# Electron interferences in the ionization of the dimers by swift ion impact: Origin of high-order frequency

H Agueny, A Makhoute, A Dubois, J P Hansen

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H Agueny, A Makhoute, A Dubois, J P Hansen. Electron interferences in the ionization of the dimers by swift ion impact: Origin of high-order frequency. Journal of Physics: Conference Series, 2015, 635 (3), pp.032094. 10.1088/1742-6596/635/3/032094. [hal-01203440]

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Electron interferences in the ionization of the dimers by swift ion impact: Origin of high-order frequency

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2015 J. Phys.: Conf. Ser. 635 032094

(http://iopscience.iop.org/1742-6596/635/3/032094)

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# Electron interferences in the ionization of the dimers by swift ion impact: Origin of high-order frequency

H. Agueny*,‡<fnref n="1" />, A. Makhoute†, A. Dubois*, J. P. Hansen‡

* Sorbonne Universités, UPMC Univ Paris 06, UMR 7614, Laboratoire de Chimie Physique-Matière et Rayonnement, F-75231 Paris Cedex 05, France

† UFR de Physique du Rayonnement et des Interactions Laser-Matière, Faculté des Sciences. Université Moulay Ismail, B.P. 11201, Zitoune, Meknès, Morocco

‡Department of Physics and Technology, Allegt. 55, University of Bergen, N-5007 Bergen, Norway

**Synopsis** We report evidence for interference phenomena beyond Young-type in electron emission spectrum from the dimers by fast ions. Prior measurements for $H_2$ have led to a wide discussion for which no definitive conclusions have been settled, whereas theoretical-side have failed to reproduce the phenomenon. The process under investigations is treated by using a nonperturbative semi-classical approach to solve the time-dependent Schrödinger equation. Our results are supported by an analytic model based on second- and third-order Born series.

Double-scattering effects were claimed to be observed and evoked to explain additional oscillatory structures in the measured spectra in fast ion-$H_2$ collisions. The first experimental observations of such additional structures were sparked off further experimental and theoretical efforts to enhance the understanding of the complete nature of the phenomenon [1]. In spite of the number of experiences performed in that context, no clear demonstration has been reached [2, 3, 4, 6]. In contrast, theoretical investigations have been unable to reproduce the phenomenon [7, 8]. This makes the numerical demonstration of the existence of such effects a real challenge.

During the conference we shall present our results stemming from a nonperturbative approach to solve the time-dependent Schrödinger equation in which all high-order mechanisms are taken into account in the dynamical stage. The purpose is to resolve this controversy and explain why calculations on $H_2$ do not get to any additional features related to high-order interference. This is achieved by investigating completely different energetic ion-molecule collisions, in which a clear footprint of high-order frequency in electron emission spectra is found. As is shown in Fig. 1 the spectrum shows up to four distinct harmonics from the full molecular treatment. In contrast, the corresponding results "2Rb" stemming from a pseudo-molecular model exhibit only first order frequency characteristic of Young-type interference. Our nonperturbative calculations are supported by a model derived from second- and third-order Born series. The latter reproduces the spectrum almost perfectly. We will also report an extension to a triatomic linear molecule which reveals additional

and strong harmonics.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Frequency distributions from calculations for 63 Mev/u collisions of $H^+ - Rb_2^+$ (black curve) and $H^+ - 2Rb$ (red curve) compared with the Fourier spectrum from the third Born model (blue curve). The model $2Rb$ is resulting from a coherent sum of the ionization wave-function from two-independent monomers separated by a distance $R_{ab}=9.2$ a.u.. Inset: Initial Electronic probability density vs. spatial coordinate $x$ ($|x|<10$ a.u.).</figcaption></figure>

## References

[1] N. Stolterfoht et al 2001 Phys. Rev. Lett. 87 023201

[2] N. Stolterfoht et al 2004 Phys. Rev. A 69 012701

[3] S. Hossain et al 2005 Phys. Rev. A 72 010701

[4] J. A. Tanis et al 2006 Phys. Rev. A 74 022707

[5] J. L. Baran et al 2008 Phys. Rev. A 78 012710

[6] D. Misra et al 2009 Phys. Rev. A 80 062701

[7] N. Sisourat et al 2007 Phys. Rev. A 76 012718

[8] L. Sælen et al 2010 Phys. Rev. A 81 022718

<figure><img src="image_3.png" /></figure>

<footnote n="1">¹E-mail: h.agueny@gmail.com</footnote>