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Physical Review A

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

Fabio Trombetta, S. Basile, G. Ferrante

Published Apr 1, 1990• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.4096

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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.

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I reply to Finkelstein’s comment [preceding paper, Phys. Rev. A 60, 1723 (1999)] and remark on the meanings conveyed by the word “amplitude.”Received 23 December 1998DOI:https://doi.org/10.1103/PhysRevA.60.1725©1999 American Physical Society

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

Xingdong Mu

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
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.
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.
Recently, we introduced [C. Ufrecht and E. Giese, Phys. Rev. A 101, 053615 (2020)] a technique to calculate the phase of light-pulse atom interferometers caused by the presence of perturbation potentials and underlined its power by an illustrative example. In the preceding Comment [B. Dubetsky, Phys. Rev. A 102, 027301 (2020)], it was pointed out that other, less idealized situations could have been calculated as well. Our Reply emphasizes that our method is correct, the results from our example can be trivially generalized to other perturbations, and intricate effects of local environments can be even more prominent but also treated by our technique.
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.