Abstract

Recently observed momentum distribution of doubly charged recoil-ions of atoms produced by femtosecond infrared laser pulses is analyzed using the so-called intense-field many-body S-matrix theory. Observed characteristics of the momentum distributions, parallel and perpendicular to the polarization axis, are reproduced by the theory. It is shown that correlated energy-sharing between the two electrons in the intermediate state and their ‘Volkov-dressing’ in the final state, can explain the origin of these characteristics.

© 2001 Optical Society of America

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  1. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
    [Crossref] [PubMed]
  2. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
    [Crossref] [PubMed]
  3. B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
    [Crossref] [PubMed]
  4. S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
    [Crossref]
  5. J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
    [Crossref]
  6. E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
    [Crossref]
  7. J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
    [Crossref]
  8. F.H.M. Faisal and A. Becker, “‘Intense-Field Many-Body S-Matrix Theory’ and mechanism of laser induced double ionization of Helium,” in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397–410.
    [Crossref]
  9. F.H.M. Faisal and A. Becker, “Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields” in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118–131.
  10. F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).
  11. A. Becker and F.H.M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B 29, L197–L202 (1996).
    [Crossref]
  12. F.H.M. Faisal and A. Becker, “Non-sequential double ionization: Mechanism and model formula,” Laser Phys. 7, 684–689 (1997).
  13. A. Becker and F.H.M. Faisal, “Interplay of electron correlation and intense field dynamics in double ionization of helium,” Phys. Rev. A 59, R1742–R1745 (1999).
    [Crossref]
  14. A. Becker and F.H.M. Faisal, “Production of high charge states of Xe in a femtosecond laser pulse,” Phys. Rev. A 59, R3182–R3185 (1999).
    [Crossref]
  15. A. Becker and F.H.M. Faisal, “S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses,” J. Phys. B 32, L335–L343 (1999).
    [Crossref]
  16. 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]
  17. F.H.M. Faisal, “Exact Solution of the Schrödinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field,” Phys. Lett. A 187, 180–184 (1994).
    [Crossref]
  18. A. Becker and F.H.M. Faisal, “Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields,” Phys. Rev. A 50, 3256–3264 (1994).
    [Crossref] [PubMed]
  19. F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press: New York, 1987).
  20. C. Joachain, Quantum Collision Theory, 3rd edn., (North-Holland, Amsterdam, 1983).
  21. H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
    [Crossref]
  22. L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP20, 1307–1314 (1965) [Zh. Eksp. Teor. Fiz.47, 1945–1957 (1964)]
  23. F.H.M. Faisal, “Multiple Absorption of Laser Photons by Atoms,” J. Phys. B 6, L89–92 (1973).
    [Crossref]
  24. P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [Crossref] [PubMed]
  25. D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
    [Crossref]
  26. A. Erdélyi (Ed.), Higher Transcendental Functions, Vol. 2, (New York: McGraw-Hill, 1953).
  27. The uncertainty in the intensity measurement is ≈15–30%, and that of momentum resolution ≈0.2–0. 4 a.u. [R. Dörner, and H. Rottke (private communication)].
  28. W. Lotz, “Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium,” Zeit. f. Phys. 216, 241–247 (1968).
    [Crossref]

2001 (1)

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

2000 (3)

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

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]

1999 (4)

A. Becker and F.H.M. Faisal, “Interplay of electron correlation and intense field dynamics in double ionization of helium,” Phys. Rev. A 59, R1742–R1745 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Production of high charge states of Xe in a femtosecond laser pulse,” Phys. Rev. A 59, R3182–R3185 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses,” J. Phys. B 32, L335–L343 (1999).
[Crossref]

F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).

1998 (2)

E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
[Crossref]

S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
[Crossref]

1997 (2)

F.H.M. Faisal and A. Becker, “Non-sequential double ionization: Mechanism and model formula,” Laser Phys. 7, 684–689 (1997).

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

1996 (2)

A. Becker and F.H.M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B 29, L197–L202 (1996).
[Crossref]

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

1994 (3)

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

F.H.M. Faisal, “Exact Solution of the Schrödinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field,” Phys. Lett. A 187, 180–184 (1994).
[Crossref]

A. Becker and F.H.M. Faisal, “Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields,” Phys. Rev. A 50, 3256–3264 (1994).
[Crossref] [PubMed]

1993 (1)

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

1980 (1)

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[Crossref]

1973 (1)

F.H.M. Faisal, “Multiple Absorption of Laser Photons by Atoms,” J. Phys. B 6, L89–92 (1973).
[Crossref]

1968 (1)

W. Lotz, “Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium,” Zeit. f. Phys. 216, 241–247 (1968).
[Crossref]

Afaneh, F.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Agostini, P.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Becker, A.

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]

A. Becker and F.H.M. Faisal, “S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses,” J. Phys. B 32, L335–L343 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Interplay of electron correlation and intense field dynamics in double ionization of helium,” Phys. Rev. A 59, R1742–R1745 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Production of high charge states of Xe in a femtosecond laser pulse,” Phys. Rev. A 59, R3182–R3185 (1999).
[Crossref]

F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).

F.H.M. Faisal and A. Becker, “Non-sequential double ionization: Mechanism and model formula,” Laser Phys. 7, 684–689 (1997).

A. Becker and F.H.M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B 29, L197–L202 (1996).
[Crossref]

A. Becker and F.H.M. Faisal, “Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields,” Phys. Rev. A 50, 3256–3264 (1994).
[Crossref] [PubMed]

F.H.M. Faisal and A. Becker, “Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields” in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118–131.

F.H.M. Faisal and A. Becker, “‘Intense-Field Many-Body S-Matrix Theory’ and mechanism of laser induced double ionization of Helium,” in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397–410.
[Crossref]

Blodgett-Ford, S.

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

Charalambidis, D.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Chin, S.L.

S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
[Crossref]

Clark, C.W.

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

Corkum, P.

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

DiMauro, L.F.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Dorn, A.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Dörner, R.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Dundas, D.

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

Faisal, F.H.M.

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]

A. Becker and F.H.M. Faisal, “S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses,” J. Phys. B 32, L335–L343 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Production of high charge states of Xe in a femtosecond laser pulse,” Phys. Rev. A 59, R3182–R3185 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Interplay of electron correlation and intense field dynamics in double ionization of helium,” Phys. Rev. A 59, R1742–R1745 (1999).
[Crossref]

F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).

F.H.M. Faisal and A. Becker, “Non-sequential double ionization: Mechanism and model formula,” Laser Phys. 7, 684–689 (1997).

A. Becker and F.H.M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B 29, L197–L202 (1996).
[Crossref]

F.H.M. Faisal, “Exact Solution of the Schrödinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field,” Phys. Lett. A 187, 180–184 (1994).
[Crossref]

A. Becker and F.H.M. Faisal, “Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields,” Phys. Rev. A 50, 3256–3264 (1994).
[Crossref] [PubMed]

F.H.M. Faisal, “Multiple Absorption of Laser Photons by Atoms,” J. Phys. B 6, L89–92 (1973).
[Crossref]

F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press: New York, 1987).

F.H.M. Faisal and A. Becker, “‘Intense-Field Many-Body S-Matrix Theory’ and mechanism of laser induced double ionization of Helium,” in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397–410.
[Crossref]

F.H.M. Faisal and A. Becker, “Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields” in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118–131.

Faucher, O.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Feuerstein, B.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Giessen, H.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Hoffmann, K.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Jagutzki, O.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Joachain, C.

C. Joachain, Quantum Collision Theory, 3rd edn., (North-Holland, Amsterdam, 1983).

Keldysh, L.V.

L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP20, 1307–1314 (1965) [Zh. Eksp. Teor. Fiz.47, 1945–1957 (1964)]

Korn, G.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Kulander, K.C.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Lambropoulos, P.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Larochelle, S.

S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
[Crossref]

Lotz, W.

W. Lotz, “Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium,” Zeit. f. Phys. 216, 241–247 (1968).
[Crossref]

Maragakis, P.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Mehring, K.J.

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

Mergel, V.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Moore, L.R.

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

Moshammer, R.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Muth-Böhm, J.

F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).

Parker, J.S.

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
[Crossref]

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

Reiss, H.R.

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[Crossref]

Rottke, H.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Sandner, W.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Schafer, K.J.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Schmitt, W.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Schröder, C.D.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Schröder, H.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Sheehy, B.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Smyth, E.S.

E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
[Crossref]

Spielberger, L.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Staudte, A.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Talebpour, A.

S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
[Crossref]

Taylor, K.T.

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
[Crossref]

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

Trump, C.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Uiterwaal, C.J.G.J.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Ullrich, J.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Urbasch, G.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Vollmer, M.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Walker, B.

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Weber, Th.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Weckenbrock, M.

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Wittmann, M.

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

Xenakis, D.

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Zhang, Jian

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Comp. Phys. Comm. (1)

E.S. Smyth, J.S. Parker, and K.T. Taylor, “Numerical integration of the time-depedent Schrödinger equation for laser-driven helium,” Comp. Phys. Comm. 114, 1–14 (1998).
[Crossref]

J. Phys. B (7)

J.S. Parker, L.R. Moore, K.J. Mehring, D. Dundas, and K.T. Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B 34, L69–L78 (2001).
[Crossref]

S. Larochelle, A. Talebpour, and S.L. Chin, “Non-sequential multiple ionization or rare gas atoms in a Ti:sapphire laser field,” J. Phys. B 31, 1201–1214 (1998).
[Crossref]

J.S. Parker, K.T. Taylor, C.W. Clark, and S. Blodgett-Ford, “Intense-field mutliphoton ionisation of a two-electron atom,” J. Phys. B 29, L33–L42 (1996).
[Crossref]

A. Becker and F.H.M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B 29, L197–L202 (1996).
[Crossref]

A. Becker and F.H.M. Faisal, “S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses,” J. Phys. B 32, L335–L343 (1999).
[Crossref]

F.H.M. Faisal, “Multiple Absorption of Laser Photons by Atoms,” J. Phys. B 6, L89–92 (1973).
[Crossref]

D. Charalambidis, D. Xenakis, C.J.G.J. Uiterwaal, P. Maragakis, Jian Zhang, H. Schröder, O. Faucher, and P. Lambropoulos “Multiphoton ionisation saturation intensities and generalised cross sections from ATI spectra,” J. Phys. B 30, 1467–1480 (1997).
[Crossref]

Laser Phys. (2)

F.H.M. Faisal, A. Becker, and J. Muth-Böhm, “Intense-Field Many-Body S-Matrix Theory: Applications to processes in intense laser fields,” Laser Phys. 9, 115–123 (1999).

F.H.M. Faisal and A. Becker, “Non-sequential double ionization: Mechanism and model formula,” Laser Phys. 7, 684–689 (1997).

Phys. Lett. A (1)

F.H.M. Faisal, “Exact Solution of the Schrödinger Equation of Two Electrons Interacting with an Intense Electromagnetic Field,” Phys. Lett. A 187, 180–184 (1994).
[Crossref]

Phys. Rev. A (4)

A. Becker and F.H.M. Faisal, “Correlated Keldysh-Faisal-Reiss theory of above-threshold double ionization of He in intense laser fields,” Phys. Rev. A 50, 3256–3264 (1994).
[Crossref] [PubMed]

A. Becker and F.H.M. Faisal, “Interplay of electron correlation and intense field dynamics in double ionization of helium,” Phys. Rev. A 59, R1742–R1745 (1999).
[Crossref]

A. Becker and F.H.M. Faisal, “Production of high charge states of Xe in a femtosecond laser pulse,” Phys. Rev. A 59, R3182–R3185 (1999).
[Crossref]

H.R. Reiss, “Effect of an intense electromagnetic field on weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
[Crossref]

Phys. Rev. Lett. (5)

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]

P. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distribution for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C.D. Schröder, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sandner “Momentum distribution of Nen+ ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000).
[Crossref] [PubMed]

B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, and K.C. Kulander “Precision measurement od strong field double ionization of helium,” Phys. Rev. Lett. 73, 1227–1230 (1994).
[Crossref] [PubMed]

Zeit. f. Phys. (1)

W. Lotz, “Electron-Impact Ionization Cross Sections and Ionization Rate Coefficients for Atoms and Ions from Hydrogen to Calcium,” Zeit. f. Phys. 216, 241–247 (1968).
[Crossref]

Other (7)

A. Erdélyi (Ed.), Higher Transcendental Functions, Vol. 2, (New York: McGraw-Hill, 1953).

The uncertainty in the intensity measurement is ≈15–30%, and that of momentum resolution ≈0.2–0. 4 a.u. [R. Dörner, and H. Rottke (private communication)].

L.V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP20, 1307–1314 (1965) [Zh. Eksp. Teor. Fiz.47, 1945–1957 (1964)]

F.H.M. Faisal and A. Becker, “‘Intense-Field Many-Body S-Matrix Theory’ and mechanism of laser induced double ionization of Helium,” in Selected Topics on Electron Physics, D.H. Campbell and H. Kleinpoppen, eds. (Plenum Press, New York, 1996) pp. 397–410.
[Crossref]

F.H.M. Faisal and A. Becker, “Effect of rescattering on ATI and e-e correlation on double ionization in intense laser fields” in Multiphoton Processes 1996, P. Lambropoulos and H. Walther, eds., Int. Nat. Conf. Ser. No. 154 (IOP: Bristol, 1997) pp. 118–131.

F.H.M. Faisal, Theory of Multiphoton Processes (Plenum Press: New York, 1987).

C. Joachain, Quantum Collision Theory, 3rd edn., (North-Holland, Amsterdam, 1983).

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Figures (6)

Fig. 1.
Fig. 1.

‘Correlation mediated energy-sharing diagram’ for laser induced non-sequential double ionization of He. For interpretation see text.

Fig. 2.
Fig. 2.

Recoil ion momentum distribution of He2+ parallel to the polarization direction, Ppar . (experimental data, panel a, [1]) and the sum-momentum of the two outgoing electrons in opposite direction (present theory, panel b, [16]).

Fig. 3.
Fig. 3.

The same as in Fig. 2 but perpendicular to the polarization direction; panel a (experiment, [1]), panel b (theory, [16]).

Fig. 4.
Fig. 4.

Sum-momentum distributions calculated without the final state ‘Volkov dressing’ of the two outgoing electrons: (a) parallel case (theory), c.f. Fig. 2; (b) perpendicular case (theory), c.f. Fig. 3.

Fig. 5.
Fig. 5.

Results of model calculations for the yields of He++-ions at λ=780 nm and τ=160 fs assuming a collision energy equal to the rescattering energy (dashed line) and to the back-scattering energy (solid line), in comparision with experimental data [3].

Fig. 6.
Fig. 6.

e - 2e’ rates as a function of the collision energy for He+ ions, as calculated from the Lotz formula [28].

Equations (33)

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H ( t ) = H i 0 + V i ( t ) ,
[ ( i d dt H i 0 ) V i ( t ) ] Ψ ( t ) > = 0
Ψ ( t ) > = ϕ i ( t ) > + t i t dt 1 G ( t , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > ,
[ i d dt H ( t ) ] G ( t , t ) = δ ( t t ) .
[ i d dt H i 0 ] ϕ i ( t ) > = 0 .
V i ( t ) = j = 1 , 2 [ 1 c p j · A ( t ) + 1 2 c 2 A 2 ( t ) ] .
H ( t ) = H f 0 ( t ) + V f ( t ) ,
[ i d dt H f 0 ( t ) ] G f 0 ( t , t ) = δ ( t t ) .
G ( t , t ) = G f 0 ( t , t ) + t i t d t 1 G f 0 ( t , t 1 ) V f ( t 1 ) G ( t 1 , t )
Ψ ( t ) > = ϕ i ( t ) > + t i t d t 1 G f 0 ( t , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
+ t i t t i t 2 d t 2 d t 1 G f 0 ( t , t 2 ) V f ( t 2 ) G ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > .
( S 1 ) f i ( t ) = i [ t i t d t 1 < ϕ f ( t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
+ t i t t i t 2 d t 2 d t 1 < ϕ f ( t 2 ) V f ( t 2 ) G ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) > ] .
H ( t ) = H 0 ( t ) + V 0 ( t ) ,
H 0 ( t ) = [ p 1 A ( t ) c ] 2 2 + [ p 2 2 2 m Z r 2 ] ; ( Z = 2 , for He ) .
G 0 ( t , t ) = i θ ( t t ) j 1 ( 2 π ) 3 d k k ϕ j + ( 2 ) >
× e i t t { [ ( k e A ( τ ) c ] 2 2 + E j } d τ < k ϕ j + ( 2 )
G ( t , t ) = G 0 ( t , t ) + t i t d t 1 G 0 ( t , t 1 ) V 0 ( t 1 ) G 0 ( t 1 , t ) + ,
( S 1 ) f i ( t ) = j = 1 S f i ( j ) ( t )
S f i ( 1 ) ( t ) = t i t d t 1 < ϕ f ( t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
S f i ( 2 ) ( t ) = t i t t i t 2 d t 2 d t 1 < ϕ f ( t 2 ) V f ( t 2 ) G 0 ( t 2 , t 1 ) V i ( t 1 ) ϕ i ( t 1 ) >
S f i ( 3 ) ( t ) = t i t t i t 3 t i t 2 d t 3 d t 2 d t 1 < ϕ f ( t 3 ) V f ( t 3 ) G 0 ( t 3 , t 2 ) V 0 ( t 2 ) V 0 ( t 2 )
× G 0 ( t 2 , t 1 ) V i ( t 1 ) | ϕ i ( t 1 ) >
S f i ( 2 ) ( t f , t i ) N S = i t i t f d t 2 < ϕ f V ( k a , k b ; r 1 , r 2 ; t 2 ) V corr ( t 2 ) Ψ i ( r 1 , r 2 ; t 2 ) >
Ψ i ( r 1 , r 2 ; t 2 ) = t i t 2 d t 1 G 0 ( r 1 , r 2 , t 2 ; r 1 , r 2 , t 1 ) V ATI ( t 1 ) ϕ 1 S ( r 1 , r 2 ; t 1 ) >
= i t i t 2 d t 1 j 1 ( 2 π ) 3 d k ϕ V ( k ; r 1 ; t 2 ) ϕ j + ( r 2 ; t 2 ) >
× < ϕ j + ( r 2 ; t 1 ) ϕ V ( k ; r 1 ; t 1 ) V ATI ( t 1 ) ϕ 1 S ( r 1 , r 2 ; t 1 ) >
S f i ( 2 ) ( , ) N S = 2 π i N δ ( k a 2 2 + k b 2 2 + E B + 2 U p N ω ) T ( N ) ( k a , k b ) ,
T ( N ) ( k a , k b ) = n j 1 ( 2 π ) 3 d k < ϕ 0 ( k a , r 1 ) ϕ 0 ( k b , r 2 ) 1 r 12 ϕ j + ( r 2 ) ϕ 0 ( k , r 1 ) >
× J N n ( α 0 · ( k a + k b k ) ; U p 2 ω ) J n ( α 0 · k ; U p 2 ω ) k 2 2 E j + E B + U p n ω + i 0
× ( E j E B k 2 2 ) < ϕ j + ( r 2 ) ϕ 0 ( k , r 1 ) ϕ 1 S ( r 1 , r 2 ) > ,
d Γ ( N ) d k a d k b = 2 π δ ( k a 2 2 + k b 2 2 + E B + 2 U p N ω ) T ( N ) ( k a , k b ) 2 .
P par . cut off ( k a ) par . + ( k b ) par . cut off Re ( 4 U p + ( 8 U p E B ) ) ,

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