Abstract

The effect of magnetic dipole interactions on the angular distribution of electrons in the tunneling ionization of atoms is considered theoretically. Linearly polarized radiation is assumed. It is shown that an asymmetry in the angular distribution of ejected electrons in the azimuthal angle appears. We conclude that the angular distribution is strongly changed by relativistic effects even at electron velocities that are small compared with the speed of the light.

© 1992 Optical Society of America

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References

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  1. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-relativistic Theory), 3rd ed. (Pergamon, New York, 1987).
  2. N. B. Delone and V P. Krainov, J. Opt. Soc. Am. B 8, 1207 (1991).
    [Crossref]
  3. V A. Pazdzersky and V. A. Yurovsky, J. Phys. B 24, 733 (1991).
    [Crossref]
  4. L. D. Landau and E. M. Lifshitz, Field Theory, 2nd ed. (Pergamon, New York, 1977).
  5. H. R. Reiss, Phys. Rev. A 42, 1563 (1990).
    [Crossref]
  6. S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
    [Crossref]
  7. S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
    [Crossref] [PubMed]

1991 (2)

N. B. Delone and V P. Krainov, J. Opt. Soc. Am. B 8, 1207 (1991).
[Crossref]

V A. Pazdzersky and V. A. Yurovsky, J. Phys. B 24, 733 (1991).
[Crossref]

1990 (1)

H. R. Reiss, Phys. Rev. A 42, 1563 (1990).
[Crossref]

1989 (1)

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

1985 (1)

S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
[Crossref]

Augst, S.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

Chin, S. L.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
[Crossref]

Delone, N. B.

Eberly, J. H.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

Krainov, V P.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-relativistic Theory), 3rd ed. (Pergamon, New York, 1987).

L. D. Landau and E. M. Lifshitz, Field Theory, 2nd ed. (Pergamon, New York, 1977).

Lavigne, P.

S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-relativistic Theory), 3rd ed. (Pergamon, New York, 1987).

L. D. Landau and E. M. Lifshitz, Field Theory, 2nd ed. (Pergamon, New York, 1977).

Meyerhofer, D. D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

Pazdzersky, V A.

V A. Pazdzersky and V. A. Yurovsky, J. Phys. B 24, 733 (1991).
[Crossref]

Reiss, H. R.

H. R. Reiss, Phys. Rev. A 42, 1563 (1990).
[Crossref]

Strickland, D.

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

Yergeau, F.

S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
[Crossref]

Yurovsky, V. A.

V A. Pazdzersky and V. A. Yurovsky, J. Phys. B 24, 733 (1991).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B (2)

V A. Pazdzersky and V. A. Yurovsky, J. Phys. B 24, 733 (1991).
[Crossref]

S. L. Chin, F. Yergeau, and P. Lavigne, J. Phys. B 18, L213 (1985).
[Crossref]

Phys. Rev. A (1)

H. R. Reiss, Phys. Rev. A 42, 1563 (1990).
[Crossref]

Phys. Rev. Lett. (1)

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, Phys. Rev. Lett. 63, 2212 (1989).
[Crossref] [PubMed]

Other (2)

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-relativistic Theory), 3rd ed. (Pergamon, New York, 1987).

L. D. Landau and E. M. Lifshitz, Field Theory, 2nd ed. (Pergamon, New York, 1977).

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Figures (2)

Fig. 1
Fig. 1

Angular distribution of electrons [Eq. (17)] for the tunneling ionization of Xe atoms by linearly polarized radiation of frequency ω = 0.1 eV and the field strength F = 5 × 108 V/cm. θm = 1.6° and an electron energy E = 790 eV Curve 1, azimuthal angle ψ = π/2; curve 2, ψ = 3π/2.

Fig. 2
Fig. 2

Curve 1, maximum ionization rate [Eq. (20)] for the angle ψ = π/2 as a function of the ratio E/En (where E is the electron energy). Curve 2, dependence of angle θm on E/En according to relation (19).

Equations (20)

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w nE = exp { 2 Im t 1 t 0 [ E ( t ) E n ] d t } .
γ = ω ( 2 E n ) 1 / 2 / F 1 .
w n E = exp { 2 ( 2 E n ) 3 / 2 / 3 F [ 2 E ( 2 E n ) 1 / 2 / F ] θ 2 } .
E F 2 / ω 2 c 2
A ( z , t ) = A 0 ê x sin ( ω t k z ) .
L = [ ( 2 + 2 + ż 2 ) / 2 ] + F ( / ω ) [ sin ω t ( k z ) F cos ω t ] .
= F cos ω t ( F / c ) ( ω z ) sin ω t + ( F / c ) ż cos ω t ,
z ¨ = ( F / c ) cos ω t ,
ÿ = 0 .
E ( t ) = ( 1 / 2 ) { υ x 2 + υ y 2 + υ z 2 2 υ x F t + ( F t ) 2 [ 1 ( υ z / c ) ] } .
E ( t 0 ) = | E n | , t 0 = Re t 0 + i Im t 0 .
Re t 0 = ( υ x / F ) ( 1 + υ z / c ) ,
Im t 0 = F 1 ( 2 | E n | + υ y 2 + υ z 2 ) 1 / 2 × { 1 + ( υ z / 2 c ) [ 1 υ x 2 ( 2 | E n | + υ y 2 + υ z 2 ) 1 ] } .
υ x = ( 2 E ) 1 / 2 , υ y = ( 2 E ) 1 / 2 θ cos ψ , υ z = ( 2 E ) 1 / 2 θ sin ψ ,
w nE ( relat ) = w nE ( nonrelat ) exp [ φ ( θ , ψ ) ] ,
φ ( θ , ψ ) = ( 4 | E n | 3 / 2 E 1 / 2 / 3 F c ) [ 3 E / | E n | ) 1 ] θ sin ψ .
w n E ( θ , ψ ) = w n E ( 0 ) exp { [ 2 E ( 2 E n ) 1 / 2 / F ] θ 2 + ( 4 E 3 / 2 E 1 / 2 / F c ) θ sin ψ } .
w n E ( θ , ψ ) = w max exp { [ 2 E ( 2 E n ) 1 / 2 / F ] ( θ θ m ) 2 } ,
θ m = ( E / 2 c 2 ) 1 / 2 sin ψ 1 .
w max ( ψ ) = w max ( 0 ) exp { [ E 2 ( 2 E n ) 1 / 2 / F c 2 ] sin 2 ψ } .

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