Abstract
Anisotropy parameters describing the angular dependence of the photoionization delay are defined. The formalism is applied to results obtained with the relativistic random phase approximation with exchange for photoionization delay from the outermost $s$-orbitals in selected rare-gas atoms. Any angular dependence in the Wigner delay is induced here by relativistic effects, while the measurable atomic delay exhibits such a dependence also in the nonrelativistic limit. The contributions to the anisotropy from the different sources are disentangled and discussed. For the heavier rare gases, it is shown that measurements of the delay for electrons ejected in specific angles, relative to, e.g., those ejected along the laser polarization, are directly related here to the Wigner delay. For a considerable range of angles, the contributions from the second photon largely get canceled when the results in different angles are compared, and this angle-relative atomic delay is then close to the corresponding Wigner delay.
Highlights
The angular distribution of electrons released in the photoionization process is conveniently described with the angular anisotropy parameters
The method is based on the random phase approximation with exchange
The IR-photon energy is kept at 1.55 eV in all the calculations. This corresponds to the wavelengths commonly used in RABBIT experiments
Summary
The angular distribution of electrons released in the photoionization process is conveniently described with the angular anisotropy parameters. Photoionization, such as the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) [5] or the attosecond streak camera [6], has provided an additional path to such information [7,8,9,10,11,12,13,14,15] In these measurements, ionization, typically by extreme ultraviolet (XUV) light, is taking place in the presence of an infrared (IR) laser field, phase-locked to the XUV field. In a relativistic context we should expect the presence of two channels for ionization of an s-orbital: s → p1/2, p3/2, to allow for an angular dependence of the delay, which is of relativistic origin, already at the one-photon level This latter case has been discussed by Kheifets et al [24], who presented Wigner delays for electrons emitted from the outermost s-orbital in rare gases. We calculate the two-photon amplitudes and quantify different contributions to the angular dependence of the experimentally accessible atomic delay
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