Fractal dimensions in the phase space of two-electron atoms

Handke, G.

doi:10.1103/physreva.50.r3561

Cited by 13 publications

(2 citation statements)

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“…Depending on various conditions, the interaction of an intense laser pulse with atomic targets exhibits a fractal behavior [20][21][22][23][24]. This suggests that the use of a theoretical framework based on fractals could be well suited for the description of the dynamics of an electron submitted to both the coulomb and the time-dependent laser electric fields.…”

Section: Introductionmentioning

confidence: 99%

Theoretical derivation of laser-dressed atomic states by using a fractal space

Duchateau

2018

Eur. Phys. J. Plus

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The derivation of approximate wave functions for an electron submitted to both a coulomb and a time-dependent laser electric fields, the so-called Coulomb-Volkov (CV) state, is addressed. Despite its derivation for continuum states does not exhibit any particular problem within the framework of the standard theory of quantum mechanics (QM), difficulties arise when considering an initially bound atomic state. Indeed the natural way of translating the unperturbed momentum by the laser vector potential is no longer possible since a bound state does not exhibit a plane wave form including explicitely a momentum. The use of a fractal space permits to naturally define a momentum for a bound wave function. Within this framework, it is shown how the derivation of laser-dressed bound states can be performed. Based on a generalized eikonal approach, a new expression for the laser-dressed states is also derived, fully symmetric relative to the continuum or bound nature of the initial unperturbed wave function. It includes an additional crossed term in the Volkov phase which was not obtained within the standard theory of quantum mechanics. The derivations within this fractal framework have highlighted other possible ways to derive approximate laserdressed states in QM. After comparing the various obtained wave functions, an application to the prediction of the ionization probability of hydrogen targets by attosecond XUV pulses within the sudden approximation is provided. This approach allows to make predictions in various regimes depending on the laser intensity, going from the non-resonant multiphoton absorption to tunneling and barrier-suppression ionization.

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Section: Introductionmentioning

confidence: 99%

Theoretical derivation of laser-dressed atomic states by using a fractal space

Duchateau

2018

Eur. Phys. J. Plus

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“…Classically, this corresponds to three particles moving along a common axis with both electrons either on the same side of the nucleus or on the opposite sides of the nucleus. A second example is the so-called s-wave model [2][3][4] (see also the earlier references cited there) in which 1/r 12 is replaced by 1/r > where r > = max(r 1 , r 2 ), i.e. the lowest order (s-wave like) term in a one-centre expansion about the nucleus.…”

Section: Introductionmentioning

confidence: 99%

On thes-wave model of two-electron atoms

Ancarani¹

2006

J. Phys. B: At. Mol. Opt. Phys.

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One of the simplest s-wave models of a two-electron atom, in which the electron–electron repulsion is replaced by the lowest order term in a one-centre expansion about the nucleus, is investigated. The comparison of the corresponding Schrödinger equation with that of the real two-electron atom for S-states leads to a simple analytical property for the variational ground-state energy of the s-wave model. As a consequence, it is demonstrated that the solution to the s-wave model recently proposed by Howard and March (2005 Phys. Rev. A 71 042501) cannot be the exact ground-state wavefunction as claimed.

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