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Physical Review A

Multiphoton-ionization transition amplitudes and the Keldysh approximation

Fabio Trombetta, S. Basile, G. Ferrante

Published Sep 1, 1989• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.40.2774

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

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

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

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.

Physical Review A•Apr 1, 1990•7 citations

Multiphoton ionization of atoms: Effect of the final-state Coulomb potential on the ionization rate

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An approximation scheme is proposed to incorporate the influence of the Coulomb potential on the photoelectron in a nonperturbative treatment of multiphoton ionization rates. The method involves an approximation to an exact rate expression; when the latter is expanded in powers of the binding potential, the zeroth-order term is the commonly used Keldysh rate. The approach is applied to hydrogenlike atoms. Photoelectron angular distributions are calculated; these compare favorably with experimental measurements and with results of some other theoretical approaches.

Physical Review A•May 1, 1991•9 citations

Adiabatic theory of nonresonant multiphoton ionization

Marvin H. Mittleman

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.

Physical Review A•Jul 1, 1989•23 citations

NON-PERTURBATIVE METHODS APPLIED TO MULTIPHOTON IONIZATION

Humberto Siqueira Brandi, L. Davidovich, Nicim Zagury

We discuss the use of non-perturbative methods in the treatment of atomic ionization. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential, in this manner a criterium concerning the range of application of these non-perturbative scheme is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented.

Le Journal de Physique Colloques•Nov 1, 1982•3 citations

On the inadequacy of the momentum-translation approximation: multiphoton ionization of atomic hydrogen

A. Rachman, G Laplanche

The cross section for multiphoton ionization of hydrogen is computed using the momentum translation method (MTA) in the cases of linearly and circularly polarized light, alternatively. Extended numerical comparison is made with well-established results obtained from the Nth-order time-dependent perturbation theory in the weak intensity limit. The MTA does not reproduce the values given by perturbation theory and considerable differences are observed. Higher order iterations than the lower one are introduced and an analysis of the leading terms of the development is made: at weak intensities the zeroth-order term that defines the MTA cancels with higher order terms and the final result obtained after making (N-1 iterations is none other than the well-known transition amplitude deduced from standard perturbation theory, defined by the remaining terms of the last iteration after mutual cancellation with lower-order ones. According to the results obtained in this work, it is not possible to affirm that the MTA is adequate to calculate atomic multiphoton ionization cross sections.

Journal of Physics B Atomic and Molecular Physics•Apr 21, 1975•2 citations
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.
An approximation scheme is proposed to incorporate the influence of the Coulomb potential on the photoelectron in a nonperturbative treatment of multiphoton ionization rates. The method involves an approximation to an exact rate expression; when the latter is expanded in powers of the binding potential, the zeroth-order term is the commonly used Keldysh rate. The approach is applied to hydrogenlike atoms. Photoelectron angular distributions are calculated; these compare favorably with experimental measurements and with results of some other theoretical approaches.
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.
We discuss the use of non-perturbative methods in the treatment of atomic ionization. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential, in this manner a criterium concerning the range of application of these non-perturbative scheme is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented.
The cross section for multiphoton ionization of hydrogen is computed using the momentum translation method (MTA) in the cases of linearly and circularly polarized light, alternatively. Extended numerical comparison is made with well-established results obtained from the Nth-order time-dependent perturbation theory in the weak intensity limit. The MTA does not reproduce the values given by perturbation theory and considerable differences are observed. Higher order iterations than the lower one are introduced and an analysis of the leading terms of the development is made: at weak intensities the zeroth-order term that defines the MTA cancels with higher order terms and the final result obtained after making (N-1 iterations is none other than the well-known transition amplitude deduced from standard perturbation theory, defined by the remaining terms of the last iteration after mutual cancellation with lower-order ones. According to the results obtained in this work, it is not possible to affirm that the MTA is adequate to calculate atomic multiphoton ionization cross sections.