Nuclear dynamics in the dissociative recombination of H3

+ and its isotopologues

Daniel ZajfmanMax-Planck-Institut für Kernphysik

andWeizmann Institute of Science

Cosmic ray ionization rate~3x10-17 s-1

)n(e)n(Hα)n(Hζ 32

Molecular hydrogendensity ~103 cm-3

Recombinationrate (est.)~5x10-7 cm3 s-1

H3+ density Electron density

~0.5 cm-3

At equilibrium:

Estimated value n(H3+)≈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(H3+)≈10-5 -10-4 cm-

3

2003

Dissociative recombination of H3+ .

Relevant potential curves

3-body decay

2-body decay

Electron-cold molecular ion reaction: Dissociative Recombination

HD+ (

2g+)

HD+ (2p

u)

A(n)+B(n’)

e-

Direct processIndirect process

Interference

KineticEnergyRelease

AB+ + e- A(n) + B(n’) + KER

Rydberg state

AB+

AB**

R

V

Recombination of H3+ : No ion-neutral

crossing

HD+ (

2g+)

HD+ (2p

u)

A(n)+B(n’)

e-

Direct processIndirect process

Interference

KineticEnergyRelease

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.

H(1s)H(1s)H(1s) eH3 Ek=4.8 eV

Two quantities of interest: The total kinetic energy of the hydrogen fragments The kinematical correlation between the fragments

Parameters

neutrals eH3

DR recombination rate coefficient for H3+ during the last 56 years

The Heavy Ion Storage Ring-MPI-Heidelberg

AB+ (hot, from the ion source)

E=~ MeV

StructureAB+ +X ?

RecombinationAB+ + e ?

The Test Storage Ring

MPIK, Heidelberg

H3+

Kinematical correlation using Two Dimensional Imaging

Electron beam

L

H(1s)H(1s)H(1s)eH3

H3+

CCD

For each events, the three projecteddistances between the c.o.m. and each hydrogen atom are measured.

2D imaging detector

cm = R1 + R2 + R3

Ri ~ Vi

H3+

ground state

R1R2 R3

Two-dimensional Particle Imaging

Single molecule dissociation imaging

(mm)

mm 0.25σy

Single molecule dissociation: How do we know that all three fragments come from a single molecular ion?

3yyy

y 321cm

For each event, calculate

Ycm as a function of storage time

Electron coolingtime

Storage time (s)

Representation of three-body fragmentation data

3

1iikin EE 2

ii

i v2m

E

Since Ekin is a constant in the DR process, two additional parameters are needed todescribe 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 systemof 3 particles with energies E1, E2, E3 and total energy Ekin is given by:

2132132 dEdE mmmπ 8CNd

Thus if the kinetic energies are chosen as coordinates of a 2-dimensional plot, a randomdistribution 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 alsovalid, and could have the advantage of having a clear geometric meaning.

For a molecular system such as H3+:

kin

132

12k

1

E3

EEη

EEE3

1η

Energy conservation

Momentum conservation

kin

ii E

Eρ

Geometry mapping

For different isotopologues, the Dalitz plot loses some of its symmetry properties, andneeds a rescaling of the coordinates. For the case m1=m2 (D2H+, H2D+):

31

EE

3mM

η

E3EE

mM

η

32

kin

12

31

Energy conservation

Momentum conservation

D2H+ H2D+

Projection of dissociation geometries on a 2D detector surface

Projection

Random dissociation patterns Dalitz plot

Random dissociation patternsTransverse Dalitz plot

Detectorsurface

3 body dissociation pattern

2

21

23

2

21

2221

R3

RRQ

RRR3

1Q

“3D” “2D”

kin

132

12k

1

E3

EEη

EEE3

1η

“2-bodyregion”

Projection

Can the normal Dalitz plot (1 2 ) be reconstructed from the projected one (Q1Q2)?

21 Q,Q

“Projected ”Measured Data

21 Q,Q

“Projected”Simulated Random Distribution

*2

*1 Q,Q

Weighted Distribution

Assumption: The dissociation is isotropic in space Valid for electron energy Ee=0 eV

Sim

ula

ted

data

in

th

e (

η1

,η2)

space

Reco

vere

d d

ata

in th

e (Q

1*,Q

2*) sp

ace

Weighted

Weighted

Weighted

Weighted

Weighted Dalitz Plots for H3+ and D3

+

Linear symmetric dissociation is the preferred correlation

H3+ D3

+

1. Overall anisotropy is weaker for D3+ than for H3

+

2. Less “two body” for D3+ than H3

+

Weighted Dalitz Plots for H2D+ and D2H+

H2D+ 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 H2D+ and D2H+

1. “Linear” configuration 2. H-D-H is the most likely, with D at rest3. Very little “two-body”

H2D+

D2H+

1. “Linear” configuration2. 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 fragmentsAre the molecular ions in theirground states?

Coulomb Explosion Imaging:A Direct Way of Measuring Molecular Structure

Preparation

• Ion source• Acceleration (MeV)• Initial quantum state?

E0

Micro-scale

Collapse

Electron stripping

t=1 s to few secs t <10-15 sec

60 Ǻ thick

Measurement

• Field free region• Charge state analysis• 3D imaging detector• Reconstruction

Macro-scale

t= few s

Velocities measurement

vd )vP(

Rd RRd )RP( 2

)(v

Storage ring!

R1

R2

R3

Coulomb Explosion Imaging of H3

+.(sensitive to the shape of the molecule)

Dissociative Recombination of H3

+.(sensitive to the dissociation dynamics )

Triangle Linear

Dalitz PlotsVibrational ground

state

Ek ~ max(R2)

H3+

2D imaging detectorTotal kinetic energy release: Ek=4.8 eV

H(1s)H(1s)H(1s)eH3

E1 E2 E3

23

22

21

2 RRRR

R2

P(R2)

R2

P(R2)

Total (transverse) Kinetic Energy Release for the 3-body Channel

Data

Reconstruction Ek=4.8 eV

Reconstruction with excess energyof up to 1 eV!

Not storage timedependency observed Measured kinetic energy release

is larger than calculated! (Very) long lived rotational excitation

H3+

However, because of the differentsymmetries, H2D+ and D2H+ shouldradiatively cool to the ground state .

The data shown previously forH3

+ and D3+ is for rotationally

excited species (kTrot~ 230 meV)

Cold (simulation)

Data

A short glimpse in the two body channel

H(1s)(v)HeH 23

For v=0, the (maximal) kinetic energy release is 9.3 eV .

What is the vibrational population distribution?

Rotationalexcitation

Phys. Rev. A, Phys. Rev. A 66, 32719 (2002)

H3+

H3+

D3+

D3+

H2(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 , 133201(2003),Kokoouline and Greene PRA ,68, 12703(2003).

The theory suggests that the kinematical correlationis towards a collinear dissociation pattern.

Theory – potential surfacesH3

+ kinematical correlation

Experimental results

Strasser et al., PRL 86, 779 (2001)

Ion Storage and Molecular Quantum Dynamics

Weizmann Institute of ScienceRehovot, Israel

D. Strasser (Berkeley)

A. DinerD. Zajfman

A. WolfD. SchwalmH. KreckelL. Lammich (Aarhus)R. Wester (Freiburg)S. Krohn (BASF)M. Lange (Canberra)J. Levin (Applied Mat.)M. GrieserR. von HahnR. RepnowD. Zajfman

Max-Planck-Institut für KernphysikHeidelberg, Germany