^{1}and Rex T. Skodje

^{1}

### Abstract

Experimental crossed-beam studies carried out previously have indicated that the dynamics of the Rydberg-atom-molecule reaction are very similar to those of the corresponding ion-molecule reaction. The equivalence of the cross sections for these related systems would open up a new approach to the experimental study of ion-molecule reactions. However, a recent experimental and theoretical study has brought to light some important qualitative differences between the Rydberg-atom reaction and the ion-molecule reaction; in particular, the experimental cross section for the Rydberg-atom reaction exhibits a higher degree of forward-backward scattering asymmetry than predicted by a quasiclassical trajectory study of the ion-molecule reaction. In this paper, the authors consider the dynamics of the Rydberg-electron over the course of a reactive collision and the implications of these dynamics for the Rydberg-atom-molecule crossed-beam experiment. Using an approach based on perturbation theory, they estimate the attenuation of the experimental signal due to the Rydberg-electron dynamics as a function of the scattering angle. They show that at least part of the experimental asymmetry can be ascribed to this angle dependent attenuation. Their results offer general insight into the practical aspects of the experimental study of ion-molecule reactions by means of their Rydberg-atom counterparts.

The authors are grateful to Xueming Yang and Dongxu Dai for many useful discussions concerning their experimental results. Support from Academia Sinica and the National Research Council of Taiwan is acknowledged.

I. INTRODUCTION

II. IMPULSIVE EFFECT OF THE REACTIVE COLLISION ON THE RYDBERG ELECTRON

III. EFFECT OF SPONTANEOUS EMISSION BY THE RYDBERG ELECTRON

IV. EFFECT OF INDUCED IONIZATION BY THE ELECTRIC FIELD

V. ESTIMATED ATTENUATION OF EXPERIMENTAL SIGNAL

VI. CONCLUSION

### Key Topics

- Ion molecule reactions
- 27.0
- Ionization
- 15.0
- Spontaneous emission
- 13.0
- Chemical reaction cross sections
- 9.0
- Hydrogen reactions
- 8.0

## Figures

Final state summed differential cross section for the reaction obtained by experiment and QCT; the experimental result is multiplied by an arbitrary scaling factor. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Final state summed differential cross section for the reaction obtained by experiment and QCT; the experimental result is multiplied by an arbitrary scaling factor. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Schematic illustration of important processes impacting final Rydberg-atom detection in a crossed-beam experiment.

Schematic illustration of important processes impacting final Rydberg-atom detection in a crossed-beam experiment.

Transition probability of RE after impulsive collision at , from initial state (, ) and averaged over all initial , going to final summed over all (, ). Open circles denote the quantum mechanical sudden approximation, and points denote the classical impulse approximation.

Transition probability of RE after impulsive collision at , from initial state (, ) and averaged over all initial , going to final summed over all (, ). Open circles denote the quantum mechanical sudden approximation, and points denote the classical impulse approximation.

Radiative lifetime of field-free hydrogen states and Stark states at with a field strength of . Open symbols denote the Stark lifetimes, and the solid circles denote the field-free lifetimes.

Radiative lifetime of field-free hydrogen states and Stark states at with a field strength of . Open symbols denote the Stark lifetimes, and the solid circles denote the field-free lifetimes.

Angular dependence of attenuation of RE signal (fraction of total signal lost) for laser polarization in the and directions. The polarization is parallel to the initial velocity of the H atom. The upper panel displays the total attenuation, while the lower three panels show the separate contributions from each loss mechanism. A scattering angle of 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Angular dependence of attenuation of RE signal (fraction of total signal lost) for laser polarization in the and directions. The polarization is parallel to the initial velocity of the H atom. The upper panel displays the total attenuation, while the lower three panels show the separate contributions from each loss mechanism. A scattering angle of 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Population of states for forward/backward scattering for initial state (, , ). Solid points denote forward scattering , and open points denote backward scattering .

Population of states for forward/backward scattering for initial state (, , ). Solid points denote forward scattering , and open points denote backward scattering .

Angular dependence of the total attenuation of the RE (fraction of total signal lost) for different collision complex lifetimes (ps). Successive curves are offset by 0.01 to facilitate comparison. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Angular dependence of the total attenuation of the RE (fraction of total signal lost) for different collision complex lifetimes (ps). Successive curves are offset by 0.01 to facilitate comparison. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Angular dependence of the total attenuation of the RE signal (fraction of total signal lost) for different product states. Successive curves are offset by 0.01 to facilitate comparison. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Angular dependence of the total attenuation of the RE signal (fraction of total signal lost) for different product states. Successive curves are offset by 0.01 to facilitate comparison. 180° corresponds to backward (rebound) scattering of the positive charge carrier.

Angular dependence of attenuation of RE signal for different mechanisms in the absence of an applied electric field. 180° corresponds to backward (rebound) scattering of the positive charge carrier. Results are shown for both polarized excitation lasers.

Angular dependence of attenuation of RE signal for different mechanisms in the absence of an applied electric field. 180° corresponds to backward (rebound) scattering of the positive charge carrier. Results are shown for both polarized excitation lasers.

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