Abstract

The complete Dirac-Volkov relativistic treatment of the first Born limit of laser-assisted potential scattering of electrons within a circularly polarized laser field has been compared to the nonrelativistic Bunkin-Fedorov approach. The dependence of the quiver energy on the electron four-momentum in an ultrastrong laser field leads to different energy transfer cross sections depending on the scattering geometry with respect to the laser propagation direction. Visible differences between the relativistic and non-relativistic differential cross sections for small-angle scattering occur already for 1016 W/cm2 intensity of near infrared wavelength and moderate electron initial energies.

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References

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  1. see, for instance, "High-field interactions and short-wavelength generation", edited by H. Milchberg and R. Freeman, part 1 of special issue of J. Opt. Soc. Am. B13, 51-222 (1996).
  2. see, for instance, "High-field interactions and short-wavelength generarion", edited by H. Milchberg and R. Freeman, part 2 of special issue of J. Opt. Soc. Am. B13, 314-468 (1996).
  3. D. L. Burke, R. C. Field, G. Horton-Smith, J. E. Spencer, D. Walz, S. C. Berrigde, W. M. Bugg, K. Shmakov, A. W. Weidemann, C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. J. Boege, T. Koffas, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, D.A. Reis, and W. Ragg, "Positron Production in Multiphoton Light-by-Light Scattering", Phys. Rev. Lett. 79, 1626-1629 (1997).
    [CrossRef]
  4. C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. Boege, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, W. Ragg, D. L. Burke, R. C. Field, G. Horton-Smith, A. C. Odian, J. E. Spencer, D. Walz, S. C. Berrigde, W. M. Bugg, K. Shmakov, and A. W. Weidemann, "Observation of Nonlinear Effects in Compton Scattering", Phys. Rev. Lett. 76, 3116-3119 (1996).
    [CrossRef] [PubMed]
  5. P. A. Norreys, M. Zepf, S. Moustaizis, A. P. Fews, J. Zhang, P. Lee, M. Bakarezos, C. N. Danson, A. Dyson, P. Gibbon, P. Loukakos, D. Neely, F. N. Walsh, J. S. Wark, and A. E. Dangor, "Efficient Extreme UV Harmonics Generated from Picosecond Laser Pulse Interactions with Solid Targets", Phys. Rev. Lett. 76, 1832-1835 (1996).
    [CrossRef] [PubMed]
  6. P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Dulieu, M. Louis-Jacquet, G. Malka, and J. L. Miquel, "Experimental Demonstration of Relativistic Self-Channeling of a Multiterawatt Laser Pulse in an Underdense Plasma", Phys. Rev. Lett. 74, 2953-2956 (1995).
    [CrossRef] [PubMed]
  7. C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, "Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons", Phys. Rev. Lett. 74, 2439-2442 (1995).
    [CrossRef] [PubMed]
  8. L. S. Brown and T. W. B. Kibble, "Interaction of Intense Laser Beams with Electrons", Phys. Rev. 133, A705 (1964).
    [CrossRef]
  9. H. R. Reiss, "Absorption of Light by Light", J. Math. Phys. 3, 59-67 (1962).
    [CrossRef]
  10. I. I. Gol'dman, "Intensity Effects in Compton Scattering", Zh. Eksp. Teor. Fiz. 46, 1412-1417 (1964) [Sov. Phys. JETP 19, 954-957 (1964)].
  11. A. I. Nikishov and V. I. Ritus, "Quantum Processes in the field of a plane electromagnetic wave and in a constantfieldI",Zh. Eksp. Teor. Fiz. 46, 776-796 (1964) [Sov. Phys. JETP 19, 529-541 (1964)].
  12. A. I. Nikishov and V. I. Ritus, "Quantum Processes in the field of a plane electromagnetic wave and in a constant field II" Zh. Eksp. Teor. Fiz. 46, 1768-1781 (1964) [Sov. Phys. JETP 19, 1191-1199 (1964)].
  13. J. H. Eberly, "Proposed Experiment for Observation of Nonlinear Compton Wavelength Shift", Phys. Rev. Lett. 15, 91-93 (1965).
    [CrossRef]
  14. T. W. B. Kibble, "Mutual Refraction of Electrons and Photons", Phys. Rev. 150, 1060 - 1069 (1966).
    [CrossRef]
  15. J. H. Eberly and H. R. Reiss, "Electron Self-Energy in Intense Plane-Wave Field", Phys. Rev. 145, 1035 (1966).
    [CrossRef]
  16. H. R. Reiss and J. H. Eberly, "Green's function in intense field electrodynamics", Phys. Rev. 151, 1058-1066 (1966).
    [CrossRef]
  17. J. H. Eberly, "Interaction of very intense light with free electrons", Prog. Opt. 7, 361-415, edited by E. Wolf, (Noth-Holland, Amsterdam, 1969).
  18. F. V. Bunkin and M. V. Fedorov, " Bremsstrahlung in a strong radiation field", Zh. Eksp. Teor. Fiz. 49, 1215-1221 (1965) [Sov. Phys. JETP 22, 844-847 (1966)].
  19. M. M. Denisov and M. V. Fedorov, "Bremsstrahlung effect on relativistic electrons in a strong radiation field", Zh. Eksp. Teor. Fiz. 53, 1340-1348 (1967) [Sov. Phys. JETP 26 779-783 (1968)].
  20. C. Szymanowski, V. Veniard, R. Taieb, A. Maquet, and C. H. Keitel, "Mott scattering in strong laser fields", Phys. Rev. A 56 3846-3859 (1997).
    [CrossRef]
  21. V. P. Krainov and S. P. Roshupkin, "Relativistic effects in the angular distribution of ejected electrons in tunneling ionization of atoms by strong electromagnetic fields", J. Opt. Soc. Am. B9, 1231-1233 (1992).
  22. V. B. Berestetzkii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, 2nd Edition (Pergamon Press, Oxford, 1982).
  23. D. M. Volkov, "Uber eine Klasse von L" osungen der Diracschen Gleichung", Z. f. Phys. 94, 250-260 (1935).
    [CrossRef]
  24. S. P. Goreslavskii, "The BSI model and relativistic ponderomotive scattering", Laser Phys. 6, 74-78 (1996).
  25. N. B. Narozhnyi and M. S. Fofanov, "Creation of a pair by a photon colliding with a short focused laser pulse", Laser Phys. 7, 141-149 (1997).
  26. C. H. Keitel, C. Szymanowski, P. L. Knight, and A. Maquet, "Radiative reaction in ultra-intense laser-atom interaction", J. Phys. B 31, L75-L83 (1998).
    [CrossRef]
  27. F. V. Hartemann and A. K. Kerman, "Classical Theory of Nonlinear Compton Scattering", Phys. Rev. Lett. 76, 624-627 (1996).
    [CrossRef] [PubMed]
  28. C. Szymanowski, R. Taieb, and A. Maquet, "Laser-assisted scattering of polarized electrons at high field intensities", Laser Phys. 8, 102-106 (1998).

Other

see, for instance, "High-field interactions and short-wavelength generation", edited by H. Milchberg and R. Freeman, part 1 of special issue of J. Opt. Soc. Am. B13, 51-222 (1996).

see, for instance, "High-field interactions and short-wavelength generarion", edited by H. Milchberg and R. Freeman, part 2 of special issue of J. Opt. Soc. Am. B13, 314-468 (1996).

D. L. Burke, R. C. Field, G. Horton-Smith, J. E. Spencer, D. Walz, S. C. Berrigde, W. M. Bugg, K. Shmakov, A. W. Weidemann, C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. J. Boege, T. Koffas, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, D.A. Reis, and W. Ragg, "Positron Production in Multiphoton Light-by-Light Scattering", Phys. Rev. Lett. 79, 1626-1629 (1997).
[CrossRef]

C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. Boege, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, W. Ragg, D. L. Burke, R. C. Field, G. Horton-Smith, A. C. Odian, J. E. Spencer, D. Walz, S. C. Berrigde, W. M. Bugg, K. Shmakov, and A. W. Weidemann, "Observation of Nonlinear Effects in Compton Scattering", Phys. Rev. Lett. 76, 3116-3119 (1996).
[CrossRef] [PubMed]

P. A. Norreys, M. Zepf, S. Moustaizis, A. P. Fews, J. Zhang, P. Lee, M. Bakarezos, C. N. Danson, A. Dyson, P. Gibbon, P. Loukakos, D. Neely, F. N. Walsh, J. S. Wark, and A. E. Dangor, "Efficient Extreme UV Harmonics Generated from Picosecond Laser Pulse Interactions with Solid Targets", Phys. Rev. Lett. 76, 1832-1835 (1996).
[CrossRef] [PubMed]

P. Monot, T. Auguste, P. Gibbon, F. Jakober, G. Mainfray, A. Dulieu, M. Louis-Jacquet, G. Malka, and J. L. Miquel, "Experimental Demonstration of Relativistic Self-Channeling of a Multiterawatt Laser Pulse in an Underdense Plasma", Phys. Rev. Lett. 74, 2953-2956 (1995).
[CrossRef] [PubMed]

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, "Observation of the Transition from Thomson to Compton Scattering in Multiphoton Interactions with Low-Energy Electrons", Phys. Rev. Lett. 74, 2439-2442 (1995).
[CrossRef] [PubMed]

L. S. Brown and T. W. B. Kibble, "Interaction of Intense Laser Beams with Electrons", Phys. Rev. 133, A705 (1964).
[CrossRef]

H. R. Reiss, "Absorption of Light by Light", J. Math. Phys. 3, 59-67 (1962).
[CrossRef]

I. I. Gol'dman, "Intensity Effects in Compton Scattering", Zh. Eksp. Teor. Fiz. 46, 1412-1417 (1964) [Sov. Phys. JETP 19, 954-957 (1964)].

A. I. Nikishov and V. I. Ritus, "Quantum Processes in the field of a plane electromagnetic wave and in a constantfieldI",Zh. Eksp. Teor. Fiz. 46, 776-796 (1964) [Sov. Phys. JETP 19, 529-541 (1964)].

A. I. Nikishov and V. I. Ritus, "Quantum Processes in the field of a plane electromagnetic wave and in a constant field II" Zh. Eksp. Teor. Fiz. 46, 1768-1781 (1964) [Sov. Phys. JETP 19, 1191-1199 (1964)].

J. H. Eberly, "Proposed Experiment for Observation of Nonlinear Compton Wavelength Shift", Phys. Rev. Lett. 15, 91-93 (1965).
[CrossRef]

T. W. B. Kibble, "Mutual Refraction of Electrons and Photons", Phys. Rev. 150, 1060 - 1069 (1966).
[CrossRef]

J. H. Eberly and H. R. Reiss, "Electron Self-Energy in Intense Plane-Wave Field", Phys. Rev. 145, 1035 (1966).
[CrossRef]

H. R. Reiss and J. H. Eberly, "Green's function in intense field electrodynamics", Phys. Rev. 151, 1058-1066 (1966).
[CrossRef]

J. H. Eberly, "Interaction of very intense light with free electrons", Prog. Opt. 7, 361-415, edited by E. Wolf, (Noth-Holland, Amsterdam, 1969).

F. V. Bunkin and M. V. Fedorov, " Bremsstrahlung in a strong radiation field", Zh. Eksp. Teor. Fiz. 49, 1215-1221 (1965) [Sov. Phys. JETP 22, 844-847 (1966)].

M. M. Denisov and M. V. Fedorov, "Bremsstrahlung effect on relativistic electrons in a strong radiation field", Zh. Eksp. Teor. Fiz. 53, 1340-1348 (1967) [Sov. Phys. JETP 26 779-783 (1968)].

C. Szymanowski, V. Veniard, R. Taieb, A. Maquet, and C. H. Keitel, "Mott scattering in strong laser fields", Phys. Rev. A 56 3846-3859 (1997).
[CrossRef]

V. P. Krainov and S. P. Roshupkin, "Relativistic effects in the angular distribution of ejected electrons in tunneling ionization of atoms by strong electromagnetic fields", J. Opt. Soc. Am. B9, 1231-1233 (1992).

V. B. Berestetzkii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, 2nd Edition (Pergamon Press, Oxford, 1982).

D. M. Volkov, "Uber eine Klasse von L" osungen der Diracschen Gleichung", Z. f. Phys. 94, 250-260 (1935).
[CrossRef]

S. P. Goreslavskii, "The BSI model and relativistic ponderomotive scattering", Laser Phys. 6, 74-78 (1996).

N. B. Narozhnyi and M. S. Fofanov, "Creation of a pair by a photon colliding with a short focused laser pulse", Laser Phys. 7, 141-149 (1997).

C. H. Keitel, C. Szymanowski, P. L. Knight, and A. Maquet, "Radiative reaction in ultra-intense laser-atom interaction", J. Phys. B 31, L75-L83 (1998).
[CrossRef]

F. V. Hartemann and A. K. Kerman, "Classical Theory of Nonlinear Compton Scattering", Phys. Rev. Lett. 76, 624-627 (1996).
[CrossRef] [PubMed]

C. Szymanowski, R. Taieb, and A. Maquet, "Laser-assisted scattering of polarized electrons at high field intensities", Laser Phys. 8, 102-106 (1998).

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Figures (2)

Fig. 1.
Fig. 1.

Envelope of differential cross section /do in atomic units as a function of energy transfer ΔQ scaled in units of the laser photon energy ω for an electrical field strength of E = 1 a.u. or vector potential A = Ec/ω = 3186a.u. . The Yukawa parameter is α = 0.25, the deflection angle equals ∠(q⃗,q⃗′) = 0.0002π and the initial kinetic energy is W kin = 100 a.u. . The different curves are explained in the text.

Fig. 2.
Fig. 2.

Envelope of differential cross section /do scaled in atomic units as a function of energy transfer ΔQ scaled in units of the laser photon energy ω for an electrical field strength of E = ωc = 5.89 a.u. or vector potential A = c 2 = 18769 a.u.. The parameter α, the deflection angle and the initial kinetic energy are the same as for Fig. 1. The different curves are explained in the text.

Equations (13)

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ψ q = x q = [ 1 + k A 2 c ( kp ) ] × u 2 QV × exp [ i ( qx ) i 0 kx ( pA ) c ( kp ) ] ,
T q q = iZ c d 4 x ψ ¯ q γ 0 exp ( α x ) x ψ q .
do = n d σ ( n ) do Q = Q + ,
d σ ( n ) do = Z 2 q c 2 q × 1 ( q q + n k ) 2 + α 2 2 × (
2 J n ( ζ ) 2 { [ c 2 + QQ c 2 + q q + A 2 2 c 2 ( ( k q ˜ ) ( kq ) + ( k q ˜ ) ( kq ) ) + ( A 2 ) 2 ω 2 2 c 6 ( kq ) ( kq ) ] ×
( 1 A 2 ω 2 c 4 ( kq ) ( kq ) ) A 2 2 c 2 [ 1 ( k q ˜ ) ( k q ˜ ) ( kq ) ( kq ) ] + ( A 2 ) 2 ω 2 c 6 ( kq ) ( kq )
+ ( A 2 ) 2 ω 2 2 c 6 ( kq ) 2 ( kq ) 2 [ ( kq ) ( k q ˜ ) + ( kq ) ( k q ˜ ) + A 2 ω 2 c 4 ] }
+ [ J n + 1 ( ζ ) 2 + J n 1 ( ζ ) 2 ] { A 2 2 c 2 [ ( k q ˜ ) ( kq ) + ( k q ˜ ) ( kq ) + 1 + ( k q ˜ ) ( k q ˜ ) 2 ω 2 ( kq ) ( kq ) ] }
+ 2 A 2 ω 2 c 4 ( kq ) ( kq ) + A 2 ω 2 c 4 ( kq ) ( kq ) ( ( kq ) ( k q ˜ ) + ( kq ) ( k q ˜ ) + A 2 ω 2 c 4 )
2 ω 2 c 2 ( kq ) ( kq ) ( QQ c 2 + q q + A 2 2 c 2 ( ( k q ˜ ) ( kq ) + ( k q ˜ ) ( kq ) ) + ( A 2 ) 2 ω 2 2 c 6 ( kq ) ( kq ) ) ) ]
+ 2 A 2 ω 2 c 4 ( kq ) ( kq ) [ q x q x + q y q y ] } + J n + 1 ( ζ ) J n 1 ( ζ ) cos ( 2 ϕ 0 ) 2 A 2 ω 2 c 4 ( kq ) ( kq )
× [ q x q x q y q y ] + J n ( ζ ) [ J n + 1 ( ζ ) + J n 1 ( ζ ) ] { 2 A 2 ω 2 c 4 ( kq ) ( kq ) [ ( Å q ) c
+ ( Åq ) c ] + ( Åq ) ( k q ˜ ) c ( kq ) + ( Åq ) c + ( Åq ) c + ( Åq ) ( k q ˜ ) c ( kq ) } ) Q = Q + .

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