Zepto- to attosecond core-level photoemission time delays in homonuclear diatomic molecules and nondipole effects in the framework of multiple scattering theory

This study theoretically investigates the angular distribution of core-level photoem ission 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 nondipole (multipole) effect. This nondipole effect reflects the zeptosecond time discrepancy in the initiation of photoelectron waves at the two absorbing atoms. Our study delves into the photoemission time delay resulting from the nondipole 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 nondipole 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. Additionally, we establish that the direct wave contribution does not exhibit angular dependence in the photoemission time delays. 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. Our findings demonstrate that the photoemission time delay serves as a valuable tool for investigating attosecond and zeptosecond photoionization dynamics, providing insights that may be overlooked in the MFPAD analysis. This study provides a basis for theoretical investigations into photoionization phenomena in nano systems containing numerous identical atoms, such as large polyatomic molecules and condensed matter, enabling the examination of photoemission time delays and nondipole effects.