Zepto to Attosecond core-level photoemission time delays in homonuclear diatomic molecules and non-dipole effects in the framework of Multiple Scattering theory

This study theoretically investigates the angular distribution of core-level photoemission time delay within a molecular frame. This phenomenon can be measured with the advancement of attosecond pulsed lasers and metrology. Our focus is on homonuclear diatomic molecules. The two-center interference patterns observed in the gerade and ungerade core-level Molecular-Frame Photoelectron Angular Distributions (MFPAD) of homonuclear diatomic molecules demonstrate symmetry breaking with respect to the direction of light propagation, attributed to the non-dipole (multipole) effect. Our study delves into the photoemission time delay resulting from the non-dipole effect through the introduction of a theoretical model. We reveal that when considering the contributions from the gerade and ungerade delocalized states in incoherent sums, the two-center interference terms cancel each other in both the MFPADs and photoemission time delays. However, a residual term persists showcasing the non-dipole effect in the photoemission time delays. Furthermore, by expanding the scattering state of photoelectrons using the Multiple Scattering theory, we demonstrate the significant role played by the scattering of photoelectrons at the molecular potential in describing the photoemission time delays of homonuclear diatomic molecules. Next, we apply our theoretical model to a nitrogen molecule, demonstrating the energy- and angular-dependent characteristics of the MFPADs and photoemission time delays through both analytical and numerical approaches. The incoherent sums of the MFPADs in both forward and backward directions exhibit equal intensity, whereas the incoherent sums of the photoemission time delays show a slight variation of a few hundred zeptoseconds compared with numerical calculations using a multiple scattering code.