Radiative Corrections to Compton Scattering

L. M. Brown; R. P. Feynman

doi:10.1103/PhysRev.85.231

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Radiative Corrections to Compton Scattering

L. M. Brown^*

R. P. Feynman^†

Cornell University, Ithaca, New York

California Institute of Technology, Pasadena, California

^*Now at Northwestern University. Part of this work was done in partial fulfillment of the requirements for the Ph.D. degree at Cornell University.
^†Now on leave at Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil.

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Phys. Rev. 85, 231 – Published 15 January, 1952

DOI: https://doi.org/10.1103/PhysRev.85.231

Abstract

Corrections of order $e^{6}$ to the differential cross section for Compton scattering of unpolarized radiation by electrons are computed. The results for corrections ascribable to virtual photons are finite, relativistically invariant, and valid at all energies, but contain a term which depends logarithmically on an assumed small photon mass $λ$ . A cross section of the same order has also been obtained for double Compton scattering in which one of the emitted photons has an energy small compared to the rest mass of the electron (with the electron initially at rest). This contains a term depending on $\ln λ$ which exactly compensates the similar term arising from virtual quanta in all observable cases. Approximations for low and high energies, as well as numerical results, are given. These disagree with results obtained previously by Schafroth.

References (14)

R. P. Feynman, Phys. Rev. 76, 749 (1949) 76, 769 (1949)
M. R. Schafroth, Helv. Phys. Acta 22, 501 (1949)
M. R. Schafroth, Helv. Phys. Acta 23, 542 (1950)
E. Corinaldesi and R. Jost, Helv. Phys. Acta 21, 183 (1948)
[1], p. 788
[1]
G. R. Lomanitz Second Order Effects in the Electron-Electron Interaction, Cornell, 1950
Omitted endnote
W. Heitler, The Quantum Theory of Radiation (Oxford University Press, London, 1944), p. 157
C. J. Eliezer, Proc. Roy. Soc. (London) A187, 210 (1946)
R. Jost, Phys. Rev. 72, 815 (1947) F. Bloch and A. Nordsieck, 52, 54 (1937)
J. Schwinger, Phys. Rev. 76, 790 (1949)
Omitted endnote
Fletcher, Miller, and Rosenhead, An Index of Mathematical Tables (Scientific Computing Service, Ltd., London, 1946), p. 343

[c1] R. P. Feynman, Phys. Rev. 76, 749 (1949) 76, 769 (1949)

[c2] M. R. Schafroth, Helv. Phys. Acta 22, 501 (1949)

[c3] M. R. Schafroth, Helv. Phys. Acta 23, 542 (1950)

[c4] E. Corinaldesi and R. Jost, Helv. Phys. Acta 21, 183 (1948)

[c5] [1], p. 788

[c6] [1]

[c7] G. R. Lomanitz Second Order Effects in the Electron-Electron Interaction, Cornell, 1950

[c8] Omitted endnote

[c9] W. Heitler, The Quantum Theory of Radiation (Oxford University Press, London, 1944), p. 157

[c10] C. J. Eliezer, Proc. Roy. Soc. (London) A187, 210 (1946)

[c11] R. Jost, Phys. Rev. 72, 815 (1947) F. Bloch and A. Nordsieck, 52, 54 (1937)

[c12] J. Schwinger, Phys. Rev. 76, 790 (1949)

[c13] Omitted endnote

[c14] Fletcher, Miller, and Rosenhead, An Index of Mathematical Tables (Scientific Computing Service, Ltd., London, 1946), p. 343

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Radiative Corrections to Compton Scattering

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