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Physical Review A

Reply to ‘‘Comment on ‘Complete Keldysh theory and its limiting cases’ ’’

Howard R. Reiss

Published Feb 1, 1992• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.45.2140

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Complete Keldysh theory and its limiting cases

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In this reply we amend the effect of misusing an analytical formula derived in 2007 Phys. Rev. A 75 013407, but containing a misprint subsequently corrected in a recently published erratum, 2013 Phys. Rev. A 87 069905(E). Two new corrected figures are included in this reply with the gradual formation of the resonance Fano profile for the lowest and third-lowest He 1P o resonant states. The comparison between our ab initio time-dependent Feshbach method and the analytical perturbative formula is rather good in the temporal domain for the time sequence shown during and after the laser pulse up to 50 fs, although still far from reaching the final asymptotic form. Other comments are also replied to. Finally, we emphasize that in the LabTalk published on 4 June 2013, we do not mention the inadequacy of any analytical formula whatsoever and the figure caption clearly refers to the asymptotic form of the Fano profile.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 26, 2014•0 citations
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.
An investigation of the foundations of strong-field theories of the Keldysh type is undertaken. It is found first that the Volkov solution, upon which the Keldysh approximation depends, exists unambiguously only in the relativistic case. Accordingly, a fully relativistic theory of atomic photoionization is formulated from first principles. A strong-field approximation (SFA) is expressed, based only on the proposition that the photoionizing field dominates the atomic potential in the final state. The nonrelativistic limit of the SFA gives exactly one of the known Keldysh-type theories, but the original Keldysh theory itself is found to neglect some fraction of the strong-field effects. It is shown on a variety of grounds that A2{\mathbf{A}}^{2}A2 terms must be fully retained in Keldysh-type theories. Important in this matter are the proper application of asymptotic conditions, the interchangeability of A\ensuremath{\cdot}p and A2{\mathbf{A}}^{2}A2 terms, and the consistent reduction to the nonrelativistic limit.
In this reply we amend the effect of misusing an analytical formula derived in 2007 Phys. Rev. A 75 013407, but containing a misprint subsequently corrected in a recently published erratum, 2013 Phys. Rev. A 87 069905(E). Two new corrected figures are included in this reply with the gradual formation of the resonance Fano profile for the lowest and third-lowest He 1P o resonant states. The comparison between our ab initio time-dependent Feshbach method and the analytical perturbative formula is rather good in the temporal domain for the time sequence shown during and after the laser pulse up to 50 fs, although still far from reaching the final asymptotic form. Other comments are also replied to. Finally, we emphasize that in the LabTalk published on 4 June 2013, we do not mention the inadequacy of any analytical formula whatsoever and the figure caption clearly refers to the asymptotic form of the Fano profile.