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

Abstract

Abstract 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, t abs , t path and t sc , 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 t path and obtained t path ( 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 t path ( 1 ) ( k , θ ) in the high energy regime ( k ≳ 3 . 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. t path ( 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 2 k R 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.