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Fragmentation of molecules: Franck-Condon model

Photo double ionization of H 2 resp. of D 2 or the correlated motion of electrons in a two center coulomb potential. Fragmentation of molecules: Franck-Condon model Experimental technique: Imaging of the momentum space Dynamics of the electrons in a single and a two center potential.

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Fragmentation of molecules: Franck-Condon model

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  1. Photo double ionization of H2 resp. of D2orthe correlated motion of electrons in a two center coulomb potential • Fragmentation of molecules: Franck-Condon model • Experimental technique: Imaging of the momentum space • Dynamics of the electrons in a single and a two center potential …if time permits: One more goody at the end ;-)

  2. Co-workers & friends: MICHIGAN: A. Landers FRANKFURT: Th. Weber R. Dörner V. Mergel A. Czasch O. Jagutzki M. Weckenbrock M. Hattaß H. Schmidt-Böcking KANSAS: L. Cocke T. Ossipov FREIBURG: M. Walter J. Briggs BERKELEY: M. Prior

  3. ... motivation- problem -principal task ... 80 eV hn + H2 2 e- + 2 H+ H+ Interaction / correlation e1 H+ e2

  4. Emission of two electrons from a single- and a double center - coulomb potential HELIUM HYDROGEN MOLECULE g e e Fixed in space molecular axis breaks symmetry >> ALIGNMENT <<

  5. Franck-Condon model:… the energy levels in the molecule (static) fragmentation kin. energy of the nuclei excess ion energy photon energy binding energy

  6. how to describe a simple molecule ?... the pro’s and contra’s and the limitations ... • Heitler - London • solution of SE with sym. wave functions (including the spin) • consideration of all exchanges/interactions • establishment of a stabile H2 possible (error in binding energy = 1.4 eV) • description of wave function only very roughly • Born - Oppenheimer • separation of the electronic motion and the motion of the nuclei • adiabatic modulation of the electrons • simplified calculations; nuclei momenta set up along molecular axis • open question: How do these systems interact or couple...? • Linear Combination of Atomic Orbitals (LCAO) • description of two electrons in the field of a H2+ ion • molecular orbital: Linear combination of atomic wave functions • good prediction of the electronic probability distribution in the molecule • error in binding energy is bigger than in H - L model

  7. The “strange” nature of the molecule/atom… which effects play an important role ? Electron emission for “equal energy-sharing” e2 • Coulomb repulsion favorites • “back-to-back emission” e1 e2 • selection rules: • ...electrons are fermions... •  complete wave function is antisymmetric • rule of Hundt: Spin is antisym. •  r-/k-space has to be sym. e1

  8. …more effects (interactions):coupling of the electrons to the binding system HELIUM HYDROGEN MOELCULE Atom: The electronic two body systems vibrates with respect to the nucleus Born-Oppenheimer: The electrons move in respect to the CM- system of the nuclei Reality: A complex 4 body system vibrates in a correlated state CM

  9. The COLTRIMS - setup… an imaging-system also for molecular fragmentation ?! electron-detector recoil-ion detector electric field magnetic field

  10. ...more features: pulsed extraction for the recoil-ions: 60 V/cm 4 psolid angle electron double hit recoil-ion double hit 3 V/cm • Magnetic field to guide the electrons • electrons up to 100 eV (for 10 Gauss) • Time of Flight and 2dim position • 3dim momentum vector • High resolution for 0 eV • < 10 meV electronic energy

  11. Characteristics of the experiment… more facts : • Projectiles = Photons • 75 eV energy of the photons • linear polarized (99.5 %) experiment at the ALS • Target = Deuterium (instead of Hydrogen) • 31.68 eV (31.752 eV for D2) dissociation energy • 2 • 9.4 eV = 18.8 eV energy of the Coulomb explosion • 24.5 eV kin. sum energy of the electrons • Imaging system • multi hit • pulsed recoil-ion extraction • data acquisition in “list mode” • two 80 mm MCP-detectors with delay line anode powered by:

  12. The new detector:… multihit rulez …!? HITEC powered by AOC & ROENTDEK DL80anode: Dt < 100ns Dt < 8ns 5200 lines computer code !!! Dt < 5ns Dt < 10ns Hexanode:

  13. Coordinates/systems of reference… where does the action takes place ? internal scattering plane 2 2 laboratory frame 1

  14. Energy distribution:… the kin. energy of the fragments after the photon absorption balance:

  15. Detection of the molecular fragments:… An image of the Coulomb explosion • The pulsed recoil-ion spectrometer • …. and its consequences: pulser 50.4 a.u. 50.4 a.u.

  16. Kin. energy of the electrons in the final state:… which role does the molecule play …? e2 e H2 e1 e1 Interference effect: First maximum ?

  17. Momentum distribution of the electrons : • A comparison ... HELIUM HYDROGEN MOLECULE

  18. Helium e He/H2 Hydrogen molecule

  19. Hydrogen molecule H2 e1 more details

  20. Azimuthal angle of the electrons:... the b - parameter P.S.: valid near photo double ionization threshold b as a function of the alignment of the molecule ?! Helium Hydrogen molecule

  21. And how about the recoil ions…? Let’s compare with the literature: H. Kossmann & V. Schmidt PRL (1989), 63, p. 2040-2043 b = - 0.685

  22. Distribution of the polar angles... do we see correlated electron emission ? equal energy sharing 1. The Helium-atom E1 = E2

  23. unequal energy sharing HELIUM ow sl e1 fast e1

  24. … let’s switch to the hydrogen-molecule equal energy sharing H2 e all orientations

  25. … just to get an overview :animated Triple Differential Cross Sections (TDCS) equal energy sharing Hydrogen molecule

  26. Helium atomandhydrogen molecule… a comparison of both systems: Helium equal energy sharing all orientations H2 Hydrogen molecule e

  27. … more movies :How does the distribution depend on the molecular orientation ? Hydrogen molecule equal energy sharing

  28. unequal energy sharing Hydrogen molecule : H2 e1 = fast e all orientations

  29. … let’s get a more detailed insightInfluence of the molecular orientation: e1 equal energy sharing H2

  30. H2 unequal energy sharing e1 fast e1 slow

  31. TRANSFER OF ANGULAR MOMENTUM:Coupling of the electrons to the molecule ?! ...which orientation is relevant ? e1 equal energy sharing H2 e1 e1+2 No angular mo- mentum transfer e2 H2

  32. Let’s probe the molecule:…molecules illuminated from within... equal energy sharing Hydrogen molecule electron-electron interaction

  33. … go even deeper : let’s scan the coulomb explosion ! equal energy sharing Hydrogen molecule vibrational states

  34. finish line … summary and future prospectWhat is still to do ? What comes next...? • COLTRIMS: An imaging-system for molecules • pulsed extraction • multi hit capable detectors • 4p solid angle • snapshots of • Experimental results • Energy-sharing depends on the orientation of the molecule !? • Final state of the electrons in momentum space • Highly differential cross sections as a function of the molecular orientation • …Future: • more D2 : What’s going on with circular polarized light ? • new experiment with HD (angular momentum transfer)/ ALS (Berkeley) • simple molecules in strong laser-fields/ Roskos (FFM)/ Corkum (Canada) …goody

  35. ...goody…:“Alignment” even in atoms ?! • circular polarized e e Helium e • linear polarized

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