Abstract

Relativistic ionization of hydrogen by intense, linearly polarized light is treated by the Strong Field Approximation (SFA). Both bound and ionized states are described by the Dirac equation, with spin effects fully included. The applied laser field is also treated relativistically. There is no recourse to the dipole approximation nor to large-component, small-component approximations. Examples are calculated for the long-pulse limit of a uniformly distributed laser field. A prediction is verified that relativistic effects will appear with linear polarization of the laser at lower intensities than with circular polarization. Strong-field atomic stabilization is found to be enhanced by relativistic effects.

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References

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  1. H. R. Reiss, "Relativistic strong-field ionization", J. Opt. Soc. Am. B 7, 574-586 (1990).
    [CrossRef]
  2. D. P. Crawford and H. R. Reiss, "Stabilization in relativistic photoionization with circularly polarized light", Phys. Rev. A 50, 1844-1850 (1994).
    [CrossRef] [PubMed]
  3. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1959).
  4. E. S. Sarachik and G. T. Schappert, "Classical theory of the scattering of intense laser radiation by free electrons", Phys. Rev. D 1, 2738-2753 (1970).
    [CrossRef]
  5. 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]
  6. D. P. Crawford, "Relativistic ionization with intense linearly polarized light", doctoral dissertation, American University, 1994.
  7. H. R. Reiss, "Energetic electrons in strong-field ionization", Phys. Rev. A 54, R1765-R1768 (1996).
    [CrossRef] [PubMed]
  8. H. R. Reiss, "Effect of an intense electromagnetic field on a weakly bound system", Phys. Rev. A 22, 1786-1813 (1980).
    [CrossRef]
  9. L. V. Keldysh, "Ionization in the field of a strong electromagnetic wave", Sov Phys. JETP 20, 1307-1314 (1965).
  10. H. R. Reiss, "High-frequency, high-intensity photoionization", J. Opt. Soc. Am. B 13, 355-362 (1966).
    [CrossRef]
  11. H. R. Reiss, "Frequency and polarization effects in stabilization", Phys. Rev. A 46, 391-394 (1992).
    [CrossRef] [PubMed]
  12. H. R. Reiss and V. P. Krainov, "Approximation for a Coulomb-Volkov solution in strong fields", Phys. Rev. A 50, R910-R912 (1994).
    [CrossRef] [PubMed]
  13. U. Mohideen, M. H. Sher, and H. W. K. Tom, "High intensity above-threshold ionization of He", Phys. Rev. Lett. 71, 509-512 (1993).
    [CrossRef] [PubMed]
  14. B. Walker, B. Sheehy, and L. F. DeMauro, "Precision measurement of strong-field double ionization of helium", Phys. Rev. Lett. 73, 1227-1230 (1994).
    [CrossRef] [PubMed]
  15. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).
  16. H. R. Reiss, "Physical basis for strong-field stabilization of atoms against ionization", Laser Phys. 7, 543-550 (1997).

Other (16)

H. R. Reiss, "Relativistic strong-field ionization", J. Opt. Soc. Am. B 7, 574-586 (1990).
[CrossRef]

D. P. Crawford and H. R. Reiss, "Stabilization in relativistic photoionization with circularly polarized light", Phys. Rev. A 50, 1844-1850 (1994).
[CrossRef] [PubMed]

L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1959).

E. S. Sarachik and G. T. Schappert, "Classical theory of the scattering of intense laser radiation by free electrons", Phys. Rev. D 1, 2738-2753 (1970).
[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]

D. P. Crawford, "Relativistic ionization with intense linearly polarized light", doctoral dissertation, American University, 1994.

H. R. Reiss, "Energetic electrons in strong-field ionization", Phys. Rev. A 54, R1765-R1768 (1996).
[CrossRef] [PubMed]

H. R. Reiss, "Effect of an intense electromagnetic field on a weakly bound system", Phys. Rev. A 22, 1786-1813 (1980).
[CrossRef]

L. V. Keldysh, "Ionization in the field of a strong electromagnetic wave", Sov Phys. JETP 20, 1307-1314 (1965).

H. R. Reiss, "High-frequency, high-intensity photoionization", J. Opt. Soc. Am. B 13, 355-362 (1966).
[CrossRef]

H. R. Reiss, "Frequency and polarization effects in stabilization", Phys. Rev. A 46, 391-394 (1992).
[CrossRef] [PubMed]

H. R. Reiss and V. P. Krainov, "Approximation for a Coulomb-Volkov solution in strong fields", Phys. Rev. A 50, R910-R912 (1994).
[CrossRef] [PubMed]

U. Mohideen, M. H. Sher, and H. W. K. Tom, "High intensity above-threshold ionization of He", Phys. Rev. Lett. 71, 509-512 (1993).
[CrossRef] [PubMed]

B. Walker, B. Sheehy, and L. F. DeMauro, "Precision measurement of strong-field double ionization of helium", Phys. Rev. Lett. 73, 1227-1230 (1994).
[CrossRef] [PubMed]

J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).

H. R. Reiss, "Physical basis for strong-field stabilization of atoms against ionization", Laser Phys. 7, 543-550 (1997).

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Figures (2)

Figure 1.
Figure 1.

Transition rate as a function of intensity for a frequency ω = 8 a.u. Both scales are logarithmic. One hundred points were computed for each decade in intensity.

Figure 2.
Figure 2.

Transition rate as a function of intensity for a frequency ω = 2 a.u. Both scales are logarithmic. Twenty five points were computed for each decade in intensity.

Equations (34)

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U p m c 2
U p < 2 ħ ω α ,
( S 1 ) fi = i dt Ψ f ( ) H I Φ i
i t Φ = H 0 Φ
i t Ψ = ( H 0 + H I ) Ψ
H I = 1 c A · p + 1 2 c 2 A 2
( S 1 ) fi = i d 4 x Ψ ¯ f ( ) 1 c A μ γ μ Φ i
( i γ μ u γ 0 V c c ) Φ = 0
( i γ μ u γ μ A μ c γ 0 V c c ) Ψ = 0
Ψ Volk ( ) = ( c 2 EV ) 1 2 ( 1 + 1 2 cp · k k μ A ν γ μ γ ν ) u
× exp [ ip · x + i k · x d ( k · x ) ( A · p cp · k A 2 2 c 2 p · k ) ] ,
p · k = p 0 k 0 p · k
= c 2 p · k .
dW d Ω = 2 a 2 π c 2 Z 3 n p ( 𝑈 A + 𝑈 B + 𝑈 C ) [ 1 + ( ρ Z ) 2 ] 4 ,
ρ = p c ( n η ) k c ,
dW d Ω = 8 ω π ( E B ω ) 5 2 n = n 0 ( n z E B ω ) 1 2 ( n z ) 2 ( J n ) 2 ,
J n ( z 1 2 χ , z 2 ) , χ = 8 1 2 ( n z E B ω ) 1 2 cos θ .
z U p ω .
𝑈 A = 1 4 𝙋 ( ρ Z ) 2 [ J n + 1 u v + J n 1 u v ] 2
× { ( E c 2 1 ) ( ξρ Z ) 2 𝑈 2 + ( E c 2 + 1 ) β 2 ν 2
+ 2 ξ ( β Z ) p c [ p c ( 1 2 sin 2 Θ cos 2 Φ ) ( n η ) ω m cos Θ ] UV } ,
𝑈 B = 𝙋 4 ( ρ a 0 Z ) 2 ( m ) 1 2 ( E m p m cos Θ ) p m sin Θ cos Φ
× { ( n v + 2 ) J n u v u 2 v [ J n 1 u v + J n + 1 u v ] }
× [ J n 1 u v + J n + 1 u v ]
× [ ( ξρ a 0 Z ) 2 𝑈 2 + 2 ( β a 0 Z ) ( 2 p m cos Θ E m m ) UV + β 2 V 2 ] ,
𝑈 C = ω m z 8 ( E m p m cos Θ ) 𝙋 ( ρ a 0 Z ) 2
× [ ( 2 + n v ) J n u v u 2 v [ J n 1 u v + J n + 1 u v ] ] 2
× [ ( ξρ a 0 Z ) 2 U 2 + 2 ( βm a 0 Z ) ξ ( p m cos Θ m ) UV + β 2 V 2 ] .
ξ ( 1 Z 2 α 2 ) ,
β ( 1 ξ )
P ( 1 + ξ ) [ Γ ( ξ ) ] 2 2 2 ( ξ 1 ) Γ ( 1 + 2 ξ ) [ 1 + ( ρ Z ) 2 ] 2 ξ ( ρ Z ) 6 .
dW d Ω NRL 8 ω B 5 2 π n = n 0 ( n z B ) 1 2 ( n z ) 2 J n 2 ( u NRL , 1 2 z ) ,
I 5 ω 3 ,
I 4 ω 3 ( 1 E B ω ) = 4 ω 3 2 ω 2 4 ω 3

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