^{1}, Dongxu Dai

^{1}, Guorong Wu

^{1}, Chia Chen Wang

^{2}, Steven A. Harich

^{3}, Michael Y. Hayes

^{4}, Xiuyan Wang

^{5}, Dieter Gerlich

^{6}, Xueming Yang

^{7}and Rex T. Skodje

^{8,a)}

### Abstract

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the dynamics to that for the system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the “spectator” Rydberg electron is addressed and several crucial issues for future theoretical work are brought out.

This work was supported by the Chinese Academy of Science of China, the National Science Council of Taiwan, National Natural Science Foundation of China, and Academia Sinica of Taiwan.

I. INTRODUCTION

II. CLASSICAL TRAJECTORY SIMULATIONS

III. RESULTS OF QCT SIMULATION

IV. COMPARISON TO EXPERIMENTAL RESULTS

V. THE ROLE OF THE RYDBERG ELECTRON

VI. CONCLUSIONS

### Key Topics

- Ion molecule reactions
- 47.0
- Rydberg states
- 24.0
- Trajectory models
- 23.0
- Hydrogen reactions
- 13.0
- Collision induced chemical reactions
- 10.0

## Figures

Contour map of the ground electronic state KBNN-PES of . The potential energy in eV is plotted as a function of and (in a.u.) for the -shaped geometry. is the distance between and the center of mass of , is the distance of .

Contour map of the ground electronic state KBNN-PES of . The potential energy in eV is plotted as a function of and (in a.u.) for the -shaped geometry. is the distance between and the center of mass of , is the distance of .

The total integral cross section (excitation function) for the reaction on the KBNN-PES as a function of collision energy. The solid curve is the result of the QCT simulation and the symbols denote the prediction of the Langevin model with a constant transmission coefficient.

The total integral cross section (excitation function) for the reaction on the KBNN-PES as a function of collision energy. The solid curve is the result of the QCT simulation and the symbols denote the prediction of the Langevin model with a constant transmission coefficient.

Product translation energy distribution for the reaction at four different collision energies.

Product translation energy distribution for the reaction at four different collision energies.

Center-of-mass total (final-state summed) differential cross section for at 0.224, 0.524, 1.024, and in . The scattering angle is defined as the angle between the incident beam and the product.

Center-of-mass total (final-state summed) differential cross section for at 0.224, 0.524, 1.024, and in . The scattering angle is defined as the angle between the incident beam and the product.

The state-specific DCS in at different collision energies for obtained from QCT with the Gaussian binning method. (a) , (b) , (c) , and (d) .

The state-specific DCS in at different collision energies for obtained from QCT with the Gaussian binning method. (a) , (b) , (c) , and (d) .

(a) The collision time distribution for the reaction at computed using all reactive trajectories. The fitted lifetime is . (b) The impact parameter fixed (and hence fixed) collision lifetimes obtained by fitting the lifetime distribution of classical ensembles.

(a) The collision time distribution for the reaction at computed using all reactive trajectories. The fitted lifetime is . (b) The impact parameter fixed (and hence fixed) collision lifetimes obtained by fitting the lifetime distribution of classical ensembles.

Energy dependence of the fitted collision lifetimes at .

Energy dependence of the fitted collision lifetimes at .

A comparison of the product rotational number distribution between the experimental and QCT results at a special scattering angle (laboratory ). In the upper panel the QCT results are obtained from the Gaussian binning method, while in the lower panel the QCT results are obtained from the histogram binning method.

A comparison of the product rotational number distribution between the experimental and QCT results at a special scattering angle (laboratory ). In the upper panel the QCT results are obtained from the Gaussian binning method, while in the lower panel the QCT results are obtained from the histogram binning method.

Experimental product rotational distributions (see Ref. 17). The broadened spectrum is the TOF distribution (expressed as product translational energy in wavenumbers) measured for the reaction at the laboratory angle of 5° at . The stick spectrum is the fitted distribution obtained for reaction at the laboratory scattering angle of 5° at . The peak denoted by for the RA spectrum is contaminated by the inelastic channel. The peak with + is assigned to the channel.

Experimental product rotational distributions (see Ref. 17). The broadened spectrum is the TOF distribution (expressed as product translational energy in wavenumbers) measured for the reaction at the laboratory angle of 5° at . The stick spectrum is the fitted distribution obtained for reaction at the laboratory scattering angle of 5° at . The peak denoted by for the RA spectrum is contaminated by the inelastic channel. The peak with + is assigned to the channel.

The total (final-state summed) DCS vs c.m. scattering angle obtained from the experiment and QCT.

The total (final-state summed) DCS vs c.m. scattering angle obtained from the experiment and QCT.

The final-state-specific DCS angular distribution for a number of product states at . In (a), the experimental results for the reaction , while in (b) is the QCT results for the reaction . The contamination of the experimental result due to the overlapping inelastic channel has been corrected through a numerical estimation of the size of the two contributions.

The final-state-specific DCS angular distribution for a number of product states at . In (a), the experimental results for the reaction , while in (b) is the QCT results for the reaction . The contamination of the experimental result due to the overlapping inelastic channel has been corrected through a numerical estimation of the size of the two contributions.

Ionization probability for computed from the classical impulse approximation as a function of the c.m. scattering angle for various values. The results are obtained by averaging Eq. (5) over the phase of the Bohr orbit and the orientation of the Rydberg state. The is an upper bound to the principle quantum number employed in our experiments to date and the ionization is lower for smaller values of . The scattering angle of 0 corresponds to backward (rebound) scattering of the positive charge carrier.

Ionization probability for computed from the classical impulse approximation as a function of the c.m. scattering angle for various values. The results are obtained by averaging Eq. (5) over the phase of the Bohr orbit and the orientation of the Rydberg state. The is an upper bound to the principle quantum number employed in our experiments to date and the ionization is lower for smaller values of . The scattering angle of 0 corresponds to backward (rebound) scattering of the positive charge carrier.

## Tables

Energetic thresholds.

Energetic thresholds.

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