Radiative Corrections for Electron Scattering in an External Field—A New Method of Calculation

Lester L. DeRaad, Jr; Richard J. Ivanetich; Kimball A. Milton; Wu-yang Tsai

doi:10.1103/PhysRevD.5.358

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Radiative Corrections for Electron Scattering in an External Field—A New Method of Calculation

Lester L. DeRaad, Jr.

Richard J. Ivanetich

Kimball A. Milton and Wu-yang Tsai

Department of Physics, University of California, Los Angeles, California 90024

Department of Physics, Harvard University, Cambridge, Massachusetts 02138

Department of Physics, University of California, Los Angeles, California 90024

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Phys. Rev. D 5, 358 – Published 15 January, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.358

Abstract

The lowest-order radiative corrections for electron scattering in an external electromagnetic field are considered, using Schwinger's source theory. Spectral forms are employed, and the range of soft photons is invariantly specified by the final-state mass resolution ( $δ M$ ; $δ M ≪ m = electron mass$ ). The differential cross section is dealt with directly, and elastic and inelastic contributions are not separated, thereby avoiding some of the usual infrared divergences. The resulting differential cross section appears as a factor ( $1 - δ$ ) multiplying the lowest-order (Born) differential cross section plus a contribution referring to the magnetic form factor; $δ$ is given by $δ = \frac{α}{2 π} \frac{q^{2}}{m^{2}} \int 0^{1} dv \frac{1}{1 + (\frac{q^{2}}{4 m^{2}}) (1 - v^{2})} [(1 + v^{2}) \ln (\frac{4 m}{δ M} \frac{v^{2}}{{(1 - v^{2})}^{\frac{3}{2}}}) - 1 - \frac{5}{2} v^{2} + \frac{1}{3} v^{4}],$ where $q$ is the momentum transfer. Also presented is a brief review of certain aspects of source theory.

References (18)

J. Schwinger, Phys. Rev. 76, 790 (1949) A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Wiley, New York, 1965)
J. Schwinger, Phys. Rev. 152, 1219 (1966)
J. Schwinger, Phys. Rev. 158, 1391 (1967)
J. Schwinger, Particles and Sources (Gordon and Breach, New York, 1969)
J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Mass., 1970)
J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Mass., to be published), Vol. II
[6]
Omitted endnote
K. A. Milton, Ph. D. thesis, Harvard University, 1971 (unpublished)
Omitted endnote
[6]
Omitted endnote
K. Mitchell, Phil. Mag. [7] 40, 351 (1949)
L. C. Maximon, Rev. Mod. Phys. 41, 193 (1969)
([5], Sec. 3-10)
R. J. Ivanetich (unpublished) Ph. D. thesis, Harvard University, 1969 (unpublished)
[6,9]
Omitted endnote

[c1] J. Schwinger, Phys. Rev. 76, 790 (1949) A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Wiley, New York, 1965)

[c2] J. Schwinger, Phys. Rev. 152, 1219 (1966)

[c3] J. Schwinger, Phys. Rev. 158, 1391 (1967)

[c4] J. Schwinger, Particles and Sources (Gordon and Breach, New York, 1969)

[c5] J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Mass., 1970)

[c6] J. Schwinger, Particles, Sources, and Fields (Addison-Wesley, Reading, Mass., to be published), Vol. II

[c7] [6]

[c8] Omitted endnote

[c9] K. A. Milton, Ph. D. thesis, Harvard University, 1971 (unpublished)

[c10] Omitted endnote

[c11] [6]

[c12] Omitted endnote

[c13] K. Mitchell, Phil. Mag. [7] 40, 351 (1949)

[c14] L. C. Maximon, Rev. Mod. Phys. 41, 193 (1969)

[c15] ([5], Sec. 3-10)

[c16] R. J. Ivanetich (unpublished) Ph. D. thesis, Harvard University, 1969 (unpublished)

[c17] [6,9]

[c18] Omitted endnote

Physical Review D

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Radiative Corrections for Electron Scattering in an External Field—A New Method of Calculation

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References (18)

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