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.