Vibrational Scattering Anisotropy Generated by Multichannel Quantum Interference Catalin Miron, 1 Victor Kimberg, 1 Paul Morin, 1 Christophe Nicolas, 1 Nobuhiro Kosugi, 2 Sergey Gavrilyuk, 3 and Faris Gel’mukhanov 3, * 1 Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France 2 Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan 3 Theoretical Chemistry, Royal Institute of Technology, S-106 91 Stockholm, Sweden (Received 29 May 2010; published 26 August 2010) Based on angularly and vibrationally resolved electron spectroscopy measurements in acetylene, we report the first observation of anomalously strong vibrational anisotropy of resonant Auger scattering through the C 1s !   excited state. We provide a theoretical model explaining the new phenomenon by three coexisting interference effects: (i) interference between resonant and direct photoionization channels, (ii) interference of the scattering channels through the core-excited bending states with orthogonal orientation of the molecular orbitals, (iii) scattering through two wells of the double-well bending mode potential. The interplay of nuclear and electronic motions offers in this case a new type of nuclear wave packet interferometry sensitive to the anisotropy of nuclear dynamics: whether which-path information is available or not depends on the final vibrational state serving for path selection. DOI: 10.1103/PhysRevLett.105.093002 PACS numbers: 33.20.Rm, 31.15.A, 33.20.Tp Our understanding of nuclear motion in molecules is intimately related to our ability to probe it. The drastic improvement of spectral resolution available from brilliant 3rd generation synchrotron radiation (SR) light sources revealed a powerful tool—vibrationally resolved resonant Auger scattering (RAS) [1–4]—which allows visualization of the nuclear motion [5–7] and, even more, to map its femtosecond dynamics [1,4]. In addition, the angular de- pendence of the scattering amplitude [8] is known to be an essential probe of molecular symmetry. X-ray absorption anisotropy has been revealed in symmetry resolved ion yield spectra as caused by vibronic coupling [9,10]. Vibrational anisotropy has been observed for core level direct photoemission lines [11], where low energy photo- electrons are emitted as a result of non-Franck-Condon transitions in the vicinity of shape resonances. However, the RAS anisotropy observed until now for high energy Auger electrons was exclusively associated to the symme- try of the electronic states [12]. There is only one known effect resulting in a large scattering anisotropy caused by the dissociative nuclear motion: the Auger-Doppler effect [1,13], which leads to the Doppler splitting of the fragment Auger emission lines [14–16]. To the best of our knowl- edge, no evidence of RAS vibrational anisotropy was observed to date for bound core-excited states. At first glance, this seems natural since within the Born- Oppenheimer (BO) approximation the electronic and nu- clear motions are decoupled. Only the electronic wave function depends on the orientation of the transition dipole and shows anisotropy with respect to the polarization of the incident radiation. Consequently, in the BO approximation vibrational motion is not influenced by the polarization of the x rays, resulting in no difference in RAS anisotropy for various vibrational states of the same final electronic state. However, our measurements show a complete breakdown of this simplified picture in the present case when multi- channel interference processes are present. We study here, experimentally and theoretically, the angularly resolved RAS or resonant photoemission in gas phase acetylene C 2 H 2 . The resonant photoabsorption pro- cess 1 u ! 1 g enhances population of the one-hole cat- ionic state 1 1 u with ejection of an Auger electron with momentum k and kinetic energy E into the continuum c k . The same electronic state can be populated by a direct valence photoionization channel, where the absorption of an x-ray photon @! leads to the emission of a photoelec- tron. The two channels have qualitatively different spectral features and anisotropic properties and are both explicitly taken into account in what follows. The RAS cross sections   ðE b Þ were recorded as a func- tion of the binding energy E b ¼ @!  E [Figs. 1(a)–1(c)] for two scattering angles  ¼ ffðk; eÞ¼ 0  ; 90  with re- spect to the polarization vector e of the linearly polarized x rays, and for several excitation energies around the top of the x-ray absorption resonance [Fig. 1(d)]. The experiment has been performed at the undulator beam line I411 at the third generation SR facility MAX II in Lund, Sweden [17]. This beam line is equipped with a modified Zeiss SX 700 PGM monochromator and with a high-resolution VG- Scienta R4000 spectrometer mounted on a rotatable cham- ber in a plane perpendicular to the photon propagation axis. The monochromator slit was adjusted to provide a photon bandwidth of about 75 meV FWHM at 284 eV, and the electron spectrometer has been operated at a pass energy of 10 eV, resulting in an electron kinetic energy resolution of about 30 meV. The experimental spectra are inherently broadened by the Doppler effect related to the thermal motion of the molecules at room temperature. The vibrational scattering anisotropy (VSA) observed in the experiment (Fig. 1) results in anomalously strong bind- PRL 105, 093002 (2010) PHYSICAL REVIEW LETTERS week ending 27 AUGUST 2010 0031-9007= 10=105(9)=093002(4) 093002-1 Ó 2010 The American Physical Society