Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Study of angular dependence of photoionization time delay in (n − 1)d → ε f channels for Zn, Cd and Hg

Sourav Banerjee, Pranawa C. Deshmukh, Anatoli S. Kheifets, V. K. Dolmatov, Steven Trent Manson

Published Jul 1, 2017• 1 citation
Publisher

Abstract

The angular dependence of Wigner-Eisenbud-Smith photoionization time delay has been investigated for the nd → ε f dipole channels in atomic Zn, Cd and Hg using the relativistic random phase approximation (RRPA). The studies have been carried out also in the nonrelativistic limit. This technique enables identification of the relativistic effects on the angular dependence of photoionization time delay.

DOI
10.1088/1742-6596/875/3/022025

Related papers

Angular anisotropy parameters for photoionization delays

Soumyajit Saha, Jimmy Vinbladh, Johanna Sörngård +2 more

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.

Physical Review A•Sep 15, 2021•9 citations

Quadrupole Photoionization Time Delay For Ne And Ar

Pratikshya Parajuli

Early investigations of the photoionization time delay focused solely on dipole contributions at low-energy. Later experimental progress demonstrated that non-dipole time delays are also measurable. This motivated us to initiate a theoretical program aimed at studying detailed quadrupole time delays in the noble gasses Ne and Ar and assessing their physical significance. In this work, we examined the angular dependence of the quadrupole photoemission time delay for Ne and Ar using the Relativistic-Random-Phase Approximation (RRPA) method. Our approach began with identifying the relevant transitions for each sub-shell and obtaining the corresponding expression for the transition amplitude. From these amplitudes, we extracted the phase and computed the associated non-dipole time delay as a function of emission angle and energy for each sub-shell. Where applicable, we evaluated the time delay across both low- and high-energy regions and compared subshells that share the same principal quantum number n. These comparisons reveal the substantial influence of relativistic interactions between different subshells and atomic species. Currently, we have obtained results for Ne and Ar for the subs-hells ns1/2, np1/2, np3/2. Future work will extend these calculations to additional atomic systems, including heavier noble gasses, various atomic ions, and confined atomic environments.

•Jul 24, 2026•0 citations

Comment on ‘Time delays in molecular photoionization’

Denitsa Baykusheva, Hans Jakob Wörner

Abstract In a recent article by Hockett et al (2016 J. Phys. B: At. Mol. Opt. Phys. 49 095602), time delays arising in the context of molecular single-photon ionization are investigated from a theoretical point of view. We argue that one of the central equations given in this article is incorrect and present a reformulation that is consistent with the established treatment of angle-dependent scattering delays (Eisenbud 1948 PhD Thesis Princeton University; Wigner 1955 Phys. Rev. 98 145–7; Smith 1960 Phys. Rev. 118 349–6; Nussenzveig 1972 Phys. Rev. D 6 1534–42).

arXiv:1611.09352•Journal of Physics B Atomic Molecular and Optical Physics•Mar 15, 2017•6 citations

Relativistic effects in time delay of atomic photoionization

Igor A. Ivanov, Anatoli S. Kheifets

We study relativistic effects in the time delay of atomic photoionization using an example of the Xe atom subjected to a circularly polarized electromagnetic pulse. We find that while relativistic effects play only a fairly small role for both the ionization probabilities and the time delay of the corotating electron with the same sign of the angular momentum projection as the circularly polarized light, these effects produce substantial change in the time delay for a counter-rotating electron with the opposite sign of the angular momentum projection.

Physical Review A•Apr 7, 2014•10 citations

Relativistic effects in photoionization time delay near the Cooper minimum of noble-gas atoms

Soumyajit Saha, Ankur Mandal, Jobin Jose +5 more

The time delay of photoemission from noble-gas atoms is analyzed in the vicinity of a Cooper minimum, showing that the presence of the Cooper minimum in one channel has a strong effect on the time delay in other channels.

Physical Review A•Nov 6, 2014•44 citations

Time delay and dilation properties in scattering theory

Heide Narnhofer

We show the identity of the Eisenbud–Wigner time delay and that of Lavine for potentials V=V1+V2, V1∼1/‖x‖1+ε, x∇V1∼1/‖x‖1+ε, V2∼1/‖x‖2+ε for x→∞. Finally we show the additivity of time delay for the same class of potentials.

Journal of Mathematical Physics•Apr 1, 1984•14 citations
The angular dependence of Wigner-Eisenbud-Smith photoionization time delay has been investigated for the nd → ε f dipole channels in atomic Zn, Cd and Hg using the relativistic random phase approximation (RRPA). The studies have been carried out also in the nonrelativistic limit. This technique enables identification of the relativistic effects on the angular dependence of photoionization time delay.
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 sss-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.
Early investigations of the photoionization time delay focused solely on dipole contributions at low-energy. Later experimental progress demonstrated that non-dipole time delays are also measurable. This motivated us to initiate a theoretical program aimed at studying detailed quadrupole time delays in the noble gasses Ne and Ar and assessing their physical significance. In this work, we examined the angular dependence of the quadrupole photoemission time delay for Ne and Ar using the Relativistic-Random-Phase Approximation (RRPA) method. Our approach began with identifying the relevant transitions for each sub-shell and obtaining the corresponding expression for the transition amplitude. From these amplitudes, we extracted the phase and computed the associated non-dipole time delay as a function of emission angle and energy for each sub-shell. Where applicable, we evaluated the time delay across both low- and high-energy regions and compared subshells that share the same principal quantum number n. These comparisons reveal the substantial influence of relativistic interactions between different subshells and atomic species. Currently, we have obtained results for Ne and Ar for the subs-hells ns1/2, np1/2, np3/2. Future work will extend these calculations to additional atomic systems, including heavier noble gasses, various atomic ions, and confined atomic environments.
Abstract In a recent article by Hockett et al (2016 J. Phys. B: At. Mol. Opt. Phys. 49 095602), time delays arising in the context of molecular single-photon ionization are investigated from a theoretical point of view. We argue that one of the central equations given in this article is incorrect and present a reformulation that is consistent with the established treatment of angle-dependent scattering delays (Eisenbud 1948 PhD Thesis Princeton University; Wigner 1955 Phys. Rev. 98 145–7; Smith 1960 Phys. Rev. 118 349–6; Nussenzveig 1972 Phys. Rev. D 6 1534–42).
We study relativistic effects in the time delay of atomic photoionization using an example of the Xe atom subjected to a circularly polarized electromagnetic pulse. We find that while relativistic effects play only a fairly small role for both the ionization probabilities and the time delay of the corotating electron with the same sign of the angular momentum projection as the circularly polarized light, these effects produce substantial change in the time delay for a counter-rotating electron with the opposite sign of the angular momentum projection.