Relativistic and Quadrupole Effects in Photoionization Time Delay in Atoms

Eisenberg-Wigner-Smith (EWS) time delay [1] in atomic photoionization is sensitive to the dynamics of atomic electrons on the attosecond time scale, the natural time scale of atomic electron motion [2]. Time delay generally has an angular dependence and calculations have been performed including only dipole transitions [3,4]. In the nonrelativistic dipole approximation, the time delay for atomic ns-states does not depend upon angle; inclusion of relativistic effects of spin-flip transitions and nondipole (quadrupole) effects renders the time-delay angle-dependent. Since the amplitude for the dominant dipole photoionization channel (without spin-flip) vanishes at certain angles as a result of angular momentum geometry, quadrupole and spin-flip transitions dominate; specifically, where the dipole amplitude vanishes, the time delay is a combination of spin-flip dipole and quadrupole photoionization time delay, and the attosecond dynamics of these channels can be investigated. Relativistic expressions have been derived showing where quadrupole and/or spin-flip channels determine the time delay. Relativistic random phase approximation (RRPA) [5] calculations for the angular dependance of time delay of ns-subshells of noble gas atoms for the angular distribution of time delay including both dipole and quadrupole channels have been studied and the phenomenology is demonstrated. [1] E. P. Wigner, Phys. Rev. 98, 145 (1955); [2] R. Pazourek, S. Nagele and J. Burgdörfer, Rev. Mod. Phys. 87, 765 (2015); [3] J. Wätzel, et al, J. Phys. B 48, 025602 (2015); [4] A. Mandal, et al, Phys. Rev. A 96, 053407 (2017); [5] W. R. Johnson and C. D. Lin, Phys. Rev. A 20, 964 (1979).