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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 17070–17075
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Double ionization of HeH+ molecules in intense laser fields

Qing Liao, Peixiang Lu, Qingbin Zhang, Zhenyu Yang, and Xinbing Wang  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 17070-17075 (2008)
http://dx.doi.org/10.1364/OE.16.017070


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Abstract

We present quantum mechanical calculations of double ionization of HeH+ molecules by intense laser pulses at various intensities. The resulting two-electron momentum distributions exhibit a clear asymmetry, which depends on the laser intensity. The asymmetric charge configuration of HeH+ is responsible for the asymmetric two-electron momentum distributions. An approach to control the dynamics of double ionization of heteronuclear molecules is proposed.

© 2008 Optical Society of America

The mechanism for double ionization of atoms varies with the intensity in intense laser fields [1

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

]. At very high intensities, double ionization is dominated by sequential double ionization (SDI), in which two electrons are independently emitted one by one via tunneling ionization. This process produces uncorrelated electron pairs. At moderate intensities, double ionization is dominated by nonsequential double ionization (NSDI), in which correlated electron pairs are emitted almost simultaneously. Since the electronic correlation plays a fundamental role in understanding the interaction of intense laser fields with matter, NSDI has attracted a large number of experimental [2

2. Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emission in multiphoton double ionization,” Nature 405, 658–661 (2000). [CrossRef] [PubMed]

, 3

3. B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling,” Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]

, 4

4. M. Weckenbrock, A. Becker, A. Staudte, S. kammer, M. Smolarski, V. R. Bhardwaj, D. M. Rayner, D. M. Villeneuve, P. B. Corkum, and R. Dörner, “Electron-electron momentum exchange in strong field double ionization,” Phys. Rev. Lett. 91, 123004 (2003). [CrossRef] [PubMed]

, 5

5. J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96, 133001 (2006). [CrossRef] [PubMed]

] and theoretical [6

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

, 7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

, 8

8. R. Kopold, W. Becker, H. Rottke, and W. Sandner, “Routes to nonsequential double ionization,” Phys. Rev. Lett. 85, 3781–3784 (2000). [CrossRef] [PubMed]

, 9

9. C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker, “Electron-electron dynamics in laser-induced nonsequential double ionization,” Phys. Rev. A 69, 043405 (2004). [CrossRef]

] investigations. It has been shown that there are two different ionization mechanisms [3

3. B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling,” Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]

] in NSDI based on the classical rescattering model [10

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

]. In this model, the first ionized electron accelerated by the oscillating laser field returns and hits its parent ion inelastically, leading to the ionization of the second one in an (e,2e)-like process or the excitation with subsequent tunneling ionization of the second one.

However, for asymmetric molecules, the two-electron momentum distributions are expected to be asymmetric because the spatial inversion symmetry is broken. To the best of our knowledge, laser-induced double ionization of HeH+, the simplest two-electron heteronuclear molecule with asymmetric electric charge on nuclei, has not yet been studied. In this paper, we investigate the two-electron momentum distributions from double ionization of HeH + molecules by linearly polarized laser pulses. This is achieved by solving the time-dependent electronic Schödinger equation of a one-dimensional HeH+ molecule model within the clamped nuclei approximation, where the motion of both electrons is restricted to the z-axis (i.e., the laser polarization axis, see Fig. 3). The molecular axis is aligned parallel to the z-axis. The He and H nuclei are localized at z=-R/2 and z=R/2, respectively. The electron-nuclear interaction and the electron-electron repulsion are represented by a two-center soft-Coulomb potential (in atomic units) V(z1,z2)=2(z1+R2)2+11(z1R2)2+12(z2+R2)2+11(z2R2)2+1+1(z1z2)2+1. Here z 1 and z 2 are the electron coordinates, R is the internuclear distance. It has been shown that one-dimensional models qualitatively reproduces all important strong-field effects including double ionization [7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

, 16

16. M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, “Strong-field ionization dynamics of a model H2 molecule,” Phys. Rev. A 65, 033403 (2002). [CrossRef]

]. The length-gauge model Hamiltonian reads H(z1,z2,t)=122z12122z22+V(z1,z2)+(z1+z2)E(t), where E(t)=E 0 f(t)sin(ωt) is the electric field of a laser pulse with amplitude E 0, envelope function f (t) and frequency ω. The ground-state energy of HeH+ is -2.8 a.u., including the ionization potential of HeH+ I (1) p=1.05 a.u. and the ionization potential of HeH2 + I (2) p=1.75 a.u. The first excited-state energy of HeH2+ is -1.23 a.u.

The two-electron momentum distributions are obtained following the method proposed in [7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

]. The two-dimensional space is partitioned into three regions: (A) {|z 1|, |z 2|<a}, (B) {|z 1|< a, |z 2|≥a}, or {|z 1|≥ a, |z 2|<a} and (C) {|z 1|, |z 2| ≥ a} with a=200 a.u. Regions B and C correspond to single and double ionization respectively. In regions A and B, the wave function is propagated exactly by means of the split-operator spectral method [17

17. M. D. Feit, J. A. Fleck Jr., and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982). [CrossRef]

]. The initial wave function for time propagation is the field-free ground state, which is obtained by propagation in imaginary time. In region C, the distances between two electrons and between electrons and nuclei are very large so that Coulomb potential V(z 1, z 2) can be neglected. Therefore, the time evolution of the wave function can be performed only in the presence of the laser field by multiplications in momentum space [18

18. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H+2 dissociative ionization in intense laser fields,” Phys. Rev. A 57, 1176 (1998). [CrossRef]

]. The three regions are smoothly divided by a splitting technique [19

19. X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74, 031405(R) (2006). [CrossRef]

]. The modulus squared of the the final momentum-space wave function in region C directly gives the two-electron momentum distribution.

Our simulations use trapezoidally shaped 760 nm laser pulses with a total duration of 8 optical cycles, switched on and off linearly over 2 optical cycles. The whole region is taken to be a box of size 1600×1600 a.u. with a spatial grid-point separation of 0.4 a.u., which represents momenta extending from -7.85 to +7.85 a.u. in each electron momentum vector. The spectral method is applied 1000 time steps per optical cycle in regions A and B, and the splitting of the wave function is applied 25 times per optical cycle. After the end of the pulse, the wave function is allowed to propagate without laser field for an additional time of 8 optical cycles. In this way, all electron pairs with absolute momenta above 0.23 a.u. are collected. The final results are insensitive to the choice of a ranging from 100 to 200 a.u.

Fig. 1. Two-electron momentum distributions from double ionization of HeH+ at intensities (a) 1×1014 W/cm2, (b) 2×1014 W/cm2, (c) 4×1014 W/cm2, (d) 6×1014 W/cm2, (e) 1×1015 W/cm2, (f) 1.4×1015 W/cm2. Grey scales from 0 to (a) 1.1×10-5, (b) 6×10-3, (c) 0.14, (d) 0.45, (e) 1, (f) 1.2.

Figure 1 shows the resulting two-electron momentum distributions from double ionization of HeH+ molecules at an internuclear distance R=4 a.u. The momentum distributions at lower laser intensities are very different from those at higher laser intensities. At lower laser intensities, the two-electron momentum distributions exhibit a ‘butterfly’ shape in the first and third quadrants [see Figs. 1(a)1(c)]. The ‘butterfly’ shape is resulted from the repulsive force between the two electrons when they are emitted almost at the same time. This means that double ionization in this laser intensity range is nonsequential. In addition, the two-electron momentum distributions exhibit a clear asymmetry with respect to the diagonal p 1=-p 2. The two electrons have the preference for ejection in the positive z-axis direction, especially at an intensity of 4×1014 W/cm2.

Fig. 2. Two-electron momentum distributions calculated by the product of the single ionization spectra of HeH+ and HeH2+ at an intensity of 1×1015 W/cm2. Grey scale from 0 to 0.8.

At higher laser intensities, the two-electron momentum distributions also exhibit a clear asymmetry with respect to the diagonal p 1=-p 2 [see Figs. 1(e) and 1(f)]. However, in contrast to at lower intensities, the two electrons have the preference for ejection in the negative z-axis direction at higher intensities. The Coulomb repulsion between the two electrons completely loses its effect on the two-electron momentum distributions in this laser intensity range and thus the ‘butterfly’ shape disappears. This shows that double ionization is sequential in this laser intensity range. It can also be proved by the product of the single ionization yields of HeH+ and HeH2+. In single ionization calculations, we also use a soft-Coulomb potential V(z)=2(z+R2)2+b1(zR2)2+b to describe the electron interacting with the parent ion. b=2.6 and 0.47 reproduce the ionization potentials of HeH + and HeH2+, respectively. The single ionization spectra f (p) for HeH+ and g(p) for HeH2+ are calculated following the method used in Ref. [18

18. S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H+2 dissociative ionization in intense laser fields,” Phys. Rev. A 57, 1176 (1998). [CrossRef]

]. Figure 2 shows the product of the two single ionization spectra F(p 1, p 2)=f(p 1)g(p 2)+f(p 2)g(p 1) at an intensity of 1×1015 W/cm2, which is in good agreement with that in Fig. 1(e).

At moderate laser intensities, the two-electron momentum distribution becomes almost symmetric with respect to both diagonals [see Fig. 1(d)]. It is expected that both SDI and NSDI mechanisms contribute to double ionization at moderate laser intensities. For atoms, the two-electron momentum distributions, whether from SDI or from NSDI, are symmetric with respect to both diagonals [7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

]. It is very interesting that the two electrons involved in SDI and in NSDI of HeH+ molecules have opposite preferences for ejection in space.

Fig. 3. (a) Contour plot of the ground state probability density of HeH+. The electron cloud is predominantly localized on the He nucleus. (b) Combined Coulomb and laser filed potentials V(z)+E(t)z for HeH2+. The green dashed line indicates the ground state energy of HeH2+. The blue and red lines correspond to E(t)=-0.168 and 0.168 a.u. respectively. |E(t)|=0.168 a.u. is the maximum of a laser field with an intensity of 1×1015 W/cm2.
Fig. 4. (a) The schematic of the permanent dipole D of HeH2+. (b) The blue and green lines correspond to the kinetic energy of the electron returning from the negative z-axis to z=-4 a.u. and from the positive z-axis to z=4 a.u. respectively. The red line indicates the laser field.

The asymmetric charge configuration of HeH2+ essentially defines a permanent dipole D. The center of negative charge of HeH2+ is near the He nucleus and the center of positive charge is R/3 right from the He nucleus. Therefore, the permanent dipole D of HeH 2+ is directed from the He nucleus to the H nucleus [see Fig. 4(a)]. The asymmetry of the two-electron momentum distributions from NSDI can be interpreted as due to the influence of the permanent dipole D of HeH2+ on the inelastic recollision process, which leads to NSDI. We demonstrate the influence of the dipole moment on the recollision process using a simple one-dimensional classical model. Suppose the electron is ionized at the origin with zero velocity at time t 0 in the presence of only the laser field with an intensity of 4×1014 W/cm2. When it returns to the origin, it moves in the present of the laser field and the Coulomb field of the dipole moment. The Coulomb field is described by E c(z)=2(z+1)[(z+1)2+1]-3/2-2(z-1)[(z-1)2+1]-3/2. Figure 4(b) shows the kinetic energy of the returning electron as a function of ionization time t 0. The maximum kinetic energy of the returning electron from the positive z-axis is about 13 eV higher than that from the negative z-axis.

The classical trajectory calculations show that the permanent dipole D attracts the electron returning from the positive z-axis while repulses it from the negative z-axis. As a consequence, double ionization is enhanced when the electron recollides with the parent ion from the positive z-axis and suppressed from the negative z-axis. Generally, the electron recollides with the parent ion from some direction when the electric field becomes nearly zero. After recollision, the electric field reverses its sign and the two electrons are ejected all the same in this direction. Thus, double ionization in the positive z-axis direction is enhanced while in the negative z-axis direction is suppressed. This explains that the two electrons in NSDI of HeH+ molecules have the preference for ejection in the positive z-axis direction.

Controlling double ionization dynamics has been demonstrated by changing molecular alignment by Zeidler et al [15

15. D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Dö, and P. B. Corkum, “Controlling attosecond double ionization dynamics via molecular alignment,” Phys. Rev. Lett. 95, 203003 (2005). [CrossRef] [PubMed]

]. In their experiment, a pump pulse created a rotational wave packet in the N2 ensemble, then a time delayed probe pulse was used to ionize the aligned N2 molecules. It was found that the two electrons involved in NSDI more likely exit the molecule in the same direction when it is parallel to the probe pulse than when it is perpendicular. However, only symmetric two-electron momentum distributions were observed because N2 is a symmetric molecule. Here, we propose another approach to control attosecond NSDI dynamics. Our simulations show that the two electrons involved in NSDI more likely exit the HeH+ molecule in the direction of its permanent dipole than in the opposite direction when the molecular axis is parallel to the laser polarization direction. However, it is expected that this preference should disappear when the molecular axis is perpendicular to the laser polarization direction, because the charge configuration of HeH+ is symmetric with respect to the axis perpendicular to the laser polarization direction. Therefore, the dynamics of double ionization can be controlled by changing the angle between the molecular axis and the laser polarization direction.

In conclusion, the two-electron momentum distributions from double ionization of HeH + molecules have been studied by solving the time-dependent Schödinger equation. For atoms, the momentum distributions are symmetric with respect to both diagonals and the symmetry is independent of the laser intensity [7

7. M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

]. However, for HeH+ molecules, the momentum distributions exhibit a clear asymmetry, which depends on the laser intensity. When HeH+ is aligned parallel to the laser polarization direction, the two electrons tend to be ejected in the direction of its permanent dipole in NSDI, while in the opposite direction in SDI. For SDI, the asymmetry is induced by the asymmetric electron probability density of the ground state. For NSDI, the asymmetry is induced by the influence of the permanent dipole on the recollision process. Since this asymmetric momentum distributions result essentially from the asymmetric charge configuration of HeH+, it is expected to occur in any heteronuclear molecules. Moreover, this implies that controlling the alignment of the heteronuclear molecule with respect to the laser polarization enables the steering of double ionization in space.

This work was supported by the National Natural Science Foundation of China under Grants No. 10574050 and No. 10774054, the National Key Basic Research Special Foundation under Grant No. 2006CB806006, and the State Key Laboratory of Precision Spectroscopy of Huadong Normal University.

References and links

1.

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

2.

Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dörner, “Correlated electron emission in multiphoton double ionization,” Nature 405, 658–661 (2000). [CrossRef] [PubMed]

3.

B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schröter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Höhr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, “Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling,” Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]

4.

M. Weckenbrock, A. Becker, A. Staudte, S. kammer, M. Smolarski, V. R. Bhardwaj, D. M. Rayner, D. M. Villeneuve, P. B. Corkum, and R. Dörner, “Electron-electron momentum exchange in strong field double ionization,” Phys. Rev. Lett. 91, 123004 (2003). [CrossRef] [PubMed]

5.

J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, “High-energy cutoff in the spectrum of strong-field nonsequential double ionization,” Phys. Rev. Lett. 96, 133001 (2006). [CrossRef] [PubMed]

6.

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

7.

M. Lein, E. K. U. Gross, and V. Engel, “Intense-field double ionization of Helium: identifying the mechanism,” Phys. Rev. Lett. 85, 4707–4710 (2000). [CrossRef] [PubMed]

8.

R. Kopold, W. Becker, H. Rottke, and W. Sandner, “Routes to nonsequential double ionization,” Phys. Rev. Lett. 85, 3781–3784 (2000). [CrossRef] [PubMed]

9.

C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker, “Electron-electron dynamics in laser-induced nonsequential double ionization,” Phys. Rev. A 69, 043405 (2004). [CrossRef]

10.

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

11.

A. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C. L. Cocke, X. M. Tong, and C. D. Lin, “Rescattering double ionization of D2 and H2 by intense laser pulses,” Phys. Rev. Lett. 91, 163002 (2003). [CrossRef] [PubMed]

12.

F. Légaré, I. V. Litvinyuk, P. W. Dooley, F. Quéré, A. D. Bandrauk, D. M. Villeneuve, and P. B. Corkum, “Time-resolved double ionization with few cycle laser pulses,” Phys. Rev. Lett. 91, 093002 (2003). [CrossRef] [PubMed]

13.

S. Saugout and C. Cornaggia, “Temporal separation of H2 double-ionization channels using intense ultrashort 10-fs laser pulses,” Phys. Rev. A 73, 041406(R) (2006). [CrossRef]

14.

C. Beylerian, S. Saugout, and C. Cornaggia, “Non-sequential double ionization of H2 using ultrashort 10 fs laser pulses,” J. Phys. B 39, L105–L112 (2006). [CrossRef]

15.

D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Dö, and P. B. Corkum, “Controlling attosecond double ionization dynamics via molecular alignment,” Phys. Rev. Lett. 95, 203003 (2005). [CrossRef] [PubMed]

16.

M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, “Strong-field ionization dynamics of a model H2 molecule,” Phys. Rev. A 65, 033403 (2002). [CrossRef]

17.

M. D. Feit, J. A. Fleck Jr., and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982). [CrossRef]

18.

S. Chelkowski, C. Foisy, and A. D. Bandrauk, “Electron-nuclear dynamics of multiphoton H+2 dissociative ionization in intense laser fields,” Phys. Rev. A 57, 1176 (1998). [CrossRef]

19.

X. M. Tong, K. Hino, and N. Toshima, “Phase-dependent atomic ionization in few-cycle intense laser fields,” Phys. Rev. A 74, 031405(R) (2006). [CrossRef]

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(190.4180) Nonlinear optics : Multiphoton processes
(260.3230) Physical optics : Ionization
(270.6620) Quantum optics : Strong-field processes

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: September 2, 2008
Revised Manuscript: October 9, 2008
Manuscript Accepted: October 9, 2008
Published: October 10, 2008

Citation
Qing Liao, Peixiang Lu, Qingbin Zhang, Zhenyu Yang, and Xinbing Wang, "Double ionization of HeH+ molecules in intense laser fields," Opt. Express 16, 17070-17075 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-17070


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References

  1. B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, "Precision measurement of strong field double ionization of helium," Phys. Rev. Lett. 73, 1227-1230 (1994). [CrossRef] [PubMed]
  2. Th. Weber, H. Giessen, M. Weckenbrock, G. Urbasch, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, M. Vollmer, and R. Dorner, "Correlated electron emission in multiphoton double ionization," Nature 405, 658-661 (2000). [CrossRef] [PubMed]
  3. B. Feuerstein, R. Moshammer, D. Fischer, A. Dorn, C. D. Schroter, J. Deipenwisch, J. R. Crespo Lopez-Urrutia, C. Hohr, P. Neumayer, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, and W. Sandner, "Separation of recollision mechanisms in nonsequential strong field double ionization of Ar: the role of excitation tunneling," Phys. Rev. Lett. 87, 043003 (2001). [CrossRef] [PubMed]
  4. M. Weckenbrock, A. Becker, A. Staudte, S. kammer, M. Smolarski, V. R. Bhardwaj, D. M. Rayner, D. M. Villeneuve, P. B. Corkum, and R. Dorner, "Electron-electron momentum exchange in strong field double ionization," Phys. Rev. Lett. 91, 123004 (2003). [CrossRef] [PubMed]
  5. J. S. Parker, B. J. S. Doherty, K. T. Taylor, K. D. Schultz, C. I. Blaga, and L. F. DiMauro, "High-energy cutoff in the spectrum of strong-field nonsequential double ionization," Phys. Rev. Lett. 96, 133001 (2006). [CrossRef] [PubMed]
  6. A. Becker and F. H. M. Faisal, "Interplay of electron correlation and intense field dynamics in the double ionization of Helium," Phys. Rev. A 59, R1742-R1745 (1999). [CrossRef]
  7. M. Lein, E. K. U. Gross, and V. Engel, "Intense-field double ionization of Helium: identifying the mechanism," Phys. Rev. Lett. 85, 4707-4710 (2000). [CrossRef] [PubMed]
  8. R. Kopold, W. Becker, H. Rottke, and W. Sandner, "Routes to nonsequential double ionization," Phys. Rev. Lett. 85, 3781-3784 (2000). [CrossRef] [PubMed]
  9. C. Figueira de Morisson Faria, H. Schomerus, X. Liu, and W. Becker, "Electron-electron dynamics in laserinduced nonsequential double ionization," Phys. Rev. A 69, 043405 (2004). [CrossRef]
  10. P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993). [CrossRef] [PubMed]
  11. A. S. Alnaser, T. Osipov, E. P. Benis, A. Wech, B. Shan, C. L. Cocke, X. M. Tong, and C. D. Lin, "Rescattering double ionization of D2 and H2 by intense laser pulses," Phys. Rev. Lett. 91, 163002 (2003). [CrossRef] [PubMed]
  12. F. Legare, I. V. Litvinyuk, P. W. Dooley, F. Quere, A. D. Bandrauk, D. M. Villeneuve, and P. B. Corkum, "Timeresolved double ionization with few cycle laser pulses," Phys. Rev. Lett. 91, 093002 (2003). [CrossRef] [PubMed]
  13. S. Saugout and C. Cornaggia, "Temporal separation of H2 double-ionization channels using intense ultrashort 10-fs laser pulses," Phys. Rev. A 73, 041406(R) (2006). [CrossRef]
  14. C. Beylerian, S. Saugout and C. Cornaggia, "Non-sequential double ionization of H2 using ultrashort 10 fs laser pulses," J. Phys. B 39, L105-L112 (2006). [CrossRef]
  15. D. Zeidler, A. Staudte, A. B. Bardon, D. M. Villeneuve, R. Do, and P. B. Corkum, "Controlling attosecond double ionization dynamics via molecular alignment," Phys. Rev. Lett. 95, 203003 (2005). [CrossRef] [PubMed]
  16. M. Lein, T. Kreibich, E. K. U. Gross, and V. Engel, "Strong-field ionization dynamics of a model H2 molecule," Phys. Rev. A 65, 033403 (2002). [CrossRef]
  17. M. D. Feit, J. A. Fleck, Jr., and A. Steiger, "Solution of the Schr ¨ odinger equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982). [CrossRef]
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