Resonant L II,III x-ray Raman scattering from HCl C. Såthe, 1 F. F. Guimarães, 2,3 J.-E. Rubensson, 1 J. Nordgren, 1 A. Agui, 4 J. Guo, 5 U. Ekström, 6 P. Norman, 6 F. Gel’mukhanov, 2 and H. Ågren 2 1 Department of Physics, Uppsala University, Box 530, S-751 21 Uppsala, Sweden 2 Theoretical Chemistry, Roslagstullsbacken 15, Royal Institute of Technology, S-106 91 Stockholm, Sweden 3 Departamento de Química, Universidade Federal de Minas Gerais, Avenue Antonio Carlos, 6627, CEP-31270-901, Belo Horizonte, MG, Brazil 4 Synchrotron Radiation Research Unit, Japan Atomic Energy Agency, 1-1-1 Kouto, Sayo-cho, Sayogun, Hyogo 679-5148, Japan 5 Advanced Light Source, Lawrence Berkeley National Laboratory, MS 6R2100, One Cyclotron Road, Berkeley, California 94720, USA 6 Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden Received 18 August 2006; published 27 December 2006 We have studied the spectral features of Cl L II,III resonant x-ray Raman scattering of HCl molecules in gas phase both experimentally and theoretically. The theory, formulated in the intermediate-coupling scheme, takes into account the spin-orbital and molecular-field splittings in the Cl 2p shells, as well as the Coulomb inter- action of the core hole with unoccupied molecular orbitals. Experiment and theory display nondispersive dissociative peaks formed by decay transitions in both molecular and dissociative regions. The molecular and atomic peaks collapse in a single narrow resonance because the dissociative potentials of core-excited and final states are parallel to each other along the whole pathway of the nuclear wave packet. DOI: 10.1103/PhysRevA.74.062512 PACS numbers: 33.90.+h, 31.15.Ne, 32.30.Rj, 32.80.Hd I. INTRODUCTION The creation and decay of excited states are fundamental to all physical processes involving energy transfer on a mi- croscopic scale. High-resolution resonant x-ray Raman scat- tering RXS of free molecules provides an excellent tool for investigating the finer details of the electronic structure, which reflects different aspects of the intramolecular interac- tion. In the case of resonant excitations below the ionization threshold, utilization of RXS opens up new prospects 1–5. One of the main advantages of RXS is the possibility to study the same final state but making use of different inter- mediate core-excited states. Such an opportunity makes the interpretation of the molecular spectrum more accurate from the point of view of both occupied and virtual molecular orbitals MO’s. The object of our combined experimental and theoretical study is the Cl L II,III RXS spectrum of the HCl molecule. This molecule was widely used in explorations of different dynamical effects accompanying x-ray excitation using the resonant Auger effect in the soft x-ray region 1,2 and RXS near the Cl K edge 6,7. One of the major difficulties is that the core hole is in the 2p orbital of the chlorine atom, which is affected by substantial spin-orbit SO splitting. This split- ting, about 1.75 eV, can be comparable with the Coulomb interaction between core and valence MO’s involved in the scattering. This forces us to invoke the intermediate-coupling scheme 8 and to solve the corresponding equations explic- itly. From our simulations of the x-ray absorption XAS and RXS spectra we are able to perform the theoretical assign- ment of the spectral lines, based on ab initio self-consistent field SCF and multiconfigurational SCF MCSCF calcula- tions of the inner-shell excited states. Special attention is paid to the RXS through the dissociative core-excited state. The article is organized as follows. We begin with a brief outline of the experiment in Sec. II. Section III includes the diagonalization of the molecular Hamiltonian with the chlo- rine L-shell spin-orbit interaction included followed by a derivation of the expression for the RXS cross sections of randomly oriented molecules. Details of the numerical simu- lations are described in Sec. IV. Analysis of simulations and comparison to the experiment are included in Sec. V. Our findings are summarized in Sec. VI. II. EXPERIMENT The experiments were carried out at beamline 7.0 at the Advanced Light Source at Lawrence Berkeley Laboratories 9. The gas was contained in a sealed gas cell connected to a manifold where we could refresh the gas sample and keep a constant gas pressure. The pressure was monitored using Pirani tubes and kept at between 1 and 10 mbar depending on the excitation energy in order to avoid saturation and maximize intensity in the RXS measurements. The windows used were 1000-Å-thick Si 4 N 3 entrance windows and 1500 -Å-thick polyimide film on a supporting mesh 10 as a win- dow in the detection direction of RXS. The XAS was mea- sured using a electrode measuring the current generated from the secondary electrons from the excitation process with a Kiethley picoamperemeter. The RXS was measured using a grazing incidence spherical grating spectrometer 11 mounted perpendicular to the incoming light and parallel to the polarization vector of the synchrotron radiation light. The slits on the monochromator were opened to get enough flux for the experiments. The grating used was a 5-m-radius spherical grating with 400 lines/ mm with the slit set to 20 m. The estimated spectral resolution is 500 meV in the x-ray emission spectra. III. SOLUTION OF EIGENVALUE PROBLEM FOR CORE- EXCITED STATE We start from diagonalization of the nonrelativistic many- electron molecular Hamiltonian H for the core-excited state PHYSICAL REVIEW A 74, 062512 2006 1050-2947/2006/746/0625128 ©2006 The American Physical Society 062512-1