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Title: Exact Keldysh theory of strong-field ionization: Residue method versus saddle-point approximation

Abstract

In recent articles [K. Mishima et al., Phys. Rev. A, 66, 033401 (2002); S. D. Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strong-field ionization of atomic systems within Keldysh theory. This should avoid the necessity of applying the method of steepest descent (saddle-point approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the 1s and an even more drastic deviation for the 2s state. Thus it was concluded that the use of the saddle-point approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully removes the otherwise drastic failure for large principal quantum numbers.

Authors:
;  [1]
  1. AG Moderne Optik, Institut fuer Physik, Humboldt-Universitaet zu Berlin, Hausvogteiplatz 5-7, D-10117 Berlin (Germany)
Publication Date:
OSTI Identifier:
20982351
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.033403; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; FAILURES; HYDROGEN; PHOTOIONIZATION; PHOTON-ATOM COLLISIONS; QUANTUM NUMBERS; RESIDUES; RYDBERG STATES; SADDLE-POINT METHOD; TRANSITION AMPLITUDES

Citation Formats

Vanne, Yulian V., and Saenz, Alejandro. Exact Keldysh theory of strong-field ionization: Residue method versus saddle-point approximation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.033403.
Vanne, Yulian V., & Saenz, Alejandro. Exact Keldysh theory of strong-field ionization: Residue method versus saddle-point approximation. United States. doi:10.1103/PHYSREVA.75.033403.
Vanne, Yulian V., and Saenz, Alejandro. Thu . "Exact Keldysh theory of strong-field ionization: Residue method versus saddle-point approximation". United States. doi:10.1103/PHYSREVA.75.033403.
@article{osti_20982351,
title = {Exact Keldysh theory of strong-field ionization: Residue method versus saddle-point approximation},
author = {Vanne, Yulian V. and Saenz, Alejandro},
abstractNote = {In recent articles [K. Mishima et al., Phys. Rev. A, 66, 033401 (2002); S. D. Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strong-field ionization of atomic systems within Keldysh theory. This should avoid the necessity of applying the method of steepest descent (saddle-point approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the 1s and an even more drastic deviation for the 2s state. Thus it was concluded that the use of the saddle-point approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully removes the otherwise drastic failure for large principal quantum numbers.},
doi = {10.1103/PHYSREVA.75.033403},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
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  • The Keldysh approximation as applied to above-threshold ionization (ATI) is compared with conventional (weak-field) perturbation theory and the Kroll-Watson theory of electron scattering in intense fields. Unlike the latter ''nonperturbative'' theory, the Keldysh approximation treats the effects of the field on the initial and final states differently, and this leads to a spurious contribution from the A/sup 2/ part of the Hamiltonian in the Axp gauge. We attempt to clarify the role of the ponderomotive potential in ATI and the influence of the A/sup 2/ term on the polarization dependence of the transition amplitude. The fundamental defect of the Keldyshmore » approximation with regard to A/sup 2/ is shown to be of little practical consequence for the experiments carried out thus far. However, it is shown that the Keldysh amplitude is not ''exact'' in the applied field, as sometimes claimed, and is best regarded as an ansatz rather than a leading term in a gauge-invariant perturbation expansion. A simple modification of the Keldysh theory is proposed.« less
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  • In this paper, the classical Keldysh approximation for evaluating the tunnel ionization rate of a bound electron under the action of an intense radiation field is revisited. We transform the original Keldysh expression for the transition amplitude to a simplified one used by Gribakin and Kuchiev [Phys. Rev. A 55, 3760 (1997)], and show that the two expressions are equivalent up to a phase factor which does not contribute to ionization. Using the residue theorem to perform the contour integral, rather than the saddle point method employed by Keldysh and others, a revised closed form analytical formula for the photoionizationmore » rate is obtained. The formula also avoids using the redundant assumption of small kinetic momentum employed by Keldysh. This paper thus realizes a long-sought goal to calculate the transition rate within only the Keldysh approximation and provides an 'exact' formula to compare with other approaches using different gauges at various levels of approximation.« less
  • We investigate high-order above-threshold ionization (HATI) of diatomic molecules having different symmetries by an elliptically polarized laser field using the modified molecular strong-field approximation. The yields of high-energy electrons contributing to the plateau region of the photoelectron spectra strongly depend on the employed ellipticity. This is more pronounced if the major axis of the polarization ellipse is parallel or perpendicular to the molecular axis and at the end of the high-energy plateau. For the O{sub 2} molecule (characterized by {pi}{sub g} symmetry) the maximum yield is observed for some value of the ellipticity {epsilon} different from zero. On the othermore » hand, in the same circumstances, the N{sub 2} molecule ({sigma}{sub g}) behaves as an atom, i.e., the yield is maximum for {epsilon}=0. These characteristics of the photoelectron spectra remain valid in a wide region of the molecular orientations and laser peak intensities. The symmetry properties of the molecular HATI spectra are considered in detail: by changing the molecular orientation one or other type of the symmetry emerges or disappears. Presenting differential ionization spectra in the ionized electron energy-emission angle plane we have observed similar interference effects as in the HATI spectra governed by a linearly polarized field.« less