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Physical Review A

Comment on ‘‘Multiphoton-ionization transition amplitudes and the Keldysh approximation’’

H. S. Antunes Neto, L. Davidovich, Peter W. Milonni

Published Apr 1, 1990• 7 citations
Publisher

Abstract

We show that the approach of Trombetta, Basile, and Ferrante [Phys. Rev. A 40, 2774 (1989)] does not establish the Keldysh ansatz as a well-defined approximation. In particular, it in effect replaces a vanishing contribution to the ionization rate by a nonvanishing one.
DOI
10.1103/physreva.41.4095

Related papers

Reply to ‘‘Comment on ‘Multiphoton-ionization transition amplitudes and the Keldysh approximation’ ’’

Fabio Trombetta, S. Basile, G. Ferrante

We reply to the preceding Comment by Antunes Neto, Davidovich, and Milonni [Phys. Rev. A 41, 4095 (1990)] on our paper dealing with the Keldysh approximation for multiphoton ionization of atoms [Phys. Rev. A 40, 2774 (1989)]. We show by a concrete example how the replacement of the free evolution operator by the atomic one, leading to the Keldysh transition amplitude, can be justified for weak- and short-range binding potentials.

Physical Review A•Apr 1, 1990•2 citations

Multiphoton-ionization transition amplitudes and the Keldysh approximation

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The Keldysh approximation to treat the multiphoton ionization of atoms is reconsidered. It is shown that, if one consistently uses the hypothesis under which the approximation should be valid (essentially, that of a weak, short-range binding potential), a Keldysh-like term results as an approximation to the first term of a uniformly convergent series in powers of the binding potential. No cancellation occurs when higher-order terms are taken into account. This result allows one to consider the Keldysh approximation as a well-defined theoretical model, without implying, however, that it is adequate to describe multiphoton ionization of real atoms.

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Milonni [preceding Comment, Phys. Rev. A 45, 2138 (1992)] raises objections to my work [Phys. Rev. A 42, 1476 (1990)] on Keldysh-like methods in photoionization. His results are shown to follow from procedures that are inappropriate to the strong-field environment of the Keldysh method. These procedures lead to physical inconsistencies. My technique is verified to be rigorous and unique.

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The Keldysh approximation to treat the multiphoton ionization of atoms is reconsidered. It is shown that, if one consistently uses the hypothesis under which the approximation should be valid (essentially, that of a weak, short-range binding potential), a Keldysh-like term results as an approximation to the first term of a uniformly convergent series in powers of the binding potential. No cancellation occurs when higher-order terms are taken into account. This result allows one to consider the Keldysh approximation as a well-defined theoretical model, without implying, however, that it is adequate to describe multiphoton ionization of real atoms.
The Keldysh-Faisal-Reiss theory of nonresonant multiphoton ionization seems to give reasonably good agreement with experiments for production rates in the above-threshold-ionization peaks. The theory has some conceptual difficulties, since physically equivalent Hamiltonians give radically different results when treated by this method. An alternate form of the S matrix is used here in which approximation must be made upon the exact wave function evolving from the initial state rather than the time-reversed form used in the Keldysh-Reiss treatment. The exact initial state is approximated by an adiabatic form which results in an S matrix that eliminates the conceptual difficulties described above.