Abstract
Compact analytic expressions have been derived by a direct expansion in ħ → 0 for the nonrelativistic amplitude of Coulomb bremsstrahlung radiation (BR), the differential (in frequency and angles of the scattered electron) BR cross section, and the triply differential BR cross section that takes into account the bremsstrahlung photon direction and polarization and the scattered electron direction. They contain the classical limit and a quantum correction of the order of ħ at an arbitrary BR frequency ω. An explicit expression has been found for the quantum correction of the order of ħ to the classical BR spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Kogan, Phys.—Usp. 43 (12), 1253 (2000).
H. A. Kramers, Philos. Mag. 46, 836 (1923).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Volume 2: The Classical Theory of Fields (Fizmatlit, Moscow, 2003; Butterworth–Heinemann, Oxford, 2004).
A. Sommerfeld, Ann. Phys. 11, 257 (1931).
A. Sommerfeld, Atomic Structure and Spectral Lines (Methuen, London, 1919; Gostekhizdat, Moscow, 1956), Vol. 2.
L. C. Biedenharn, Phys. Rev. 102, 262 (1956).
V. I. Gervids and V. I. Kogan, Preprint No. 2720, IAE (Kurchatov Institute of Atomic Energy, Moscow, 1976).
V. I. Gervids and V. I. Kogan, Bremsstrahlung Radiation of Electrons in a Static Potential: A Review (TsNIIatominform, Moscow, 1988) [in Russian].
S. D. Drell and K. Huang, Phys. Rev. 99, 686 (1955).
V. V. Babikov, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, Ed. by M. A. Leontovich (Academy of Sciences of the Soviet Union, Moscow, 1958), Vol. 2, p. 226 [in Russian].
R. J. Gould, Am. J. Phys. 38, 189 (1970).
V. P. Krainov, J. Phys. B: At., Mol. Opt. Phys. 33, 1585 (2000).
V. P. Krainov, J. Exp. Theor. Phys. 92 (6), 960 (2001).
G. Wentzel, Z. Phys. 27, 257 (1924).
K. Alder, A. Bohr, T. Huus, B. Mottelson, and A. Winther, Rev. Mod. Phys. 28, 432 (1956).
M. D. Thorsley and M. C. Chidichimo, J. Math. Phys. 42, 1921 (2001).
D. Marcuse, Bell Syst. Tech. J. 41, 1557 (1962).
M. V. Fedorov, Atomic and Free Electrons in a Strong Laser Field (World Scientific, Singapore, 1997).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 4: V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Nauka, Moscow, 1989; Butterworth–Heinemann, Oxford, 1994).
M. Gavrila, in Collisions Theory for Atoms and Molecules, Ed. by F. A. Gianturco (Plenum, New York, 1989), p. 139.
N. L. Manakov, S. I. Marmo, and V. V. Volovich, Phys. Lett. A 27, 42 (1995).
N. L. Manakov, S. I. Marmo, and A. G. Fainshtein, J. Exp. Theor. Phys. 81 (5), 860 (1995).
A. A. Krylovetsky, N. L. Manakov, S. I. Marmo, and A. F. Starace, Phys. Rev. A: At., Mol., Opt. Phys. 72, 035401 (2005).
W. Heitler, The Quantum Theory of Radiation Courier, New York, 1954; Inostrannaya Literatura, Moscow, 1956).
H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1955; Nauka, Moscow, 1974), Vol. 2.
26._V. I. Kogan and A. B. Kukushkin, Sov. Phys. JETP 60 (4), 665 (1984).
V. I. Kogan, A. B. Kukushkin, and V. S. Lisitsa, Phys. Rep. 213, 1 (1992).
G. Elwert, Ann. Phys. 34, 178 (1939).
H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1955; Nauka, Moscow, 1973), Vol. 1.
D. V. Gal’tsov and Yu. V. Grats, Theor. Math. Phys. 28 (2), 730 (1976).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.L. Manakov, A.A. Krylovetsky, S.I. Marmo, 2015, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 148, No. 5, pp. 835–845.
Rights and permissions
About this article
Cite this article
Manakov, N.L., Krylovetsky, A.A. & Marmo, S.I. Bremsstrahlung radiation from slow electrons in a Coulomb field: Classical limit and quantum correction. J. Exp. Theor. Phys. 121, 727–736 (2015). https://doi.org/10.1134/S1063776115110059
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776115110059