114 The Young's double-slit experiment (YDSE) provides the simplest and most fundamental example in which the superposition of two coherent waves of light leads to interference oscillations of the light intensity. Photoionization of homonuclear diatomic molecules represents conceptually a similar phenomenon for the electron waves. The interference of the coherent electron waves emitted from two indistinguishable atoms leads to intrinsic interference oscillations. Cohen and Fano [1] were the first to derive the equation for the total photoionization cross section for the H 2 molecule including this YDSE effect. Subsequent theoretical [2] and experimental studies of ionization of H 2 and D 2 molecules with different projectiles were performed. Core-level photoemission from molecules like N 2 provides a new opportunity to investigate coherent emission of photoelectron waves [3,4]). For core-level photoionization of these molecules, an additional complication appears due to the presence of the gerade and ungerade 1 σ bound orbitals with a slight energy gap between them. This gap is 0.1 eV and is even smaller than the vibrational splitting of ~0.3 eV. The experiment was carried out at the high- resolution soft X-ray photochemistry beamline BL27SU . The light source of the beamline is a figure- 8 undulator which provides linearly polarized radiation. The photoelectron spectra were recorded using a high resolution Scienta SES-2002 analyzer. The analyzer bandwidth was set to ~31 meV. The overall bandwidth was determined separately by measuring Xe 5 p photoelectrons at the same monochromator and analyzer settings. Figure 1 shows the N 1 s photoelectron spectrum recorded at photon energy of 831 eV. The experimental spectra were decomposed by least- squares curve fitting into 1 σ g and 1 σ u components with the individual vibrational progressions. The partial cross section ratios of σ g / σ u for the photoionization of the 1 σ g and 1 σ u shells corresponding to the 0 → 0 and 0 → 1 vibrational transitions and are plotted in Fig. 2 as a function of the photoelectron momentum k in atomic unit (a.u.) in order to display clearly the oscillations. The results of previous measurements [5] are also included. The ab initio calculations using RPA method are compared with measurement. At low momenta k < 1.5 a.u. the ratios are defined by the σ * shape resonance, and only at k > 1.5 a.u. the CF oscillations become apparent. There is a good qualitative agreement between the theory and the experiment for both vibrational transitions. The main difference between the 1 σ g and 1 σ u shells is connected with the symmetry of these states. From the dipole selection rules, only odd partial waves contribute to the photoionization of the 1 σ g shell, and only even partial waves to the 1 σ u shell. The interference modulation is mainly connected with the onset of transitions to the states of increasing orbital angular momentum at increasing photon energies, while the different parity of the photoelectron partial waves for the 1 σ g and 1 σ u shells causes the shift of interference modulation for these shells by π . Due to this, the cross section ratio 1 σ g / 1 σ u observed experimentally is greatly enhanced, although generally the interference modulation is expected to be relatively small. And the sum of the contributions from the 1 σ g and 1 σ u shells will not display any CF Y Yo ou un ng g''s s D Do ou ub bl le e- -s sl li it t E Ex xp pe er ri im me en nt t u us si in ng g C Co or re e- -l le ev ve el l P Ph ho ot to oe em mi is ss si io on n f fr ro om m N N 2 2 Chemical Science 3000 2000 1000 0 Count 422.0 421.5 421.0 420.5 420.0 Electron Kinetic Energy (eV) σ u σ g N 2 K -shell 1 0 1 0 Fig. 1. Photoelectron spectrum at photon energy of 831 eV, parallel to the polarization vector. oscillations. From another point of view, at high electron kinetic energy with the plane wave approximation, the original CF interference pattern is shown in Fig. 2 as the dash- dotted line. Apparently, the phase of the interference pattern is shifted from both the experimental and ab initio ones. To explain this disagreement, we take the sum over the vibrational components for the experimental spectra and obtain the ratios as shown in Fig. 3. By the multiple scattering theory, the Cohen-Fano interference pattern is shifted by twice the phase of the photoelectron scattering by the neighboring N atom. Taking the reported value of phase shift, we obtain the dash-dotted line in Fig. 3. The agreement with the experiment is improved in comparison with the original Cohen-Fano approach but it is still far from being fair. We can obtain the improved value of the scattering phase using a least-squares fitting, shown as the solid line in Fig. 3. 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Cross Section Ratio σ g / σ u 7 6 5 4 3 2 1 0 500 600 700 800 900 1000 Electron Momentum (a. u.) N 2 K -shell vibrationally resolved / Measured v = 0 / Measured v = 1 RPA v = 0 RPA v = 1 Cohen-Fano Photon Energy (eV) 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 6 5 4 3 2 1 / Experiment Original Cohen-Fano Fit Modified Cohen-Fano RPA 500 600 700 800 900 Cross Section Ratio σ g / σ u Electron Momentum (a. u.) Photon Energy (eV) N 2 K -shell Fig. 2. Comparison of experimental cross section ratios with ab initio calculations. Fig. 3. Ratios of 1 σ g and 1 σ u partial photoionization cross sections of N 2 summed over the vibrational components. X.-J. Liu*, N.A. Cherepkov, F. Gel'mukhanov and K. Ueda Institute of Multidisciplinary Research for Advanced Materials, Tohoku University *E-mail: xiliu@mail.tagen.tohoku.ac.jp Reference [1] H.D. Cohen and U. Fano: Phys. Rev. 150 (1966) 30. [2] O.A. Fojón et al .: J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 3035. [3] D. Rolles et al .: Nature 437 (2005) 711. [4] X.-J. Liu, N.A. Cherepkov, S.K. Semenov, V. Kimberg, F. Gel'mukhanov, G. Prümper, T. Lischke, T. Tanaka, M. Hoshino, H. Tanaka and K. Ueda: J. Phys. B 39 (2006) 4801 . [5] M. Ehara et al .: J. Chem. Phys. 124 (2006) 124311. 115
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