Dipole and Quadrupole Contributions to Photoionization Time Delay in Atoms

The study of Wigner time delay [1] in atomic photoionization provides information of on the dynamics of atomic electrons in transition on the attosecond time scale, the time scale of atomic electron motion [2].  This time delay generally has an angular dependence and calculations have been carried out looking at this angular dependence including only dipole transitions [3,4].  Owing to angular momentum geometry, the amplitude for dipole photoionization vanishes at certain angles.  Under such circumstances, the amplitude for quadrupole transitions dominates and can be studied; in particular, at angles where the dipole amplitude vanishes, the time delay exhibited is that of quadrupole photoionization, thereby allowing us to get information on the attosecond dynamics of quadrupole transitions.  Fully relativistic calculations have been performed to delineate the circumstances under which the quadrupole channels dominate.  In addition, calculations have been carried out using relativistic random phase approximation (RRPA) [5] for noble gas atoms for the angular distribution of time delay including both dipole and quadrupole channels where the transition from dipole-dominance to quadrupole dominance is seen as a function of the angle between the photoelectron momentum and photon polarization. [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).