Abstract

We studied theoretically the influence of relativistic effects on the energy distribution of electrons in the tunneling ionization of atoms by a field of linearly polarized super-intense laser radiation. It was shown that the energy distribution of ejected electrons is determined by relativistic law though the electron kinetic energy can be less than its rest energy. The relativistic probability of ionization along the field strength decreases exponentially with the electron kinetic energy, but more quickly than in the non-relativistic case.

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References

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  1. N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg 1985).
    [CrossRef]
  2. N.B. Delone and V.P. Krainov, "Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation", J. Opt. Soc. Am. B 8, 1207-1211 (1991).
    [CrossRef]
  3. N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg 1994).
    [CrossRef]
  4. H.R. Reiss, "Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes", Prog. Quantum Electron. 16, 1-71 (1992).
    [CrossRef]
  5. V.P. Krainov and S.P. Roshchupkin, "Relativistic eects in the angular distribution of ejected electronds in tunneling ionization of atoms by strong electromagnetic field", J. Opt. Soc. Am. B 9, 1231-1233 (1992).
    [CrossRef]
  6. V.P. Krainov and B. Shokri, "Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field", Laser Phys. 5, 793-796 (1995).
  7. L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon 1977).
  8. M.V. Ammosov, N.B. Delone and V.P. Krainov, "Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field", Sov. Phys. JETP 64, 1191-1194 (1986).
  9. P.B. Corkum, N.H. Burnett and F. Brunel, "Above-threshold ionization in the long-wavelength limit", Phys. Rev. Lett. 62, 1259-1262 (1989).
    [CrossRef] [PubMed]
  10. B. Buerke, J.P. Knauer, S.J. McNaught and D.D. Meyerhofer, "Precision tests of laser-tunneling ionization models": in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75-76 (1997).

Other

N.B. Delone and V.P. Krainov, Atoms in Strong Light Fields (Springer, Berlin-Heidelberg 1985).
[CrossRef]

N.B. Delone and V.P. Krainov, "Energy and angular electron spectra for the tunnel ionization of atoms by strong low-frequency radiation", J. Opt. Soc. Am. B 8, 1207-1211 (1991).
[CrossRef]

N.B. Delone and V.P. Krainov, Multiphoton Processes in Atoms (Springer, Berlin-Heidelberg 1994).
[CrossRef]

H.R. Reiss, "Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes", Prog. Quantum Electron. 16, 1-71 (1992).
[CrossRef]

V.P. Krainov and S.P. Roshchupkin, "Relativistic eects in the angular distribution of ejected electronds in tunneling ionization of atoms by strong electromagnetic field", J. Opt. Soc. Am. B 9, 1231-1233 (1992).
[CrossRef]

V.P. Krainov and B. Shokri, "Angular distribution of relativistic electrons in the tunneling ionization of atoms by an ac field", Laser Phys. 5, 793-796 (1995).

L.D. Landau and E.M. Lifshitz, Field Theory (Oxford, Pergamon 1977).

M.V. Ammosov, N.B. Delone and V.P. Krainov, "Tunnel ionization of complex atoms and atomic ions by an alternating electromagnetic field", Sov. Phys. JETP 64, 1191-1194 (1986).

P.B. Corkum, N.H. Burnett and F. Brunel, "Above-threshold ionization in the long-wavelength limit", Phys. Rev. Lett. 62, 1259-1262 (1989).
[CrossRef] [PubMed]

B. Buerke, J.P. Knauer, S.J. McNaught and D.D. Meyerhofer, "Precision tests of laser-tunneling ionization models": in Applications of High Field and Short Wavelength Sources VII, OSA Technical Digest Series 7, 75-76 (1997).

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Equations (9)

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ω if exp { 2 Im 0 t 0 [ E f ( t ) + E i ] dt } .
γ = ω 2 E i F 1 .
E f ( t ) = 1 2 p 0 2 c 2 + c 4 c 2 + p 2 c 2 + c 4 2 p 0 2 c 2 + c 4 .
2 F sin ωt ω = ( 1 + c 4 p 0 2 c 2 + c 4 ) ( p p 0 ) + c 2 3 ( p 0 2 c 2 + c 4 ) ( p 3 p 0 3 ) .
E e = p 0 2 c 2 + c 4 c 2 < c 2
ω if = ω 0 exp [ 2 E e γ 3 3 ω E e 2 γ ω c 2 ] .
Δ E e ( non rel ) ~ 3 ω 2 γ 3 .
E e > γ 2 c 2
Δ E e ( rel ) ~ c γ ω .

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