nuclear dynamics in the dissociative recombination of h 3 + and its isotopologues daniel zajfman...
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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