Angular Dependence of the Transition from Dipole to Quadrupole Photoionization Time Delay in Atoms

Wigner time delay [1] in atomic photoionization is sensitive to the transition 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]. The amplitude for dipole photoionization vanishes at certain angles as a result of angular momentum geometry. In such a case, quadrupole transitions dominate; specifically, where the dipole amplitude vanishes, the time delay is quadrupole photoionization time delay, and the attosecond dynamics of quadrupole transitions can be investigated. Relativistic expressions have been derived showing where quadrupole channels determine the time delay. Relativistic random phase approximation (RRPA) [5] calculations for the angular dependance of time delay of s-subshells of noble gas atoms for the angular distribution of time delay including both dipole and quadrupole channels have been performed as a function of the angle between the photoelectron momentum and photon polarization and the transition from dipole to quadrupole time delay is exhibited. [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).