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Relativistic Two-photon Matrix Elements for Attosecond Delays
Version 1
: Received: 20 June 2022 / Approved: 22 June 2022 / Online: 22 June 2022 (04:46:15 CEST)
A peer-reviewed article of this Preprint also exists.
Vinbladh, J.; Dahlström, J.M.; Lindroth, E. Relativistic Two-Photon Matrix Elements for Attosecond Delays. Atoms 2022, 10, 80. Vinbladh, J.; Dahlström, J.M.; Lindroth, E. Relativistic Two-Photon Matrix Elements for Attosecond Delays. Atoms 2022, 10, 80.
Abstract
The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science using the Dirac-Fock formalism. A direct comparison of the Wigner-Smith-Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the Relativistic Random Phase Approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as Argon, show negligible relativistic effects, while heavier elements, such a Krypton and Xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notable close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner-Smith-Eisenbud delay and a universal continuum--continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.
Keywords
attoscience; attophysics; photoionization; above-threshold ionization; Wigner-Smith-Eisenbud delay; Dirac-Fock; RRPA; RABBIT; Krypton; Xenon
Subject
Physical Sciences, Atomic and Molecular Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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