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Nuclear dynamics in the dissociative recombination of H 3 + and its isotopologues

Nuclear dynamics in the dissociative recombination of H 3 + and its isotopologues. Daniel Zajfman Max-Planck-Institut für Kernphysik and Weizmann Institute of Science. Observations: B. J. McCall et al , Science 279 , 1910 (1998) T. R. Geballe et al , Astrophys. J. 510 , 251 (1999)

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Nuclear dynamics in the dissociative recombination of H 3 + and its isotopologues

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  1. Nuclear dynamics in the dissociative recombination of H3+ and its isotopologues Daniel Zajfman Max-Planck-Institut für Kernphysik and Weizmann Institute of Science

  2. Observations: B. J. McCall et al, Science 279, 1910 (1998) T. R. Geballe et al, Astrophys. J. 510, 251 (1999) B. J. McCall et al, Nature, 422, 500 (2003) n(H3+)≈10-5 -10-4 cm-3 2003 At equilibrium: Cosmic ray ionization rate~3x10-17 s-1 H3+ density Electron density ~0.5 cm-3 Molecular hydrogen density ~103 cm-3 Recombination rate (est.)~5x10-7 cm3 s-1 Estimated value n(H3+)≈1.2x10-7 cm-3

  3. Dissociative recombination of H3+ . Relevant potential curves 3-body decay 2-body decay

  4. Electron-cold molecular ion reaction: Dissociative Recombination V AB+ + e- A(n) + B(n’) + KER AB** Indirect process Direct process AB+ Interference Rydberg state e- Kinetic Energy Release A(n)+B(n’) R

  5. Recombination of H3+ : No ion-neutral crossing V AB+ + e- A(n) + B(n’) + KER AB** Indirect process Direct process AB+ Interference Rydberg state e- Kinetic Energy Release A(n)+B(n’) R

  6. Parameters DR recombination rate coefficient for H3+ during the last 56 years Let’s take an experimental look at the dynamics of the 3 body dissociation dynamics. Ek=4.8 eV Two quantities of interest: The total kinetic energy of the hydrogen fragments The kinematical correlation between the fragments

  7. Structure AB+ +X ? Recombination AB+ + e ? The Heavy Ion Storage Ring-MPI-Heidelberg AB+ (hot, from the ion source) E=~ MeV

  8. The Test Storage Ring MPIK, Heidelberg

  9. 2D imaging detector Kinematical correlation using Two Dimensional Imaging H3+ ground state Electron beam H3+ CCD L H3+ R2 R1 For each events, the three projected distances between the c.o.m. and each hydrogen atom are measured. R3 cm = R1 + R2 + R3 Ri ~ Vi

  10. Two-dimensional Particle Imaging Single molecule dissociation imaging

  11. (mm) Single molecule dissociation: How do we know that all three fragments come from a single molecular ion? For each event, calculate Ycm as a function of storage time Storage time (s) Electron cooling time

  12. Representation of three-body fragmentation data Since Ekin is a constant in the DR process, two additional parameters are needed to describe the full information. Dalitz plots (see also Müller et al., PRL, 93, 2718 (1999) Based on the work of Dalitz (Phil. Mag. 44, 1068 (1953)), and starting from simple phase space consideration, the number of states in a phase space cell, for a system of 3 particles with energies E1, E2, E3 and total energy Ekin is given by: Thus if the kinetic energies are chosen as coordinates of a 2-dimensional plot, a random distribution will lead to a uniform event density (in the kinematically allowed region)

  13. Energy conservation Momentum conservation If kinetic energies are good representation variables, then any combination of them is also valid, and could have the advantage of having a clear geometric meaning. For a molecular system such as H3+ : Geometry mapping

  14. For different isotopologues, the Dalitz plot loses some of its symmetry properties, and needs a rescaling of the coordinates. For the case m1=m2 (D2H+, H2D+): Energy conservation H2D+ D2H+ Momentum conservation

  15. Projection of dissociation geometries on a 2D detector surface Detector surface 3 body dissociation pattern simulation simulation “2-body region” Projection “2D” “3D” Random dissociation patterns Dalitz plot Random dissociation patterns Transverse Dalitz plot Projection

  16. Weighted Distribution “Projected” Simulated Random Distribution Can the normal Dalitz plot (1 2 ) be reconstructed from the projected one (Q1Q2)? “Projected” Measured Data Assumption: The dissociation is isotropic in space  Valid for electron energy Ee=0 eV

  17. Weighted Weighted Simulated data in the (η1,η2) space Recovered data in the (Q1*,Q2*) space Weighted Weighted

  18. Weighted Dalitz Plots for H3+ and D3+ D3+ H3+ Linear symmetric dissociation is the preferred correlation • Overall anisotropy is weaker for D3+ than for H3+ • Less “two body” for D3+ than H3+

  19. Two-body breakup Linear - Equal momenta for outer fragments Linear -Equal velocities for outer fragments Linear - Equal energies for outer fragments Weighted Dalitz Plots for H2D+ and D2H+ D2H+ H2D+

  20. Two-body breakup Linear - Equal momenta for outer fragments Linear -Equal velocities for outer fragments Linear - Equal energies for outer fragments Kinematical correlation for H2D+ and D2H+ H2D+ 1. “Linear” configuration 2. H-D-H is the most likely, with D at rest 3. Very little “two-body” D2H+ 1. “Linear” configuration 2. D-D-H is the most likely, with symmetric energy (~ velocity) for the outer fragments Are the molecular ions in their ground states?

  21. Coulomb Explosion Imaging: A Direct Way of Measuring Molecular Structure Preparation Collapse Measurement R1 R3 E0 R2 60 Ǻ thick • Ion source • Acceleration (MeV) • Initial quantum state? • Field free region • Charge state analysis • 3D imaging detector • Reconstruction Electron stripping Velocities measurement Macro-scale Micro-scale t=1 s to few secs t <10-15 sec t= few s Storage ring!

  22. Vibrational ground state Dalitz Plots Dissociative Recombination of H3+. (sensitive to the dissociation dynamics ) Coulomb Explosion Imaging of H3+. (sensitive to the shape of the molecule) Linear Triangle

  23. 2D imaging detector P(R2) R2 P(R2) R2 Total kinetic energy release: Ek=4.8 eV E1 E2 E3 H3+ Ek ~ max(R2)

  24. Total (transverse) Kinetic Energy Release for the 3-body Channel Data H3+ Reconstruction Ek=4.8 eV Reconstruction with excess energy of up to 1 eV! Not storage time dependency observed Measured kinetic energy release is larger than calculated!  (Very) long lived rotational excitation

  25. The data shown previously for H3+ and D3+ is for rotationally excited species (kTrot~ 230 meV) However, because of the different symmetries, H2D+ and D2H+ should radiatively cool to the ground state. Cold (simulation) Data

  26. A short glimpse in the two body channel For v=0, the (maximal) kinetic energy release is 9.3 eV. What is the vibrational population distribution? Phys. Rev. A, Phys. Rev. A 66, 32719 (2002) D3+ H3+ Rotational excitation H3+ D3+

  27. Low kinetic energy release in the 2-body channel H2(v) + H(2l) Very high rotational states (E>1eV)!

  28. Theory vs. Experiment: Collinear dissociation pattern Theory – potential surfaces H3+ kinematical correlation Experimental results The theory suggests that the kinematical correlation is towards a collinear dissociation pattern. Kokoouline, Greene and Esry, Nature (2001) Kokoouline and Greene PRL ,90 , 133201(2003), Kokoouline and Greene PRA ,68, 12703(2003). Strasser et al., PRL 86, 779 (2001)

  29. Ion Storage and Molecular Quantum Dynamics Weizmann Institute of Science Rehovot, Israel Max-Planck-Institut für Kernphysik Heidelberg, Germany A. Wolf D. Schwalm H. Kreckel L. Lammich (Aarhus) R. Wester (Freiburg) S. Krohn (BASF) M. Lange (Canberra)J. Levin (Applied Mat.) M. Grieser R. von Hahn R. Repnow D. Zajfman D. Strasser (Berkeley) A. Diner D. Zajfman

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