Theoretical study of ion-pair formation in electron recombination with H 3 + Royal Society Discussion meeting on Physics, Chemistry and Astronomy of H 3 + January Åsa Larson 1, Johanna Roos 1 and Ann E. Orel 2 1 Dept. of Applied Physics, Royal Institute of Technology, Stockholm, Sweden 2 Dept. of Applied Science, UC Davis, Davis, California, USA

(Resonant) Ion-Pair formation in electron recombination (RIP)

High-energy resonant states for H 3 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). 1979, K. C. Kulander and M. F. Guest [1] 1984, H. H. Michels and R. H. Hobbs [2] 1D studies [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) H H -

1994, A. E. Orel et al. 2D study using the Complex Kohn Variational method Resonance position E i and width  i Triple intersection More detailed calculations: [1] A. E. Orel, K. C. Kulander and B. H. Lengsfield III, J. Chem. Phys. 100, 1756 (1994) z (a 0 ) r z C 2v symmetry

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., (1993) [2] A. E. Orel and K. C. Kulander, Phys. Rev. Lett., (1993)

Measured cross section for ion-pair formation [1] B. Peart et al. J. Phys. B, (1979) [2] F. B. Yousif et al. J. Phys. B, 26, 4249 (1993) [3] S. Kalhori et al. Phys. Rev. A, (2004) The H - fragments were detected (the two channels H H - and H + + H + H - cannot be seperated). Cross section depends on the vibrational excitation The magnitude of the cross section is about 2 · cm 2 in all experiments.

H 3 + vs H 2 + 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

H 3 + vs H 2 + 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?

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!

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.

3.Transform from the adiabatic to the corresponding diabatic states using the CI coefficients. Calculate also the couplings beween the neutral states. → Theoretical study of the ion-pair formation

Initiate wave packets on the resonant states (electron recombination) Include autoionization using complex resonant potentials. Theoretical study of the ion-pair formation 4.Study the dynamics using wave packets. Propagate the wavepackets on coupled potentials

Theoretical study of the ion-pair formation 5. Calculate the cross section for ion-pair formation by analyzing the dissociating flux [1]. z stop [1] D. J. Haxton et al., Phys. Rev A., (2004); G. G. Balint-Kurti et al., Comp. Phys. Comm (1991)

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.

1D study Add the couplings to the Rydbergs at small z. Add also the couplings to the Rydbergs at large z

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!

2D study Diabatic ion-pair state alone 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. z r Potential energy (H)

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. Add the effects from the Rydberg states (plan B)

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.

Summary To describe the ion-pair formation in H 3 + 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: D 3 +, HD 2 +, H 2 D +