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

Cosmic ray ionization rate~3x s -1 Molecular hydrogen density ~10 3 cm -3 Recombination rate (est.)~5x10 -7 cm 3 s -1 H 3 + density Electron density ~0.5 cm -3 At equilibrium: Estimated value n(H 3 + )≈1.2x10 -7 cm -3 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(H 3 + )≈ cm

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

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

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

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

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

The Test Storage Ring MPIK, Heidelberg

H3+H3+ Kinematical correlation using Two Dimensional Imaging Electron beam L H3+H3+ CCD For each events, the three projected distances between the c.o.m. and each hydrogen atom are measured. 2D imaging detector cm = R 1 + R 2 + R 3 R i ~ V i H 3 + ground state R1R1 R2R2 R3R3

Two-dimensional Particle Imaging Single molecule dissociation imaging

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

Representation of three-body fragmentation data Since E kin is a constant in the DR process, two additional parameters are needed to describe the full information. Dalitz plots 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 E kin 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) (see also Müller et al., PRL, 93, 2718 (1999)

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 + ): Energy conservation Momentum conservation D2H+D2H+ H2D+H2D+

Projection of dissociation geometries on a 2D detector surface Projection Random dissociation patterns Dalitz plot Random dissociation patterns Transverse Dalitz plot Detector surface 3 body dissociation pattern “3D” “2D” “2-body region” 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 E e =0 eV

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

Weighted Dalitz Plots for H 3 + and D 3 + Linear symmetric dissociation is the preferred correlation H3+H3+ D3+D3+ 1.Overall anisotropy is weaker for D 3 + than for H Less “two body” for D 3 + than H 3 +

Weighted Dalitz Plots for H 2 D + and D 2 H + H2D+H2D+ D2H+D2H+ Two-body breakup Linear - Equal momenta for outer fragments Linear -Equal velocities for outer fragments Linear - Equal energies for outer fragments

Kinematical correlation for H 2 D + and D 2 H + 1. “Linear” configuration 2. H-D-H is the most likely, with D at rest 3. Very little “two-body” H2D+H2D+ D2H+D2H+ 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 Ion source Acceleration (MeV) Initial quantum state? E0E0 Micro-scale Collapse Electron stripping t=1  s to few secs t < sec 60 Ǻ thick Measurement Field free region Charge state analysis 3D imaging detector Reconstruction Macro-scale t= few  s Velocities measurement Storage ring! R1R1 R2R2 R3R3

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

E k ~ max(R 2 ) H3+H3+ 2D imaging detector Total kinetic energy release: E k =4.8 eV E1E1 E2E2 E3E3 R2R2 P(R 2 ) R2R2

Total (transverse) Kinetic Energy Release for the 3-body Channel Data Reconstruction E k =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 H3+H3+

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

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? Rotational excitation Phys. Rev. A, Phys. Rev. A 66, (2002) H3+H3+ H3+H3+ D3+D3+ D3+D3+

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

Kokoouline, Greene and Esry, Nature (2001) Kokoouline and Greene PRL,90, (2003), Kokoouline and Greene PRA,68, 12703(2003). The theory suggests that the kinematical correlation is towards a collinear dissociation pattern. Theory – potential surfaces H 3 + kinematical correlation Experimental results Strasser et al., PRL 86, 779 (2001)

Ion Storage and Molecular Quantum Dynamics Weizmann Institute of Science Rehovot, Israel D. Strasser (Berkeley) A. Diner D. Zajfman 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 Max-Planck-Institut für Kernphysik Heidelberg, Germany