Abstract

We present a distorted-wave formulation of atomic ionization by short laser pulses based on Coulomb–Volkov states. The method is applied to atomic-hydrogen targets, for different interaction times and frequencies. Results are compared with the predictions of an exact numerical treatment, and good agreement is obtained as long as the convergence conditions of the perturbative series hold. The applicability of the method depends on the field intensity but not on the pulse duration, permitting a unified description of various ionization mechanisms.

© 2003 Optical Society of America

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References

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  1. T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
    [CrossRef] [PubMed]
  2. E. Cormier and P. Lambropoulus, “Above-threshold ionization spectrum of hydrogen using B-spline functions,” J. Phys. B 30, 77–91 (1997).
    [CrossRef]
  3. H. G. Muller and F. C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81, 1207–1210 (1998).
    [CrossRef]
  4. A. D. Konsorskiy and L. P. Presnyakov, “Dynamics of interactions of short laser pulses with atoms: role of close-coupling effects,” J. Phys. B 34, L263–L668 (2001).
  5. G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
    [CrossRef]
  6. G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
    [CrossRef]
  7. M. Nisoli, S. de Silvesti, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
    [CrossRef] [PubMed]
  8. M. Jain and N. Tzoar, “X-ray absorption in atoms in the presence of an intense laser field,” Phys. Rev. A 18, 538–545 (1978).
    [CrossRef]
  9. A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
    [CrossRef] [PubMed]
  10. D. V. Milosevic and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
    [CrossRef]
  11. A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
    [CrossRef]
  12. J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
    [CrossRef] [PubMed]
  13. D. M. Volkov, “Uber eine klasse von losungen de Diracschen gleichung,” Z. Phys. 94, 250–260 (1935).
    [CrossRef]
  14. G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
    [CrossRef]
  15. M. R. C. McDowell and J. P. Colleman, Introduction to the Theory of Ion–Atom Collisions (North-Holland, Amsterdam, 1970).
  16. J. E. Miraglia, “Generalised impulse approximation,” J. Phys. B 15, 4205–4217 (1982).
    [CrossRef]
  17. J. E. Miraglia and J. Macek, “Quantum-mechanical impulse approximation for single ionization of hydrogen-like atoms by multicharged ions,” Phys. Rev. A 43, 5919–5928 (1991).
    [CrossRef] [PubMed]
  18. M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
    [CrossRef]
  19. A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).
  20. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
  21. F. H. M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–L92 (1973).
    [CrossRef]
  22. H. R. Reiss, “Effect of an intense electromagnetic field on a weakly bound system,” Phys. Rev. A 22, 1786–1813 (1980).
    [CrossRef]
  23. M. S. Gravielle and J. E. Miraglia, “Some Nordsieck integrals of interest in radiation and atomic collision theory,” Comput. Phys. Commun. 69, 53–58 (1992).
    [CrossRef]

2001 (2)

A. D. Konsorskiy and L. P. Presnyakov, “Dynamics of interactions of short laser pulses with atoms: role of close-coupling effects,” J. Phys. B 34, L263–L668 (2001).

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

2000 (3)

G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
[CrossRef]

A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
[CrossRef]

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

1998 (2)

D. V. Milosevic and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

H. G. Muller and F. C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81, 1207–1210 (1998).
[CrossRef]

1997 (2)

1996 (1)

J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
[CrossRef] [PubMed]

1995 (1)

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

1992 (1)

M. S. Gravielle and J. E. Miraglia, “Some Nordsieck integrals of interest in radiation and atomic collision theory,” Comput. Phys. Commun. 69, 53–58 (1992).
[CrossRef]

1991 (1)

J. E. Miraglia and J. Macek, “Quantum-mechanical impulse approximation for single ionization of hydrogen-like atoms by multicharged ions,” Phys. Rev. A 43, 5919–5928 (1991).
[CrossRef] [PubMed]

1988 (1)

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

1982 (1)

J. E. Miraglia, “Generalised impulse approximation,” J. Phys. B 15, 4205–4217 (1982).
[CrossRef]

1980 (1)

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

1978 (1)

M. Jain and N. Tzoar, “X-ray absorption in atoms in the presence of an intense laser field,” Phys. Rev. A 18, 538–545 (1978).
[CrossRef]

1973 (1)

F. H. M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–L92 (1973).
[CrossRef]

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

1953 (1)

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[CrossRef]

1935 (1)

D. M. Volkov, “Uber eine klasse von losungen de Diracschen gleichung,” Z. Phys. 94, 250–260 (1935).
[CrossRef]

Bachau, H.

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

Basile, A.

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

Burlon, R.

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

Cormier, E.

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
[CrossRef]

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

E. Cormier and P. Lambropoulus, “Above-threshold ionization spectrum of hydrogen using B-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

de Silvesti, S.

Ditmire, T.

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Donneley, T.

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Duchateau, G.

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
[CrossRef]

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

Ehlotzky, F.

A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
[CrossRef]

D. V. Milosevic and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
[CrossRef] [PubMed]

Faisal, F. H. M.

F. H. M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–L92 (1973).
[CrossRef]

Falcone, R. W.

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Ferencz, K.

Ferrante, G.

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

Gayet, R.

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
[CrossRef]

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

Gell-Mann, M.

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[CrossRef]

Goldberger, M. L.

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[CrossRef]

Gravielle, M. S.

M. S. Gravielle and J. E. Miraglia, “Some Nordsieck integrals of interest in radiation and atomic collision theory,” Comput. Phys. Commun. 69, 53–58 (1992).
[CrossRef]

Illescas, C.

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

Jain, M.

M. Jain and N. Tzoar, “X-ray absorption in atoms in the presence of an intense laser field,” Phys. Rev. A 18, 538–545 (1978).
[CrossRef]

Jaron, A.

A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
[CrossRef]

J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
[CrossRef] [PubMed]

Kaminski, J. Z.

A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
[CrossRef]

J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
[CrossRef] [PubMed]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Konsorskiy, A. D.

A. D. Konsorskiy and L. P. Presnyakov, “Dynamics of interactions of short laser pulses with atoms: role of close-coupling effects,” J. Phys. B 34, L263–L668 (2001).

Kooiman, F. C.

H. G. Muller and F. C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81, 1207–1210 (1998).
[CrossRef]

Krausz, F.

Lambropoulus, P.

E. Cormier and P. Lambropoulus, “Above-threshold ionization spectrum of hydrogen using B-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

Leone, C.

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

Macek, J.

J. E. Miraglia and J. Macek, “Quantum-mechanical impulse approximation for single ionization of hydrogen-like atoms by multicharged ions,” Phys. Rev. A 43, 5919–5928 (1991).
[CrossRef] [PubMed]

Milosevic, D. V.

D. V. Milosevic and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

Miraglia, J. E.

M. S. Gravielle and J. E. Miraglia, “Some Nordsieck integrals of interest in radiation and atomic collision theory,” Comput. Phys. Commun. 69, 53–58 (1992).
[CrossRef]

J. E. Miraglia and J. Macek, “Quantum-mechanical impulse approximation for single ionization of hydrogen-like atoms by multicharged ions,” Phys. Rev. A 43, 5919–5928 (1991).
[CrossRef] [PubMed]

J. E. Miraglia, “Generalised impulse approximation,” J. Phys. B 15, 4205–4217 (1982).
[CrossRef]

Muller, H. G.

H. G. Muller and F. C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81, 1207–1210 (1998).
[CrossRef]

Nisoli, M.

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Perry, M. D.

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Pons, B.

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Presnyakov, L. P.

A. D. Konsorskiy and L. P. Presnyakov, “Dynamics of interactions of short laser pulses with atoms: role of close-coupling effects,” J. Phys. B 34, L263–L668 (2001).

Reiss, H. R.

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

Sartania, S.

Spielmann, Ch.

Svelto, O.

Szipcs, R.

Terentev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

Trombetta, F.

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

Tzoar, N.

M. Jain and N. Tzoar, “X-ray absorption in atoms in the presence of an intense laser field,” Phys. Rev. A 18, 538–545 (1978).
[CrossRef]

Volkov, D. M.

D. M. Volkov, “Uber eine klasse von losungen de Diracschen gleichung,” Z. Phys. 94, 250–260 (1935).
[CrossRef]

Comput. Phys. Commun. (1)

M. S. Gravielle and J. E. Miraglia, “Some Nordsieck integrals of interest in radiation and atomic collision theory,” Comput. Phys. Commun. 69, 53–58 (1992).
[CrossRef]

Eur. Phys. J. D (1)

G. Duchateau, E. Cormier, and R. Gayet, “A simple non-perturbative approach of atom ionization by intense and ultra-short laser pulses,” Eur. Phys. J. D 11, 191–196 (2000).
[CrossRef]

J. Phys. B (5)

A. D. Konsorskiy and L. P. Presnyakov, “Dynamics of interactions of short laser pulses with atoms: role of close-coupling effects,” J. Phys. B 34, L263–L668 (2001).

E. Cormier and P. Lambropoulus, “Above-threshold ionization spectrum of hydrogen using B-spline functions,” J. Phys. B 30, 77–91 (1997).
[CrossRef]

F. H. M. Faisal, “Multiple absorption of laser photons by atoms,” J. Phys. B 6, L89–L92 (1973).
[CrossRef]

G. Duchateau, C. Illescas, B. Pons, E. Cormier, and R. Gayet, “Ionization dynamics in interactions of atoms with ultra-short and intense laser pulses,” J. Phys. B 33, L571–L576 (2000).
[CrossRef]

J. E. Miraglia, “Generalised impulse approximation,” J. Phys. B 15, 4205–4217 (1982).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

M. Gell-Mann and M. L. Goldberger, “The formal theory of scattering,” Phys. Rev. 91, 398–408 (1953).
[CrossRef]

Phys. Rev. A (8)

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

J. E. Miraglia and J. Macek, “Quantum-mechanical impulse approximation for single ionization of hydrogen-like atoms by multicharged ions,” Phys. Rev. A 43, 5919–5928 (1991).
[CrossRef] [PubMed]

M. Jain and N. Tzoar, “X-ray absorption in atoms in the presence of an intense laser field,” Phys. Rev. A 18, 538–545 (1978).
[CrossRef]

A. Basile, F. Trombetta, G. Ferrante, R. Burlon, and C. Leone, “Multiphoton ionization of hydrogen by a strong multimode field,” Phys. Rev. A 37, 1050–1052 (1988).
[CrossRef] [PubMed]

D. V. Milosevic and F. Ehlotzky, “Coulomb and rescattering effects in above-threshold ionization,” Phys. Rev. A 58, 3124–3127 (1998).
[CrossRef]

A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, “Stimulated radiative recombination and x-ray generation,” Phys. Rev. A 61, 023404 (2000).
[CrossRef]

J. Z. Kamiński, A. Jaroń, and F. Ehlotzky, “Coulomb effects in multiphoton above-threshold ionization,” Phys. Rev. A 53, 1756–1761 (1996).
[CrossRef] [PubMed]

G. Duchateau, E. Cormier, H. Bachau, and R. Gayet, “Coulomb–Volkov approach of atom ionization by intense and ultrashort laser pulses,” Phys. Rev. A 63, 053411 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

H. G. Muller and F. C. Kooiman, “Bunching and focusing of tunneling wave packets in enhancement of high-order above-threshold ionization,” Phys. Rev. Lett. 81, 1207–1210 (1998).
[CrossRef]

T. Ditmire, T. Donneley, R. W. Falcone, and M. D. Perry, “Strong x-ray emission from high-temperature plasmas produced by intense irradiation of clusters,” Phys. Rev. Lett. 75, 3122–3125 (1995).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

A. M. Perelomov, V. S. Popov, and M. V. Terentev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924 (1966).

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Z. Phys. (1)

D. M. Volkov, “Uber eine klasse von losungen de Diracschen gleichung,” Z. Phys. 94, 250–260 (1935).
[CrossRef]

Other (1)

M. R. C. McDowell and J. P. Colleman, Introduction to the Theory of Ion–Atom Collisions (North-Holland, Amsterdam, 1970).

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Figures (4)

Fig. 1
Fig. 1

Electron energy spectra of hydrogen ionization predicted by the time-dependent Schrödinger equation (open circles), (SD)+ (solid curve), (SD)- (dotted–dashed curve), and (DD) (dashed curve) models and by the SCV approach (dotted curve) for laser parameters E0=0.1 a.u., τ=5 a.u., and ω=0.05 a.u.

Fig. 2
Fig. 2

Same as Fig. 1 but for laser parameters E0=0.1 a.u., τ=30 a.u., and ω=0.05 a.u.

Fig. 3
Fig. 3

Same as Fig. 1 but for laser parameters E0=0.1 a.u., τ=30 a.u., and ω=1 a.u.

Fig. 4
Fig. 4

Same as Fig. 1 but for laser parameters E0=0.1 a.u., τ=150 a.u., and ω=0.25 a.u.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

F(t)=F0sin(ωt+φ)sin2(πt/τ)0<t<τ0 elsewhere
A±(t)=-tdtF(t),
i Ψ(r, t)t=[H0+V(t)]Ψ(r, t),
ΨkV(r, t)=exp(-iεt)exp(ikr)exp[iD-(k, r, )],
D±(k, r, t)=A±(t)r-k tA±(t)-½t[A±(t)]2,
χiICV+(r, t)=1(2π)3/2 dkexp(-iεit)φ˜i(k)×exp[ikr+iD+(k, r, t)],
=ϕi[r-α+(t)]exp[iD+(0, r, t)],
χiCV+(r, t)=ϕi(r, t)exp[iD+(0, r, t)].
χfCV-(r, t)=ϕf(r, t)exp[iD-(kf, r, t)],
Tfi+=limt+ϕf(t)|Ψi+(t)post form,
Tfi-=limt-Ψf-(t)|ϕi(t)prior form,
Tfi+=afi--i -+dtχfCV-(t)|Wf(t)|Ψi+(t),
Tfi-=afi+-i -+dtΨf-(t)|Wi(t)|χiCV+(t),
afi+=limt+ϕf(t)|χiCV+(t)post form,
afi-=limt-χfCV-(t)|ϕi(t)prior form.
H(t)-i ddt|χjCVs(t)=Wj(t)|χjCVs(t),
Wi(t)χiCV+(r, t)=-ιrϕi(r, t)A(t)exp[iD+(0, r, t)],
Wf (t)χfCV-(r, t)=-ι[rϕf(r, t)-ιkf]A(t)exp[iD+--(kf, r, t)].
TfiSD+=afi--i -+ tχfCV-(t)|Wf(t)|ϕi(t)=-i -+ tχfCV-(t)|V(t)|ϕi(t),
TfiDD+=afi--i -+ tχfCV-(t)|Wf(t)|χiCV+(t),
TfiSD-=afi+-i -+ tϕf(t)|Wi(t)|χiCV+(t)=-i -+ tϕf(t)|V(t)|χiCV+(t),
TfiDD-=afi+-i -+ tχfCV-(t)|Wi(t)|χiCV+(t).
TfiSCV=afi+=afi-
PfiEkΩk=k|Tfi|2,
PfiEk=k dΩk|Tfi|2.
EC=½ 0τdtF(t)

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