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Free-electron vortices in photoelectron momentum distributions from molecules with coupled electronic-nuclear motion

Paul Winter and Manfred Lein*

  • *Contact author: lein@itp.uni-hannover.de
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Phys. Rev. A 114, 043117 – Published 26 October, 2026

DOI: https://doi.org/10.1103/s4cm-rhrm

Abstract

Counterrotating, circularly polarized, time-delayed pulses generate electron wave packets that interfere in momentum space and form spiral-shaped free-electron vortices. By numerically solving the time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation for one-photon single ionization of H2, we show that these spirals rotate within the polarization plane as a function of the nuclear energy. A kinematical model, based on the instantaneous sharing of photon energy between the freed electron and the parent molecular ion, predicts this rotation and agrees quantitatively with the simulations. We further demonstrate that integrating over vibrational energies diminishes the visibility of the interference structure. Results from fixed-nuclei and atomlike reference calculations resemble single vibrational channels, whereas incoherent summation over multiple vibrational states leads to blurring and noticeable shifts of the apparent rotation. The joint-energy spectrum exhibits pronounced electron-nuclear correlation lines. In the case of corotating pulses, these lines are related to the interference rings in the momentum distribution. Conversely, for counterrotating pulses, they originate from a dipolar modulation of the spiral pattern, caused by the nonisotropic molecular orbital.

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Phys. Rev. A 114, 043117– Published 26 October, 2026
  • Received 22 May 2026
  • Accepted 7 October 2026
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