  We report a theoretical study of the angular distribution of core-level
photoemission time delay in a molecular frame, which is converting into
possible measure with the development of attosecond pulsed lasers and
metrology, focusing on homonuclear diatomic molecules. Two-center interference
patterns in gerade and ungerade core-level molecular-frame photoelectron
angular distributions (MFPADs) of homonuclear diatomic molecules exhibit
symmetry-broken with respect to the direction of light propagation due to the
non-dipole (multipole) effect. In this study, we investigate the photoemission
time delay due to the non-dipole effect by introducing a theoretical model. We
show that in incoherent sums, considering the average of the contributions from
the gerade and ungerade delocalized core states, two-center interference terms
cancel each other out in both of the MFPADs and photoemission time delays;
however, there remains a residual term exhibiting the non-dipole effect for the
photoemission time delays. By expanding the scattering state of photoelectrons
with Multiple Scattering theory, we also demonstrate that the scattering effect
at the molecular potential plays a crucial role in the descriptions of the
photoemission time delays of homonuclear diatomic molecules. Furthermore, we
demonstrated that the direct wave contribution does not show angular dependence
in the photoemission time delays. We then apply the theoretical model to a
nitrogen molecule to show the energy- and angular dependence of the MFPADs and
photoemission time delays both analytically and numerically. While the
incoherent sums of the MFPADs in a given and opposite direction have the same
intensity, the incoherent sums of the photoemission time delays depicts a few
hundred zeptosecond difference from numerical calculations by multiple
scattering code.
