Theoretical study of ion-pair formation in electron recombination with H3

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Theoretical study of ion-pair formation in
electron recombination with H3

• Royal Society Discussion meeting on Physics,
  Chemistry and Astronomy of H3
• January 18-2006
• Åsa Larson1, Johanna Roos1 and Ann E. Orel2
• 1Dept. of Applied Physics, Royal Institute of
  Technology, Stockholm, Sweden
• 2Dept. of Applied Science, UC Davis, Davis,
  California, USA

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(Resonant) Ion-Pair formation in electron
recombination (RIP)
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High-energy resonant states for H3
1979, K. C. Kulander and M. F. Guest 1 1984,
H. H. Michels and R. H. Hobbs 2 1D studies
H2 H-

• The high-energy resonant states cannot explain
  the DR at low energies if not the taget ions are
  vibrationally excited.
• The resonant states will produce a high-energy
  peak in the cross section of DR where both
  neutral and ionic fragments are formed (ion-pair
  formation).

1 K. C. Kulander and M. F. Guest, J. Phys B
At. Mol. Phys, 12, L501 (1979) 2 H. H. Michels
and R. H. Hobbs, Astrophys. J, 286, L27 (1984)
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More detailed calculations
z (a0)

• 1994, A. E. Orel et al.
• 2D study using the Complex Kohn Variational
  method
• Resonance position Ei and width ?i
• Triple intersection

1 A. E. Orel, K. C. Kulander and B. H.
Lengsfield III, J. Chem. Phys. 100, 1756
(1994)
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High-energy peak in the DR cross section

• 1993, First experimental observation of the
  high-energy peak. (CRYRING) 1
• Neutral fragmants detected
• 1993, A. E. Orel et al. 2
• Wave packet propagation in 2D assuming that
  everything dissociates into the neutral fragments
  (no couplings, potentials become flat).

1 M. Larsson et al. Phys. Rev Lett., 70 430
(1993) 2 A. E. Orel and K. C. Kulander, Phys.
Rev. Lett., 71 4315 (1993)
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Measured cross section for ion-pair formation

• The H- fragments were detected (the two channels
  H2 H- and H H H- cannot be seperated).
• Cross section depends on the vibrational
  excitation
• The magnitude of the cross section is about 2
  10-18 cm2 in all experiments.

1 B. Peart et al. J. Phys. B, 12 3441
(1979) 2 F. B. Yousif et al. J. Phys. B, 26,
4249 (1993) 3 S. Kalhori et al. Phys. Rev. A,
69 022713-1 (2004)
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H3 vs H2

• Potentials
• Lowest resonant state goes diabatically to the
  ion-pair limit
• ?E 5.4 eV

Potentials Lowest resonant state goes
diabatically to the ion-pair limit ?E 1.91 eV
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H3 vs H2

• Cross section for ion-pair formation
• 2 of total DR cross section
• A bump in the cross section

Cross section for ion-pair formation 5 of
total DR cross section Resonant structure
due to the quantum interference between competing
pathways
Why are they so different?
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Theoretical study of the ion-pair formation

1. Calculate the resonant states using the Complex
   Kohn Variational method ?

Note all calculations are carried out in 2D!
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Theoretical study of the ion-pair formation
2. Calculate the ionic and neutral adiabatic
potentials using CI with a basis set including
diffuse orbitals to describe Rydberg states.
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Theoretical study of the ion-pair formation
3. Transform from the adiabatic to the
corresponding diabatic states using the CI
coefficients. Calculate also the couplings beween
the neutral states. ?
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Theoretical study of the ion-pair formation
4. Study the dynamics using wave packets.
Include autoionization using complex resonant
potentials.
Propagate the wavepackets on coupled potentials
Initiate wave packets on the resonant states
(electron recombination)
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Theoretical study of the ion-pair formation
5. Calculate the cross section for ion-pair
formation by analyzing the dissociating flux 1.
zstop
1 D. J. Haxton et al., Phys. Rev A., 69
062714-1 (2004) G. G. Balint-Kurti et al.,
Comp. Phys. Comm. 63 126 (1991)
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1D study
Ion-pair state alone. Autoionization is included
and lowest vibrational level of the ion is
assumed.
Include the second resonance and the direct and
indirect couplings between them.
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1D study
Add the couplings to the Rydbergs at small z.
Add also the couplings to the Rydbergs at large z
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1D study

• Compare with experimental cross section

• Questions
• Why is the shape so different ?
• Why is the magnitude a factor 5 too large?

Perform 2D wave packet calculation!
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2D study
Diabatic ion-pair state alone
Potential energy (H)
z
r
Much better shape of the cross section! Add the
couplings to the second resonance The 2nd
dimension will smear out the interference effects
between the two resonant states.
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Add the effects from the Rydberg states (plan B)

• In the 1D study the couplings to the Rydberg
  states reduced the cross section about 40 ,
  assume the same is true in the 2D study.

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Use the Landau-Zener model to estimate the loss
of flux to the Rydberg states. Define the
reaction path as the classical path on the
ion-pair state.

• Assume the flux coupled to the Rydberg state is
  lost.
• Assume the flux can jump back to the ion-pair
  state.

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Summary

• To describe the ion-pair formation in H3 it is
  crucial to include at least two dimensions in the
  dynamics.
• The second dimension will smear out the
  interference effects.
• Flux will be lost due to the couplings to the
  Rydberg states.
• To do
• The wave packets propagating on 6 coupled
  potentials (two resonant states and 4 Rydberg
  states) are running now.
• Study the effects from vibrational excitation of
  the ion.
• Study the reaction for other isotopologous D3,
  HD2 , H2D