Nondipole Effects in Time Delay of Photoelectrons from Atoms, Negative Ions, and Endohedrals
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Non-dipole Effects in Time Delay of Photoelectrons from Atoms, Negative Ions, and Endohedrals M. Ya. Amusia+∗1) , L. V. Chernysheva∗ + Racah
Institute of Physics, the Hebrew University, 91904 Jerusalem, Israel
∗ Ioffe
Physical-Technical Institute, 194021 St. Petersburg, Russia Submitted 15 October 2020 Resubmitted 15 October 2020 Accepted 15 October 2020
In this Letter, we investigate the non-dipole effects in time delay of photoelectrons emitted by multielectron atoms, negative ions, and respective endohedrals. We present the necessary general formulas in the frame of the random phase approximation with exchange (RPAE) applied to atoms, negative ions, and properly adjusted to endohedrals. We concentrate on low photon energy region, where non-dipole effects are very small in the cross-sections, but become observable in angular distributions. We not only derive the formulas for non-dipole effects in time delay, but perform corresponding numeric calculations. We demonstrate how the non-dipole corrections can be isolated in experiment. Concrete calculations are performed for noble gas atoms Ar and Xe, isoelectronic to them negative ions Cl− and I− and endohedrals Ar(Cl− )@C60 and Xe(I− )@C60 . We found that the forward-backward photoelectron time delay differences give direct information on non-dipole effects. They proved to be quite measurable and prominently affected by the presence of the fullerenes shell. DOI: 10.1134/S0021364020220014
1. The aim of this Letter is to find the contribution of non-dipole corrections to the time delay of electrons that due to low-energy photon absorption leave atoms A, negative ions A− and endohedrals A@CN or A− @CN that present A or A− stuffed inside the fullerenes shell CN constructed of N carbon atoms C. Ionization by a photon with low energy ω 2) is a process determined predominantly by dipole transition matrix elements. The non-dipole contribution to the absolute photoionization cross-section is much smaller than the dipole term, being different by additional factor (ωrA /c)2 1, where rA is the atomic radius and c is the speed of light. The smallness of the non-dipole cross-section is enhanced by a numeric small factor. However, the role of non-dipole term is much bigger in the angular distributions of photoelectrons that differ from the respective dipole terms by a factor (ωrA /c), which is much bigger than (ωrA /c)2 (ωrA /c) 1 (see, e.g., [1]). The investigation of non-dipole transitions is stimulated by the interest to quadrupole transitions and quadrupole phase shifts of the outgoing electron wave-functions. Apart from angular distribution, there exists another source of information on these
quantities, namely the time delay of electrons released from an atom, ion, or endohedral under the action of the incoming photon. The theoretic approach to temporal description of processes in quantum objects has been developed long ago in a number of publications [2–5]. The construction of lasers with attosecond pulses permitted to measure the duration of atomic photoionization processe
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