Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fiel
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fields Dmitry A. Tumakov1,a , Dmitry A. Telnov1,b , G¨ unter Plunien2 , Vladimir A. Zaytsev1 , and Vladimir M. Shabaev1 1 2
Department of Physics, St. Petersburg State University, Universitetskaya Naberezhnaya 7/9, St. Petersburg 199034, Russia Institut f¨ ur Theoretische Physik, Technische Universit¨ at Dresden, Mommsenstrasse 13, Dresden D-01062, Germany Received 1 June 2020 / Received in final form 15 July 2020 / Accepted 6 August 2020 Published online 17 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties.
1 Introduction With recent advancement of the laser technologies making it possible to generate extremely intense short pulses, the light-matter interaction phenomena draw much attention both in the theory and experiment [1–4]. The most powerful free-electron laser facilities, such as XFEL [5] at Hamburg and LCLS [6] at Stanford, are expected to produce electromagnetic fields with the peak brilliance of up to 5 × 1033 photons/s/mm2 /mrad2 /0.1% bandwidth and wavelengths down to 0.05 nm. Such extremely strong and high-frequency fields take the electronic dynamics of the target to the relativistic domain. Interaction of these fields with highly-charged ions is of particular interest, given the fact that such ions have their own strong Coulomb fields where the electronic motion is essentially relativistic. In this respect, we should mention the shortly upcoming High-Intensity Laser Ion-Trap Experiment (HILITE) experiment [7–9], which is intended to study the lightmatter interaction using the Penning trap. For the correct theoretical description of such processes, a relativistic treatment should be invoked to capture the electron dynamics: not only the bound electron is relativistic for the ions with high nucleus charge Z, but also the ionized electrons can reach the relativistic velocities. Various approaches exist
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