Nuclear dynamics in the dissociative recombination of H

Nuclear dynamics in the dissociative recombination of H 3+ and its isotopologues Daniel Zajfman Max-Planck-Institut für Kernphysik and Weizmann Institute of Science

2003 At equilibrium: Cosmic ray ionization rate~3 x 10 -17 s-1 H 3+ density Molecular hydrogen density ~103 cm-3 Recombination rate (est. )~5 x 10 -7 cm 3 s-1 Electron density ~0. 5 cm-3 Estimated value n(H 3+)≈1. 2 x 10 -7 cm-3 Observations: B. J. Mc. Call et al, Science 279, 1910 (1998) T. R. Geballe et al, Astrophys. J. 510, 251 (1999) B. J. Mc. Call et al, Nature, 422, 500 (2003) n(H 3+)≈10 -5 -10 -4 cm-3

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

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

Recombination of H 3+ : No ion-neutral crossing V AB+ + e- A(n) + B(n’) + KER AB** Indirect process Direct process AB+ Interference Rydberg state Kinetic Energy Release e- A(n)+B(n’) R

Parameters DR recombination rate coefficient for H 3+ during the last 56 years Let’s take an experimental look at the dynamics of the 3 body dissociation dynamics. Ek=4. 8 e. V Two quantities of interest: The total kinetic energy of the hydrogen fragments The kinematical correlation between the fragments

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

The Test Storage Ring MPIK, Heidelberg

Kinematical correlation using Two Dimensional Imaging H 3 + ground state Electron beam H 3+ CCD 2 D imaging detector L H 3+ For each events, the three projected distances between the c. o. m. and each hydrogen atom are measured. cm = R 1 + R 2 + R 3 Ri ~ V i R 1 R 2 R 3

Two-dimensional Particle Imaging Single molecule dissociation imaging

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 Electron cooling time Storage time (s) (mm)

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 E 1, E 2, E 3 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)

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 H 3+ : Energy conservation Momentum conservation Geometry mapping

For different isotopologues, the Dalitz plot loses some of its symmetry properties, and needs a rescaling of the coordinates. For the case m 1=m 2 (D 2 H+, H 2 D+): D 2 H+ Energy conservation Momentum conservation H 2 D +

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

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

Weighted Recovered data in the (Q 1*, Q 2*) space Weighted Simulated data in the (η 1, η 2) space Weighted

Weighted Dalitz Plots for H 3+ and D 3+ H 3+ Linear symmetric dissociation is the preferred correlation 1. 2. Overall anisotropy is weaker for D 3+ than for H 3+ Less “two body” for D 3+ than H 3+

Weighted Dalitz Plots for H 2 D+ and D 2 H+ H 2 D+ Two-body breakup Linear - Equal momenta for outer fragments Linear -Equal velocities for outer fragments Linear - Equal energies for outer fragments D 2 H+

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

Coulomb Explosion Imaging: A Direct Way of Measuring Molecular Structure Preparation Collapse Measurement R 1 R 3 E 0 R 2 60 Ǻ thick • Ion source • Acceleration (Me. V) • Initial quantum state? Electron stripping Macro-scale Micro-scale t=1 s to few secs Storage ring! • Field free region • Charge state analysis • 3 D imaging detector • Reconstruction t <10 -15 sec t= few s Velocities measurement

Vibrational ground state Dalitz Plots Dissociative Recombination Coulomb Explosion Imaging of H 3+. (sensitive to the shape of the molecule) (sensitive to the dissociation dynamics ) Triangle Linear

2 D imaging detector Total kinetic energy release: Ek=4. 8 e. V E 1 E 2 E 3 H 3 + Ek ~ max(R 2) P(R 2) R 2

Total (transverse) Kinetic Energy Release for the 3 -body Channel H 3 + Data Reconstruction Ek=4. 8 e. V Reconstruction with excess energy of up to 1 e. V! Not storage time dependency observed Measured kinetic energy release is larger than calculated! (Very) long lived rotational excitation

However, because of the different symmetries, H 2 D+ and D 2 H+ should radiatively cool to the ground state. Cold (simulation) Data The data shown previously for H 3+ and D 3+ is for rotationally excited species (k. Trot~ 230 me. V)

A short glimpse in the two body channel For v=0, the (maximal) kinetic energy release is 9. 3 e. V. What is the vibrational population distribution? Phys. Rev. A, Phys. Rev. A 66, 32719 (2002) D 3+ H 3+ Rotational excitation H 3+ D 3+

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

Theory – potential surfaces H 3+ 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)

Ion Storage and Molecular Quantum Dynamics 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 Weizmann Institute of Science Rehovot, Israel D. Strasser (Berkeley) 1. A. Diner 2. D. Zajfman