler, Phys. Rev. 183, 1387 (1969)

[c3] R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Brittin and L. G. Dunham (Interscience, New York, 1959), Vol. I, p. 315

[c4] Omitted endnote

[c5] K. M. Watson, Phys. Rev. 89, 575 (1953) L. D. Faddeev, Zh. Eksperim. i Teor. Fiz. 39, 1459 (1960) [Soviet Phys. JETP 12, 1014 (1961)]

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Eikonal Approximation for Three-Particle Scattering

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