Abstract

The S-matrix amplitude of nonsequential double ionization, written down in the Volkov state basis, has been calculated by a saddle-point method. The distribution in the total and relative momenta of the two emitted electrons is given in analytical form. The result obtained is discussed in the context of the recently measured differential momentum distributions in argon.

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References

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  1. L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Zh. Eksp. Teor. Fiz. 47, 1945-1956 (1964).
  2. M. Lewenstain, Ph. Balcou, M. Yu. Ivanov, Anne L'Huilier, P.B. Corkum, "Theory of high-harmonic generation by low - frequency laser field," Phys. Rev. A 49, 2117- 2132 (1994).
    [CrossRef]
  3. M. Lewenstain, K.C. Kulander, K.J. Schafer, and P.H. Bucksbaum, "Rings in above - threshold ionization," Phys. Rev. A 51, 1495-1507 (1995).
  4. M. Yu. Kuchiev, "ATI as a source for multiply charged ion production in a laser field," J. Phys. B: At. Mol. Opt. Phys. 28, 5093-5115 (1995).
    [CrossRef]
  5. F.H.M. Faisal and A. Becker, "Mechanism of direct double ionization of helium in intense laser fields," in Super-Intense Laser-Atom Physics 1996, H.G. Muller and M.V. Fedorov eds. (NATO ASI Series, Ser. 3, vol. 13, Kluver Academic Publishers, London, 1996).
    [CrossRef]
  6. S.P. Goreslavskii and S.V. Popruzhenko, "Rescattering and quantum interference near the classical cutoffs," J. Phys. B: At. Mol. Opt. Phys. 32, L531-L538 (1999).
    [CrossRef]
  7. S.P. Goreslavskii and S.V. Popruzhenko, "Tunneling limit in the theory of photoelectron rescattering by the parent ion, " Zh. Eksp. Teor. Fiz. 117, 895-905 (2000), (JETP 90, 778-787).
  8. R. Kopold, W. Becker, M. Kleber, "Quantum path analysis of high-order above-threshold ionization," Opt. Comm. 179, 39-50 (2000).
    [CrossRef]
  9. S.P. Goreslavskii and S.V. Popruzhenko, "Electron momentum distributions for double ionization in the strong field limit," (NATO ASI Series, Kluver Academic Publishers, London, 2001), (to be published).
  10. A. Becker and F.H.M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3546-3549 (2000).
    [CrossRef] [PubMed]
  11. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger , O. Jagutzki, V. Mergel, F. Afanch, G. Urbasch, M. Volmer, H. Giessen, and R. Doerner, "Recoil-Ion Momentum Distribution for Single and Double Ionization of Helium in Strong Laser Fields," Phys. Rev. Lett. 84, 443-446 (2000).
    [CrossRef] [PubMed]
  12. Th. Weber , H. Giessen., M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Volmer,and R. Doerner, "Correlated Electron Emission in Multiphoton Double Ionization," Nature 405, 658-661 (2000).
    [CrossRef] [PubMed]
  13. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afanch, G. Urbasch, M. Volmer, H. Giessen,a nd R. Doerner, "Sequential and nonsequential contributions to double ionization in strong laser fields," J. Phys. B: At. Mol. Opt. Phys. 33, L127- L133 (2000).
    [CrossRef]
  14. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schroder, J. Ullrich, H. Rottke, C. Tramp, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner, Phys. Rev. Lett., 84, 447-50 (2000).
    [CrossRef] [PubMed]
  15. P.B. Corkum, "Plasma Perspective on Strong - Field Multiphoton Ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  16. R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to Nonsequential Double Ionization," Phys. Rev. Lett. 85, 3781-3784 (2000).
    [CrossRef] [PubMed]

Other

L.V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Zh. Eksp. Teor. Fiz. 47, 1945-1956 (1964).

M. Lewenstain, Ph. Balcou, M. Yu. Ivanov, Anne L'Huilier, P.B. Corkum, "Theory of high-harmonic generation by low - frequency laser field," Phys. Rev. A 49, 2117- 2132 (1994).
[CrossRef]

M. Lewenstain, K.C. Kulander, K.J. Schafer, and P.H. Bucksbaum, "Rings in above - threshold ionization," Phys. Rev. A 51, 1495-1507 (1995).

M. Yu. Kuchiev, "ATI as a source for multiply charged ion production in a laser field," J. Phys. B: At. Mol. Opt. Phys. 28, 5093-5115 (1995).
[CrossRef]

F.H.M. Faisal and A. Becker, "Mechanism of direct double ionization of helium in intense laser fields," in Super-Intense Laser-Atom Physics 1996, H.G. Muller and M.V. Fedorov eds. (NATO ASI Series, Ser. 3, vol. 13, Kluver Academic Publishers, London, 1996).
[CrossRef]

S.P. Goreslavskii and S.V. Popruzhenko, "Rescattering and quantum interference near the classical cutoffs," J. Phys. B: At. Mol. Opt. Phys. 32, L531-L538 (1999).
[CrossRef]

S.P. Goreslavskii and S.V. Popruzhenko, "Tunneling limit in the theory of photoelectron rescattering by the parent ion, " Zh. Eksp. Teor. Fiz. 117, 895-905 (2000), (JETP 90, 778-787).

R. Kopold, W. Becker, M. Kleber, "Quantum path analysis of high-order above-threshold ionization," Opt. Comm. 179, 39-50 (2000).
[CrossRef]

S.P. Goreslavskii and S.V. Popruzhenko, "Electron momentum distributions for double ionization in the strong field limit," (NATO ASI Series, Kluver Academic Publishers, London, 2001), (to be published).

A. Becker and F.H.M. Faisal, "Interpretation of momentum distribution of recoil ions from laser induced nonsequential double ionization," Phys. Rev. Lett. 84, 3546-3549 (2000).
[CrossRef] [PubMed]

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger , O. Jagutzki, V. Mergel, F. Afanch, G. Urbasch, M. Volmer, H. Giessen, and R. Doerner, "Recoil-Ion Momentum Distribution for Single and Double Ionization of Helium in Strong Laser Fields," Phys. Rev. Lett. 84, 443-446 (2000).
[CrossRef] [PubMed]

Th. Weber , H. Giessen., M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Volmer,and R. Doerner, "Correlated Electron Emission in Multiphoton Double Ionization," Nature 405, 658-661 (2000).
[CrossRef] [PubMed]

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afanch, G. Urbasch, M. Volmer, H. Giessen,a nd R. Doerner, "Sequential and nonsequential contributions to double ionization in strong laser fields," J. Phys. B: At. Mol. Opt. Phys. 33, L127- L133 (2000).
[CrossRef]

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schroder, J. Ullrich, H. Rottke, C. Tramp, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner, Phys. Rev. Lett., 84, 447-50 (2000).
[CrossRef] [PubMed]

P.B. Corkum, "Plasma Perspective on Strong - Field Multiphoton Ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to Nonsequential Double Ionization," Phys. Rev. Lett. 85, 3781-3784 (2000).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Momentum distribution of double ions along the polarization axis, obtained by integration of the distribution (6) over the relative momentum. Left panel is for He 2+ at intensity 6.6·1014 Wcm -2, full squares show the result of ref. [10]. Right panel is for Ar 2+ at intensities 2.0·1014 Wcm -2 (red), 3.8·1014 Wcm-2 (blue), 15·1014 Wcm -2 (black).

Fig. 2.
Fig. 2.

Momentum distribution of the two emitted electrons along the polarization axis in the case of P =q =0 for Ar atoms at laser intensity 2,0·1014 Wcm -2. Right panel presents the same distribution at a larger scale and here the quantum domain is shown by white color. Momenta are shown in atomic units and 2qx =p 1x -p 2x in our notations.

Fig. 3.
Fig. 3.

The same as in Fig.2 but for intensity 3.8·1014 Wcm -2.

Fig. 4.
Fig. 4.

The same as in Fig.2 but for intensity 15·1014 Wcm -2.

Equations (9)

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M ( 2 e ) ( P , q ) = i k + d t 1 Ψ P q ( t 1 ) 1 r 12 Ψ k 0 + ( t 1 ) M ( e ) ( k , t 1 )
M ( e ) ( k , t 1 ) = i t 1 d t Ψ k 0 + ( t ) V F ( t ) Ψ 0 ( t )
Ψ k ( r , t ) = exp ( i Π k ( t ) r i 2 t Π k 2 ( τ ) d τ )
I 1 F sin ω t 0 + F ω 2 [ ω ( t 1 t 0 ) cos ω t 0 sin ω t 1 + sin ω t 0 ] = 0
1 2 Π k ( t 0 ) 2 ( t 1 ) = I 2 + q 2 + 1 4 Σ P 2 ( t 1 )
d W ( 2 e ) ( P , q ) = ( w + w + 2 ( w w + ) 1 2 sin S + ) d 3 P d 3 q
S = I 1 t 0 + I 2 t 1 + q 2 t 1 + 1 4 t 1 d t Σ P 2 ( t ) 1 2 t 0 t 1 d t Π k ( t 0 ) 2 ( t )
w ( P , q ) A ( e 2 e ) ( Σ P ( t 1 ) , q , Π k ( t 0 ) ( t 1 ) ) 2 sin 2 ω t 0 Δ 2 ( t 1 , t 0 ) D ( t 1 , t 0 ) exp ( 2 F a 3 F ( t 0 ) )
A ( e 2 e ) ( P * , q * , k * ) ( 2 I 2 + ( P * k * ) 2 ) 2 [ ( k * + q * P * 2 ) 2 + ( k * q * P * 2 ) 2 ]

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