Comment on "Classical Simulations Including Electron Correlations for
Sequential Double Ionization" [arXiv:1204.3956

Chandre, Cristel

Kamor, Adam

Mauger, Francois

Uzer, Turgay

English

arXiv

Comment on "Classical Simulations Including Electron Correlations for Sequential Double Ionization

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Comment on ”Classical Simulations Including ElectronCorrelations for Sequential Double Ionization”Cristel Chandre, Adam Kamor, Francois Mauger, Turgay UzerTo cite this version:Cristel Chandre, Adam Kamor, Francois Mauger, Turgay Uzer. Comment on ”Classical Simula-tions Including Electron Correlations for Sequential Double Ionization”. 2012. <hal-00723409>HAL Id: hal-00723409https://hal.archives-ouvertes.fr/hal-00723409Submitted on 9 Aug 2012HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Comment on “Classical Simulations Including Electron Correlations for SequentialDouble Ionization”In a recent Letter [1], the authors investigate trajecto-ries of a two-electron atomic system which models argonsubmitted to a strong, close to circularly polarized laserpulse. In the field-free case, the following classical Hamil-tonian is considered:H =1|r1 − r2|+∑i=1,2[p2i2−2ri+ VH(ri, pi)], (1)where ri ∈ R3 is the coordinate vector of the i-th electronin a frame centered at the nucleus, pi are the canonicallyconjugate momenta, and ri = |ri| and pi = |pi|. Herethe Heisenberg core potential VH is given byVH(r, p) =ξ24αr2eα(1−r4p4ξ4), (2)and is supposed to incorporate the Heisenberg uncer-tainty principle in a classical way [2]. Using Hamilto-nian (1), the authors of Ref. [1] analyze the double ion-ization of argon in order to interpret the experimentallymeasured ionization times of Ref. [3], and in particularthe anomalous ionization time of the second electron. Ina very striking way, Hamiltonian (1) is able to capturea shorter than expected ionization time of the secondelectron in excellent agreement with the experiment. Be-low, we show that this excellent agreement is only theresult of tweaking the parameter α in the potential (2),and that this result breaks down as α is varied, in con-trast with what the authors claim [1] “the results of ourcalculations do not depend on this parameter.” Theirresult is therefore not structurally stable and does nothold as α is made arbitrarily large, which is the regimewhere the potential has been designed (for the constraintrp & ξ to be satisfied) [2]. Commonly used values for αare 4 or 5, which is a compromise between the constraintand the speed of the integration given the stiffness of theproblem. In Ref. [1], the choice of one of the param-eters (ξ, α) relies on the second ionization potential ofthe atom (E2 = −1.01 for argon). More precisely, theminimum of the one electron Hamiltonian (kinetic en-ergy plus Coulomb interaction with the nucleus plus theHeisenberg core potential) has to be equal to E2. As aresult, ξ is chosen equal toξ =√−2E2(1 + 12α) . (3)The parameter α is chosen arbitrarily, provided that theground state of the one electron Hamiltonian occurs ata configuration where rp = ξ, which requires that α &1.256 (the solution of ex − 1 − 2x = 0). This translatesinto a minimum value for ξ, approximately equal to 1.190.2 3 4 5 6 710152025α∆ TFIG. 1. Mean-value of the time delays between the two suc-cessive ionizations in Hamiltonian (1) for I = 4 PW · cm−2.The other parameters are set as the ones in Ref. [3] for a pulseduration of 33 fs. The continuous curve is for 3D calculationsand the dashed curve corresponds to 2D calculations.For α = 2, the one electron energy minimum occurs atξ ≈ 1.259 and not at ξ = 1.225 as stated in Ref. [1].However choosing a value of ξ given by Eq. (3) results inan empty ground state energy surface at Eg = −1.59 a.u.for the two electron system, and thus a different value ofξ has to be considered. In the following, we consider thevalue chosen in Ref. [1], i.e., ξ = 1.225.In Fig. 1, we represent the time difference between theionization of the two electrons for the parameters consid-ered in Ref. [3] (laser wavelength 788 nm, ellipticity 0.77,pulse duration 33 fs) and for an intensity of 4 PW ·cm−2.We see that the time difference is in agreement with themeasured one (on the order of 10 fs) for α = 2, as inRef. [1]. However it increases as α is made larger, up toreaching a value comparable to the one obtained usingsoft-Coulomb potentials (on the order of 30 fs), both forthe 2D and the 3D calculations. Therefore we argue thatthe quantitative agreement on ionization times is onlycoincidental. The relevance of adding the Heisenbergcore potential has not been demonstrated. Note thata quantitative agreement with the experimental resultshas been obtained in Ref. [4] using soft-Coulomb poten-tial, i.e., without invoking the Heisenberg core potential.We reached similar conclusions by using soft Coulombpotentials with varying effective charge for the electron-nucleus interaction and by decreasing the influence of theelectron-electron correlation.In order to obtain qualitative agreement with experi-mental results (e.g., the knee shape of the double ioniza-tion probability versus intensity or the patterns of the ionmomentum distribution), it has been shown in the past2few decades that the specific choice of the potential doesnot matter. This means that the theoretical or numericalinterpretation of these experiments is structurally stable.However using these models to obtain quantitative agree-ment is more subtle since it requires a fine tuning of theHamiltonian model of the atom. This problem is centralwhether one works in the quantum or classical frame-work.C. Chandre1, A. Kamor1,2, F. Mauger1, and T. Uzer21 Centre de Physique The´orique, CNRS – Aix-MarseilleUniversite´, Campus de Luminy, Case 907, 13288 Mar-seille cedex 09, France2 School of Physics, Georgia Institute of Technology, At-lanta, Georgia 30332-0430, USA[1] Y. Zhou, C. Huang, Q. Liao, and P. Lu, Phys. Rev. Lett.109, 053004 (2012).[2] C.L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834(1980).[3] A.N. Pfeiffer, C. Cirelli, M. Smolarski, R. Do¨rner, and U.Keller, Nature Phys. 7, 428 (2011).[4] X. Wang, J. Tian, A.N. Pfeiffer, C. Cirelli, U. Keller andJ.H. Eberly, preprint (2012).

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