OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 8, Iss. 7 — Mar. 26, 2001
  • pp: 401–410
« Show journal navigation

Photoionization of atoms described by Fermi Molecular Dynamics: toward a firmer theoretical basis

K. J. LaGattuta  »View Author Affiliations


Optics Express, Vol. 8, Issue 7, pp. 401-410 (2001)
http://dx.doi.org/10.1364/OE.8.000401


View Full Text Article

Acrobat PDF (470 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The application of Fermi Molecular Dynamics (FMD) to the modeling of the photoionization of atoms by a short pulse of long wavelength laser radiation is examined in detail. Depression of the single ionization threshold to values of the electric field strength below the classical over-the-barrier threshold, a common occurrence in FMD, is shown to arise from the preexcitation of bound electrons into a continuum of unphysical low-lying excited states. A connection is made to analogous calculations performed with the quantum Hamilton-Jacobi equation, in which the time-dependent quantum potential (Q) plays a role similar to that played in FMD by the so-called Heisenberg potential (VH ). Replacement of VH by Q in the FMD equations of motion results in a large reduction in the number of excitations to unphysical bound states, while producing no essential change in the photoionization probability.

© Optical Society of America

1 Introduction

The photoionization of atoms by short pulses of long wavelength laser radiation is a topic which has received much attention over the past ten years. Many experimental measurements of photoionization probabilities for the single as well as the multiple ionization of isolated atoms have been performed[1

1. D. Fittinghoff, P. Bolton, B. Chang, and K. Kulander, “Observations of nonsequential double ionization of helium with optical tunneling,” Phys. Rev. Lett. 69, 2642–2645 (1992). [CrossRef] [PubMed]

, 2

2. K. Kondo, A. Sagisaka, T. Tamida, Y. Nabekawa, and S. Watanabe, “Wavelength dependence of nonsequential double ionization in He,” Phys. Rev. A48, R2531–R2533 (1993).

, 3

3. B. Walker, E. Mevel, B. Yang, P. Berger, J. P. Chamberet, A. Antonetti, L. F. Dimauro, and P. Agostini, “Double ionization in the perturbative and tunneling regimes,” Phys. Rev. A48, R894–R897 (1993).

, 4

4. S. Augst, A. Talebpour, S. L. Chin, Y. Beaudoin, and M. Chaker, “Nonsequential triple ionization of argon atoms in a high-intensity laser field,” Phys. Rev. A52, R917–R919 (1995).

], and many theoretical papers explaining these experimental results have appeared[5

5. P. Lambropoulos, “Mechanisms for multiple ionization of atoms by strong pulsed lasers,” Phys. Rev. Lett. 55, 2141–2144 (1985). [CrossRef] [PubMed]

, 6

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

, 7

7. T. Brabec, M. Ivanov, and P. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A54, R2551–R2554 (1996).

, 8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

, 9

9. A. Becker and F. H. M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B29, L197–L202 (1996).

, 10

10. K. LaGattuta, “Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation,” J. Phys. B33, 2489–2494 (2000).

]. Much emphasis has been placed in these accounts on observations of enhanced probabilities for multiple ionization; i.e., beyond what would be expected assuming the existence of a purely sequential path to multiple ionization[5

5. P. Lambropoulos, “Mechanisms for multiple ionization of atoms by strong pulsed lasers,” Phys. Rev. Lett. 55, 2141–2144 (1985). [CrossRef] [PubMed]

]. A hypothesis describing a boomeranging of the first electron to be released in the field of the laser, followed by a collisional ionization of one or more electrons still bound to the target, has gained some acceptance[6

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

, 7

7. T. Brabec, M. Ivanov, and P. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A54, R2551–R2554 (1996).

, 8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

, 9

9. A. Becker and F. H. M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B29, L197–L202 (1996).

, 10

10. K. LaGattuta, “Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation,” J. Phys. B33, 2489–2494 (2000).

].

However, an unambiguous theoretical demonstration of the existence of this recollisional mechanism has been difficult. Attempts to visualize the boomeranging electron trajectory have not been entirely successful, in part because of an unavoidable rapid spreading of the launched wave-packet. More indirect means have tended to support the recollisional picture[9

9. A. Becker and F. H. M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B29, L197–L202 (1996).

], while new work, seeming to offer more direct support, has been published within the past year[11

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

, 12

12. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C. Schroter, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sander, “Momentum distributions of Ne(n+) ions created by an intense ultrashort laser pulse,” Phys. Rev. Lett. 84, 447–450 (2000). [CrossRef] [PubMed]

, 13

13. 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]

]. Nevertheless, the overall situation still does not seem to be entirely satisfactory.

Past calculations based on Fermi Molecular Dynamics (FMD), for the double ionization of helium[8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

], and for the multiple ionization of argon[10

10. K. LaGattuta, “Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation,” J. Phys. B33, 2489–2494 (2000).

], have clearly demonstrated the validity of the boomeranging mechanism, in the quasiclassical picture. However, trajectories visualized in FMD have not been able to provide conclusive evidence for the existence of this underlying mechanism. The reason for this is that the connections between FMD and the real world as described by quantum mechanics have been unclear.

In this paper we report the discovery of a firmer connection between FMD and the world as described by quantum mechanics. In the following, we outline this connection in the context of the photoionization of atomic hydrogen.

We begin by describing the solution of the time-dependent Schrodinger equation (TDSE) for this problem, in the long wavelength regime and for a short laser pulse, using a well-known numerical technique[14

14. K. LaGattuta, “Laser effects in photoionization: numerical solution of coupled equations for a three-dimensional Coulomb potential,” JOSA B7, 639–646 (1990).

]. This establishes a benchmark standard against which to compare subsequent FMD based calculations.

Next, the TDSE is rewritten as a pair of coupled equations, one having the form of a continuity equation for a probability density and the other the form of a Hamilton-Jacobi (HJ) equation, as suggested originally by Bohm[15

15. D. Bohm, “A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. I,” Phys. Rev. 85, 166–179 (1952). [CrossRef]

]. The HJ equation contains a source term referred to as the quantum potential (Q), which can be obtained from the solution of the continuity equation. Alternately, Q can be obtained directly, at every value of the time, from the full solution to the TDSE. This particular form of the HJ equation, containing Q, has been referred to as the quantum Hamilton-Jacobi equation[16

16. C. Lopreore and R. Wyatt, “Quantum wave packet dynamics with trajectories,” Phys. Rev. Lett. 82, 5190–5193 (1999). [CrossRef]

].

Finally, we point out that the quasiclassical terms in the FMD equation for the total force on the electron, describing the identical physical problem, mimic Q in significant detail. We discuss the implications of this finding.

2 The TDSE and the Quantum Hamilton-Jacobi Equation

The TDSE is often written as two coupled equations, one for the real and one for the imaginary part of the wavefunction; viz.,

H(t)Ψreal=Ψimagt
H(t)Ψimag=Ψrealt
(1)

where Ψ=Ψreal+iΨimag, and where H(t) is the (generally time-dependent) Hamilton operator. For the problem of one electron moving in the field of a singly charged ion, and acted also upon by an external electric field, the Hamilton can be taken to be

H(t)=12r21rr.E(t)
(2)

where the field of a linearly polarized laser will be written as

E(t)=x̂Epulse(t)sin(ωt+ϕ)
(3)

with Epulse(t) the laser envelope function and ϕ the laser phase, all in atomic units (a.u.); viz., m=-e=ħ=1.

If instead, however, the wavefunction is written as

Ψ=Rexp(iS)
(4)

where R=R(r⃗, t) and S=S(r⃗, t) are purely real functions of the coordinates and the time, then eqn 1 transforms into the following pair of coupled equations:

ρt+r.(ρrS)=0
(5)

and

S/t=12(rS)2+Q1/rr.E(t)
(6)

The probability density ρ=R 2 is the solution of a continuity equation (eqn 5) while the phase S is the solution of the so-called quantum Hamilton-Jacobi equation (eqn 6). The function Q appearing in eqn 6 has been referred to as the quantum potential[16

16. C. Lopreore and R. Wyatt, “Quantum wave packet dynamics with trajectories,” Phys. Rev. Lett. 82, 5190–5193 (1999). [CrossRef]

]:

Q=12Rr2R
(7)

An equation of motion, analogous to the classical Hamilton’s equation for the force on the electron is obtained upon taking the gradient of both sides of eqn 6:

dυ/dt=r(Q1/rr.E(t))
(8)

where

υrS
(9)

and

d/dt/t+υ.r
(10)

Eqn 8 has the form of a Newton’s equation describing the total force on an electron, moving with velocity υ⃗. It contains, on the right-hand-side, a sum of the purely classical forces and a term -∇rQ which may be thought of as a force of quantum origin.

We now proceed to the description of the results obtained from an explicit calculation, based upon eqn 1. The conditions chosen for this benchmark case of an electron bound initially in the 1s orbit of atomic hydrogen were: a linearly polarized laser field of peak electric field strength E 0=0.035a.u., for a frequency of ω=0.1a.u., and a laser pulse length of tpulse=1300a.u., including a sine squared turn-on and turn-off ramp of duration tramp=150a.u. The calculation included an absorbing potential which was zero for all r<20a.u., and peaked up sharply at r=25a.u. The absorber eliminated problems which would otherwise have arisen from outgoing flux, representing ionized states, reflecting from the end of the mesh, located at r=25a.u.

A standard technique was used to solve the TDSE in spherical polar coordinates, with eight partial waves (0≤≤7), and on a radial mesh of size Δr=0.25a.u. We chose these laser parameters in order to minimize the number of partial waves necessary, while at the same time allowing the tunneling and/or the multiphoton regimes to be sampled. Under these conditions, the ionization probability was computed to be Pioniz≈0.05.

Fig. 1. Values of the quantum potential Q(x, t) are plotted along the verticle axis as a function of x and t; primarily positive values of Q appear.

In Fig. 1 we display the values of Q arising from this full solution of the TDSE. Values of Q(x, t) are plotted along the verticle axis of this 3D plot as a function of the x-coordinate, which is parallel to the applied electric field, and the time t. For the most part, only positive values of Q are visible in Fig. 1. In Fig. 2, we plot the underside of this surface; i.e., the negative values of Q.

Several features are evident in Figs. 1 and 2. First, the repulsive peak centered at the origin (x=0) occurs for all t. We will refer to this central peak again, presently. But first, of more interest is the seemingly chaotic line of mountains and very deep valleys which appears for values of x in the region 6<|x|<8a.u., for all times t after the turn-on transient; i.e., for t≥150a.u. The line of very deep valleys appears also to show a spatial periodicity, with a period of Δx≈7a.u. This period is just twice the quiver amplitude; i.e., Δx≈2α 0=2E 0/ω 2. The form of the Newton’s equation (eqn 8) when combined with the these features of Q, cries out for some interpretation.

Fig. 2. Same as Fig. 1, but the surface has been inverted; now primarily negative values of Q(x, t) appear.

The usual interpretation of the small amount of ionization disclosed by the calculation is that the complex probability amplitude Ψ tunnels through a real potential barrier set up partly by the applied electric field and partly by the Coulomb potential. Note that the value of the peak electric field strength chosen is significantly less than the OBI field strength for this problem; viz., E 0=0.035<EOBI=0.0625a.u., so that any ionization which occurs should only be due to tunneling.

However, a different interpretation is suggested by the form of eqns 7 and 8, with Q from Figs. 1 and 2. Namely, a real probability current exists which flows like a particle, obeying a Newton’s equation of motion, while under the influence of an additional force derived from a time-dependent quantum potential, Q. This Q is such that the otherwise real and solid potential barrier set up by the potential -1/r-r⃗.E⃗(t) is infiltrated by a collection of shifting fissures, any one of which can be penetrated by the real particle, if the particle arrives at the entrance to a fissure while it is open, with the right velocity, and manages to pass all the way through the fissure before it closes. Hence, whereas in the conventional picture of quantum mechnanics it is the particle which has ghostly or wave-like properties, while the potential experienced by the particle is altogether real, in the Bohmian picture it is the particle which is altogether real while the potential acquires ghostly or unusual properties. Not too surprisingly perhaps, the location of the line of fissures or valleys is at |x|≈2α 0, as has already been noted.

Fig. 3. Values of vx=dS/dx, from the quantum HJ equation, are plotted along the verticle axis as a function of x and t.

We call attention now to another unusual implication of eqns 7 and 8, as seen in the light of the full solution of the TDSE; namely, the velocity of the Bohmian particle, as given by eqn 9. This is displayed in Fig. 3. Note in particular that the velocity is zero over an extended range of x-values centered around x=0, for all t; i.e., out to a value of |x|≈2α 0. For larger values of |x|, the velocity exhibits seemingly chaotic behavior, correlated with the rapid changes in Q.

We conclude this section with a more careful discussion of the behavior of both Q and ∇rS, in a region around x=0, and for both y~0 and z~0. Since Q is given by eqn 7, one expects that under the conditions of this problem (Ψ(t=0)=Φ1s=2exp(-r) and E 0<EOBI), and in the vicinity of the origin, Q will be well-approximated by

Q12+1/r
(11)

for all time t>0, and will be given by this expression exactly, for t=0; see Fig. 1. Similarly, the total force on the electron will be

dυ/dt=r(Q1/r)=0
(12)

exactly, for t=0. Then, from eqn 9, the “velocity” of the electron is

rS=0
(13)

3 The Predictions of FMD

The approach to modeling photionization with FMD has been described many times before[8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

, 10

10. K. LaGattuta, “Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation,” J. Phys. B33, 2489–2494 (2000).

, 17

17. D. Wasson and S. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A39, 5676–5685 (1989).

]. One may assume, therefore, that the FMD equations are well-known, and do not require much in the way of reintroduction. Only very briefly then, we summarize these equations here as follows: First, consistent with eqn 2, the Hamiltonian H(t) for this problem is now written as

H(t)=p2/21/rr.E(t)+VH(r,p)
(14)

where E⃗(t) is still given by eqn 3, and

VH(r,p)AHr2exp(BHr4p4)
(15)

is the so-called FMD Heisenberg potential. The constants AH and BH (both positive real numbers) are chosen according to a simple prescription[8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

]; see the remarks following eqn 20. The FMD equations of motion (Hamilton’s equations) are:

dr/dt=pH(t)
(16)

and

dp/dt=rH(t)
(17)

In particular, the total force on the electron is now

dp/dt=r(VH1/rr.E(t))
(18)

which is identical to eqn 8 if VH is substituted for Q (and p⃗ for v⃗.)

For the system under consideration, the six FMD equations (eqns 16 and 17) were solved for 10, 000 randomly oriented choices of the initial vectors r⃗ and p⃗, for a fixed value of the initial laser phase ϕ. All of the relevant laser parameters were taken from the preceding section.

The average value of the photoionization probability was computed to be Pioniz≈0.02. This result might be thought to be somewhat puzzling, however, since the peak applied electric field strength is less than the OBI threshold value; i.e., E 0=0.035<EOBI=0.0625a.u. Moreover, one can show that an effect of the purely repulsive Heisenberg potential VH(r, p) must be to raise the OBI threshold, not to lower it. The answer to this puzzle may be found in Fig. 4 (solid curve), where we show the spectrum of final electron total energies computed in the FMD calculation.

Fig. 4. A spectrum of values of the final electron total energy ∊ (a.u.) is plotted, as computed with FMD: for the case in which the FMD Heisenberg potential VH has been invoked (solid curve); for the case in which VH has been replaced by Q (chain curve).

Upon inspection of the Fig. 4 it is immediately clear that there has been a promotion of the electron to an unphysical continuum of low-lying bound excited states during the laser pulse. Then, ionization will have occurred whenever the applied electric field strength attained values greater than the OBI threshold value for that particular excited state energy.

We note in passing that the spectrum of positive energies excited in the FMD calculations has not been compared with that predicted by the TDSE, since we did not compute this latter quantity explicitly. However, past calculations based on the TDSE, for slightly different choices of laser parameters[18

18. K. LaGattuta, “Laser effects in photoionization II. Numerical solution of coupled equations for atomic hydrogen,” Phys. Rev. A41, 5110–5116 (1990).

], suggest that the spectrum of positive energy states displayed in Fig. 4 (solid curve) is quite reasonable.

4 FMD and the Quantum Hamilton-Jacobi Equation

We begin here by pointing out two more detailed correspondences between FMD and the quantum Hamilton-Jacobi equation. Note first that the total force -∇r⃗(Q-1/r) is exactly zero in the quantum HJ equation, for t=0, and approximately zero in the vicinity of the origin for all t>0 (eqn 12). This condition also holds true for the total force on the electron according to the FMD equation of motion (eqn 18); viz.,

dp/dt=r(VH1/r)=0
(19)

exactly, for t=0, and approximately in the vicinity of the origin, for t>0, by construction[8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

]. Second, note that the velocity of the electron is also exactly zero for t=0, and approximately zero in the vicinity of the origin, for t>0, in the quantum HJ description (eqn 13). Moreover, the velocity of the electron is identically behaved in the FMD description; i.e.,

υ=p+pVH(r,p)=0
(20)

exactly, for t=0, and approximately in the vicinity of the origin, for t>0, again by construction[8

8. K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

]. (Here, “by construction” means that the FMD ground-state is a minimum energy time-independent configuration attained when the total force on the electron, and the velocity of the electron, are both zero. These two conditions determine, generally, the values of the constants AH and BH in the FMD Heisenberg potential, eqn 15. In terms of these constants and the ground state energy ∊, the values of |r⃗| and |p⃗| are also determined.)

Consequently, the FMD Heisenberg potential and the quantum potential Q from the quantum HJ equation are similarly behaved, under the conditions mentioned. Further investigation shows that VH(r, p,) behaves similarly to Q(r, t), if individual trajectories obtained from solutions of the FMD equations are used to define a surface of VH values labeled by r and t. Identical remarks can be made about a comparison of values of the function ∇rS(r, t), from the quantum HJ equation, and the function p⃗+∇pVH(r, p) computed from the FMD equations.

Results for the spectrum of final electron energies determined in this calculation appear in Fig. 4 (chain curve). The corresponding value of the ionization probability computed was Pioniz≈0.06. Upon comparing the two curves in Fig. 4, it is evident that there has been a suppression of excitations to the unphysical region lying below the n=2 threshold (at =-0.125a.u.), with some promotion to higher energy continuum states. At the same time, no essential change has occurred in the value of Pioniz. This seems to be an encouraging result. The source of the increase in the production of high energy continua (for ≥0.4a.u.), when VH is replaced by Q, is presently unknown and seems to be an undesirable feature.

5 Summary

The approach to modeling the photoionization of atoms by long wavelength, short pulse, lasers with FMD has been placed on a somewhat firmer footing. A correspondence has been developed between the quantum Hamilton-Jacobi equation and the equations of FMD.

In particular, the time-dependent quantum potential Q, from the quantum HJ equation, has been shown to have similar properties to the FMD Heisenberg potential VH. Thus, the FMD equation for the total force on an electron has been shown to make predictions for the photoionization probability Pioniz which are similar to those of the quantum HJ equation. Moreover, the behavior of the electron “velocity” predicted by the quantum HJ equation has been shown to be similar to the predictions of the FMD equation for dr⃗/dt.

References and links

1.

D. Fittinghoff, P. Bolton, B. Chang, and K. Kulander, “Observations of nonsequential double ionization of helium with optical tunneling,” Phys. Rev. Lett. 69, 2642–2645 (1992). [CrossRef] [PubMed]

2.

K. Kondo, A. Sagisaka, T. Tamida, Y. Nabekawa, and S. Watanabe, “Wavelength dependence of nonsequential double ionization in He,” Phys. Rev. A48, R2531–R2533 (1993).

3.

B. Walker, E. Mevel, B. Yang, P. Berger, J. P. Chamberet, A. Antonetti, L. F. Dimauro, and P. Agostini, “Double ionization in the perturbative and tunneling regimes,” Phys. Rev. A48, R894–R897 (1993).

4.

S. Augst, A. Talebpour, S. L. Chin, Y. Beaudoin, and M. Chaker, “Nonsequential triple ionization of argon atoms in a high-intensity laser field,” Phys. Rev. A52, R917–R919 (1995).

5.

P. Lambropoulos, “Mechanisms for multiple ionization of atoms by strong pulsed lasers,” Phys. Rev. Lett. 55, 2141–2144 (1985). [CrossRef] [PubMed]

6.

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

7.

T. Brabec, M. Ivanov, and P. Corkum, “Coulomb focusing in intense field atomic processes,” Phys. Rev. A54, R2551–R2554 (1996).

8.

K. J. LaGattuta and James S. Cohen, “Quasiclassical modeling of helium double photoionization,” J. Phys. B31, 5281–5291 (1998).

9.

A. Becker and F. H. M. Faisal, “Mechanism of laser-induced double ionization of helium,” J. Phys. B29, L197–L202 (1996).

10.

K. LaGattuta, “Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation,” J. Phys. B33, 2489–2494 (2000).

11.

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

12.

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

13.

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]

14.

K. LaGattuta, “Laser effects in photoionization: numerical solution of coupled equations for a three-dimensional Coulomb potential,” JOSA B7, 639–646 (1990).

15.

D. Bohm, “A suggested interpretation of the quantum theory in terms of ‘hidden’ variables. I,” Phys. Rev. 85, 166–179 (1952). [CrossRef]

16.

C. Lopreore and R. Wyatt, “Quantum wave packet dynamics with trajectories,” Phys. Rev. Lett. 82, 5190–5193 (1999). [CrossRef]

17.

D. Wasson and S. Koonin, “Molecular-dynamics simulations of atomic ionization by strong laser fields,” Phys. Rev. A39, 5676–5685 (1989).

18.

K. LaGattuta, “Laser effects in photoionization II. Numerical solution of coupled equations for atomic hydrogen,” Phys. Rev. A41, 5110–5116 (1990).

OCIS Codes
(000.3860) General : Mathematical methods in physics
(020.4180) Atomic and molecular physics : Multiphoton processes
(260.3230) Physical optics : Ionization
(270.6620) Quantum optics : Strong-field processes

ToC Category:
Focus Issue: Laser-induced multiple ionization

History
Original Manuscript: February 6, 2001
Published: March 26, 2001

Citation
Kenneth LaGattuta, "Photoionization of atoms described by Fermi Molecular Dynamics: toward a firmer theoretical basis," Opt. Express 8, 401-410 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-7-401


Sort:  Journal  |  Reset  

References

  1. D. Fittinghoff, P. Bolton, B. Chang, and K. Kulander, "Observations of nonsequential double ionization of helium with optical tunneling," Phys. Rev. Lett. 69, 2642-2645 (1992). [CrossRef] [PubMed]
  2. K. Kondo, A. Sagisaka, T. Tamida, Y. Nabekawa, and S. Watanabe, "Wavelength dependence of nonsequential double ionization in He," Phys. Rev. A 48, R2531-R2533 (1993).
  3. B. Walker, E. Mevel, B. Yang, P. Berger, J. P. Chamberet, A. Antonetti, L. F. Dimauro, and P. Agostini, "Double ionization in the perturbative and tunneling regimes," Phys. Rev. A 48, R894-R897 (1993).
  4. S. Augst, A. Talebpour, S. L. Chin, Y. Beaudoin, and M. Chaker, "Nonsequential triple ionization of argon atoms in a high-intensity laser field," Phys. Rev. A52, R917-R919 (1995).
  5. P. Lambropoulos, "Mechanisms for multiple ionization of atoms by strong pulsed lasers," Phys. Rev. Lett. 55, 2141-2144 (1985). [CrossRef] [PubMed]
  6. P. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993). [CrossRef] [PubMed]
  7. T. Brabec, M. Ivanov, and P. Corkum, "Coulomb focusing in intense field atomic processes," Phys. Rev. A 54, R2551-R2554 (1996).
  8. K. J. LaGattuta and James S. Cohen, "Quasiclassical modeling of helium double photoionization," J. Phys. B 31, 5281-5291 (1998).
  9. A. Becker and F. H. M. Faisal, "Mechanism of laser-induced double ionization of helium," J. Phys. B 29, L197-L202 (1996).
  10. K. LaGattuta, "Multiple ionization of argon atoms by long-wavelength laser radiation: a fermion molecular dynamics simulation," J. Phys. B 33, 2489-2494 (2000).
  11. Th. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dorner, "Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields," Phys. Rev. Lett. 84, 443-446 (2000). [CrossRef] [PubMed]
  12. R. Moshammer, B. Feuerstein, W. Schmitt, A. Dorn, C. Schroter, J. Ullrich, H. Rottke, C. Trump, M. Wittmann, G. Korn, K. Hoffmann, and W. Sander, "Momentum distributions of Ne(n+) ions created by an intense ultrashort laser pulse," Phys. Rev. Lett. 84, 447-450 (2000). [CrossRef] [PubMed]
  13. 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]
  14. K. LaGattuta, "Laser effects in photoionization: numerical solution of coupled equations for a three-dimensional Coulomb potential," J. Opt. Soc. Am. B 7, 639-646 (1990).
  15. D. Bohm, "A suggested interpretation of the quantum theory in terms of `hidden' variables. I," Phys. Rev. 85, 166-179 (1952). [CrossRef]
  16. C. Lopreore and R. Wyatt, "Quantum wave packet dynamics with trajectories," Phys. Rev. Lett. 82, 5190-5193 (1999). [CrossRef]
  17. D. Wasson and S. Koonin, "Molecular-dynamics simulations of atomic ionization by strong laser fields," Phys. Rev. A 39, 5676-5685 (1989).
  18. K. LaGattuta, "Laser effects in photoionization II. Numerical solution of coupled equations for atomic hydrogen," Phys. Rev. A 41, 5110-5116 (1990).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited