A multiple scattering theoretical approach to time delay in high energy core-level photoemission of heteronuclear diatomic molecules

We present analytical expressions of momentum-resolved core-level photoemission time delay in a molecular frame of a heteronuclear diatomic molecule upon photoionization by a linearly polarized soft x-ray attosecond pulse. For this purpose, we start to derive a general expression of photoemission time delay based on the first order time dependent perturbation theory within the one electron and single channel model in the fixed-in-space system (atoms, molecules and crystals) and apply it to the core-level photoemission within the electric dipole approximation. By using multiple scattering theory and applying series expansion, plane wave and muffin-tin approximations, the core-level photoemission time delay t is divided into three components, tabs, tpath and tsc, which are atomic photoemission time delay, delays caused by the propagation of photoelectron among the surrounding atoms and the scattering of photoelectron by them, respectively. We applied a single scattering approximation to tpath and obtained tpath(1)(k,θ) for a linearly polarized soft x-ray field with polarization vector parallel to the molecular axis for a heteronuclear diatomic molecule, where θ is the angle of measured photoelectron from the molecular axis. The core-level photoemission time delay t is approximated well with this simplified expression tpath(1)(k,θ) in the high energy regime ( k 33.5 a.u.-1, where k is the amplitude of photoelectron momentum k ), and the validity of this estimated result is confirmed by comparing it with multiple scattering calculations for C 1s core-level photoemission time delay of CO molecules. tpath(1)(k,θ) shows a characteristic dependence on θ, it becomes zero at θ = 0°, exhibits extended x-ray absorption fine structure type oscillation with period 2kR at θ = 180°, where R is the bondlength, and gives just the travelling time of photoelectron from the absorbing atom to the neighbouring atom at θ = 90°. We confirmed these features also in the numerical results performed by multiple scattering calculations.