Transition of angular-dependent WES time delay from Dipole to Quadrupole and Spin-Flip Dynamics in Kr and Xe

The angular dependence of attosecond time delay in atomic photoionization, considering both dipole and quadrupole transitions, is calculated for ns subshells of Kr and Xe. Generally, no-spin-flip (NSF) dipole transitions have significantly higher amplitudes compared to spin-flip (SF) dipole and quadrupole transitions. However, under certain conditions, the NSF dipole transition amplitude vanishes, causing SF dipole and quadrupole transitions to dominate. At the non-relativistic dipole level, the WES time delay for atomic ns photoionization is angle-independent. However, using a fully relativistic approach, significant . However, incorporating relativistic and quadrupole introduces significant angular dependence because the NSF dipole amplitude vanishes at a 90-degree angle to the photon polarization. Thus, at the larger angles, the time delay is largely by quadrupole and spin-flip transitions, particularly in the energy range of the Cooper minimum, and this was seen in detail for Ar 3s photoionization [1]. The present investigation extends this work to Kr and Xe.