## Accurate computational methods for two-electron atom-laser interactions

Optics Express, Vol. 8, Issue 7, pp. 436-440 (2001)

http://dx.doi.org/10.1364/OE.8.000436

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### Abstract

We discuss the application of quantitatively accurate computational methods to the study of laser-driven two-electron atoms in short intense laser pulses. The fundamental importance of such calculations to the subject area is emphasized. Calculations of single- and double-electron ionization rates at 390 nm are presented.

© Optical Society of America

*I*>>10

^{12}W cm

^{-2}) perturbation theory and most other simplified treatments of the Schrödinger equation become useless in the theoretical description of laser-driven helium. At these intensities, even a task as seemingly straightforward as the calculation of accurate ionization rates has been until very recently an unsolved problem. In the past few years, new theoretical methods have been introduced that have proven capable of yielding reliable and quantitatively accurate solutions to the intense field helium Schrödinger equation. The first of these methods, and the subject of this letter, is a time-dependent numerical integration (TDNI) of the full-dimensional Schrödinger equation [1

1. E S Smyth, J S Parker, and K T Taylor, “Numerical integration of the time-dependent Schrödinger equation for laser-driven helium,” Comput. Phys. Commun. **114**, 1–14 (1998). [CrossRef]

*R*-Matrix Floquet (RMF) method [2

2. P G Burke, P Francken, and C J Joachain, “*R*-matrix-Floquet theory of multiphoton processes,” J. Phys. B: At. Mol. Opt. Phys. **24**, 751–790 (1991). [CrossRef]

3. M Dörr, M Terao-Dunseath, J Purvis, C J Noble, P G Burke, and C J Joachain, “*R*-matrix-Floquet theory of multiphoton processes. II. Solution of the asymptotic equations in the velocity gauge,” J. Phys. B: At. Mol. Opt. Phys. **25**, 2809–2829 (1992). [CrossRef]

4. J S Parker, D H Glass, L R Moore, E S Smyth, K T Taylor, and P G Burke, “Time-dependent and time-independent methods applied to multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. **33**, L239–L247 (2000). [CrossRef]

5. R Hasbani, E Cormier, and H Bachau, “Resonant and non-resonant ionization of helium by XUV ultrashort and intense laser pulses,” J. Phys. B: At. Mol. Opt. Phys. **33**, 2101–2116 (2000). [CrossRef]

6. A Scrinzi and B Piraux, “Two-electron atoms in short intense laser pulses,” Phys. Rev. A **58**, 1310–1321 (1998). [CrossRef]

*I*>10

^{14}W cm

^{-2}). The results were obtained from a time-dependent numerical integration (TDNI) of the full-dimensional helium Schrödinger equation.

7. J S Parker, E S Smyth, and K T Taylor, “Intense-field multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. **31**, L571–L578 (1998). [CrossRef]

8. J S Parker, L R Moore, E S Smyth, and K T Taylor, “One- and two-electron numerical models of multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. **33**, 1057–1067 (2000). [CrossRef]

1. E S Smyth, J S Parker, and K T Taylor, “Numerical integration of the time-dependent Schrödinger equation for laser-driven helium,” Comput. Phys. Commun. **114**, 1–14 (1998). [CrossRef]

10. J S Parker, L R Moore, D Dundas, and K T Taylor, “Double ionization of helium at 390 nm,” J. Phys. B: At. Mol. Opt. Phys. **33**, L691–L698 (2000). [CrossRef]

^{14}to 2.2×10

^{15}W cm

^{-2}. The single-ionization rates are also presented in tabular form (Table 1) since they are believed to be correct to within 1% to 3%. The estimated error for double-ionization is in the 5% to 15% range.

4. J S Parker, D H Glass, L R Moore, E S Smyth, K T Taylor, and P G Burke, “Time-dependent and time-independent methods applied to multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. **33**, L239–L247 (2000). [CrossRef]

*L*

_{max}in the basis set, the radius

*R*of the integration volume, and the number of terms

*N*in the Legendre polynomial expansion of the dielectronic Coulomb term. By making

*δr*small and making the other parameters large, solutions of the finite-difference model become arbitrarily close to those of the true Schrödinger equation. In the calculation of double-ionization, if

*N*is changed from 3 to 4, then results change by 16% typically. When

*N*is changed from 4 to 5, then results change by 2%. We therefore truncate

*N*at 5 and accept 2% as a likely estimate of error induced by this truncation. Adding together all such error gives an error estimate of 5% to 10%. At intensities at which resonances are observed (8.0×10

^{14}W cm

^{-2}) uncertainties can be higher. It would be straightforward to reduce these errors to something like those of the single-ionization rate calculations (1% to 3%). A factor of two or three increase in computer time would be sufficient. If a requirement for double-ionization rates at this level of accuracy were identified, then the expenditure of this amount of CPU time would be routine.

## Acknowledgements

## References and links

1. | E S Smyth, J S Parker, and K T Taylor, “Numerical integration of the time-dependent Schrödinger equation for laser-driven helium,” Comput. Phys. Commun. |

2. | P G Burke, P Francken, and C J Joachain, “ |

3. | M Dörr, M Terao-Dunseath, J Purvis, C J Noble, P G Burke, and C J Joachain, “ |

4. | J S Parker, D H Glass, L R Moore, E S Smyth, K T Taylor, and P G Burke, “Time-dependent and time-independent methods applied to multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. |

5. | R Hasbani, E Cormier, and H Bachau, “Resonant and non-resonant ionization of helium by XUV ultrashort and intense laser pulses,” J. Phys. B: At. Mol. Opt. Phys. |

6. | A Scrinzi and B Piraux, “Two-electron atoms in short intense laser pulses,” Phys. Rev. A |

7. | J S Parker, E S Smyth, and K T Taylor, “Intense-field multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. |

8. | J S Parker, L R Moore, E S Smyth, and K T Taylor, “One- and two-electron numerical models of multiphoton ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. |

9. | J S Parker, L R Moore, K J Meharg, D Dundas, and K T Taylor, “Double-electron above threshold ionization of helium,” J. Phys. B: At. Mol. Opt. Phys. |

10. | J S Parker, L R Moore, D Dundas, and K T Taylor, “Double ionization of helium at 390 nm,” J. Phys. B: At. Mol. Opt. Phys. |

**OCIS Codes**

(020.0020) Atomic and molecular physics : Atomic and molecular physics

(140.0140) Lasers and laser optics : Lasers and laser optics

**ToC Category:**

Focus Issue: Laser-induced multiple ionization

**History**

Original Manuscript: February 5, 2001

Published: March 26, 2001

**Citation**

Jonathan Parker, Laura Moore, and K. Taylor, "Accurate computational methods for two-electron atom-laser interactions," Opt. Express **8**, 436-440 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-7-436

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### References

- E. S. Smyth, J. S. Parker and K. T. Taylor, "Numerical integration of the time-dependent Schrödinger equation for laser-driven helium," Comput. Phys. Commun. 114, 1-14 (1998). [CrossRef]
- P. G. Burke, P. Francken and C. J. Joachain, "R-matrix-Floquet theory of multiphoton processes," J. Phys. B: At. Mol. Opt. Phys. 24, 751-790 (1991). [CrossRef]
- M. Dörr, M. Terao-Dunseath, J. Purvis, C. J. Noble, P. G. Burke and C. J. Joachain, "R-matrix-Floquet theory of multiphoton processes. II. Solution of the asymptotic equations in the velocity gauge," J. Phys. B: At. Mol. Opt. Phys. 25, 2809-2829 (1992). [CrossRef]
- J. S. Parker, D. H. Glass, L. R. Moore, E. S. Smyth, K. T. Taylor and P. G. Burke, "Time-dependent and time-independent methods applied to multiphoton ionization of helium," J. Phys. B: At. Mol. Opt. Phys. 33, L239-L247 (2000). [CrossRef]
- R. Hasbani, E. Cormier and H. Bachau, "Resonant and non-resonant ionization of helium by XUV ultrashort and intense laser pulses," J. Phys. B: At. Mol. Opt. Phys. 33, 2101-2116 (2000). [CrossRef]
- A. Scrinzi and B. Piraux, "Two-electron atoms in short intense laser pulses," Phys. Rev. A 58, 1310-1321 (1998). [CrossRef]
- J. S. Parker, E. S. Smyth and K. T. Taylor, "Intense-field multiphoton ionization of helium," J. Phys. B: At. Mol. Opt. Phys. 31, L571-L578 (1998). [CrossRef]
- J. S. Parker, L. R. Moore, E. S. Smyth and K. T. Taylor, "One- and two-electron numerical models of multiphoton ionization of helium," J. Phys. B: At. Mol. Opt. Phys. 33, 1057-1067 (2000). [CrossRef]
- J. S. Parker, L. R. Moore, K. J. Meharg, D. Dundas and K. T. Taylor, "Double-electron above threshold ionization of helium," J. Phys. B: At. Mol. Opt. Phys. 34, L69-L78 (2001). [CrossRef]
- J. S. Parker, L. R. Moore, D. Dundas and K. T. Taylor, "Double ionization of helium at 390 nm," J. Phys. B: At. Mol. Opt. Phys. 33, L691-L698 (2000). [CrossRef]

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