^{1}, Tomás González-Lezana

^{1,a)}, Octavio Roncero

^{1}, Pascal Honvault

^{2}, Jean-Michel Launay

^{3}, Niyazi Bulut

^{4,b)}, F. Javier Aoiz

^{4}, Luis Bañares

^{4}, Alexandre Trottier

^{5}and Eckart Wrede

^{5}

### Abstract

The reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum,, special emphasis has been made at two specific collision energies, 0.1 and . The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.

N.B. acknowledges a postdoctoral fellowship by the Spanish Ministry of Education and Science (MEC) under the program “Estancias de jóvenes doctores y tecnólogos extranjeros en España.” This work has been funded by MEC of Spain under Grant Nos. FIS2004-02461, CTQ2004-02415, and CTQ2005-08493-C02-01 and from the Comunidad de Madrid under the Contrato Programa Comunidad de Madrid-Universidad Complutense de Madrid (Grant No. 910729). A.T. and E.W. thank the EPSRC for financial support. The EQM calculations were performed on vector supercomputers, through a grant from the “Institut du Développment des Ressources en Informatique Scientifique” (IDRIS) in Orsay (France). E.C.N. T.G.L., and O.R. would also like to acknowledge the use of the computer resources, technical expertise, and assistance provided by the Red Españolade Supercomputación (Barcelona Supercomputing Center and Centro de Supercomputación y Visualización de Madrid).

I. INTRODUCTION

II. THEORY

A. Time independent exact quantum method

B. Quantum wave packet method

C. Statistical quantum method

D. Quasiclassical trajectory method

III. EXPERIMENT

A. Apparatus

B. Simulation of laboratory kinetic energy spectra

IV. RESULTS

A. Reaction probabilities as a function of collision energy

B. Dynamics at collision energy

1. Opacity function

2. Integral cross sections

3. Differential cross sections

4. Kinetic energy spectra

C. Dynamics at collision energy

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Hydrogen reactions
- 53.0
- Trajectory models
- 42.0
- Rydberg states
- 33.0
- Collision induced chemical reactions
- 32.0
- Chemical reaction cross sections
- 16.0

## Figures

Total and vibrationally state resolved reaction probabilities as a function of collision energy, at zero total angular momentum, , for the reaction calculated by means of the EQM (gray solid line), QWP (red dashed line), SQM (blue dotted line), and QCT (solid line) approaches.

Total and vibrationally state resolved reaction probabilities as a function of collision energy, at zero total angular momentum, , for the reaction calculated by means of the EQM (gray solid line), QWP (red dashed line), SQM (blue dotted line), and QCT (solid line) approaches.

Total reaction probabilities as a function of collision energy, at , 20, 30, and 40, for the reaction calculated by means of the QWP (grey solid line), SQM (dashed line), and QCT (solid line) approaches. For , the inset shows the comparison of these three methods with the EQM probabilities (dark gray line) calculated around collision energy.

Total reaction probabilities as a function of collision energy, at , 20, 30, and 40, for the reaction calculated by means of the QWP (grey solid line), SQM (dashed line), and QCT (solid line) approaches. For , the inset shows the comparison of these three methods with the EQM probabilities (dark gray line) calculated around collision energy.

Opacity function or reaction probability in terms of the total angular momentum calculated at collision energy for the reaction by means of the EQM (full squares with solid line), QWP (gray full triangles and solid line), SQM (empty circles and dashed line), and QCT (solid line) approaches.

Opacity function or reaction probability in terms of the total angular momentum calculated at collision energy for the reaction by means of the EQM (full squares with solid line), QWP (gray full triangles and solid line), SQM (empty circles and dashed line), and QCT (solid line) approaches.

Integral cross sections (in ) calculated at for the reaction by means of the EQM (full squares and solid line), QWP (solid diamonds and dotted line), SQM (empty circles and dashed line), and QCT (empty triangles and solid line) methodologies.

Integral cross sections (in ) calculated at for the reaction by means of the EQM (full squares and solid line), QWP (solid diamonds and dotted line), SQM (empty circles and dashed line), and QCT (empty triangles and solid line) methodologies.

Total differential cross section (in ) calculated at collision energy for the reaction using the EQM (gray solid line), QWP (dotted line), SQM (dashed line), and QCT (solid line) methods. The theoretical DCSs are compared with the experimental results of Ref. 3, which are shown in full squares and solid line. The experimental results, restricted to the angular range , have been scaled to the EQM DCS at . The inset shows a magnification of the angular range between 20° and 140°.

Total differential cross section (in ) calculated at collision energy for the reaction using the EQM (gray solid line), QWP (dotted line), SQM (dashed line), and QCT (solid line) methods. The theoretical DCSs are compared with the experimental results of Ref. 3, which are shown in full squares and solid line. The experimental results, restricted to the angular range , have been scaled to the EQM DCS at . The inset shows a magnification of the angular range between 20° and 140°.

Rotationally state resolved differential cross sections (in ) calculated at collision energy forthe reactions by means of the EQM (dark solid line), QWP (light solid line), SQM (dashed line), and QCT (dotted-dashed line) methods. As in Fig. 5, the theoretical distributions are compared with the state-to-state experimental cross sections reported by Song *et al.* (Ref. 3) (shown in solid squares with solid line). The insets show a magnification of the angular range between 20° and 140°.

Rotationally state resolved differential cross sections (in ) calculated at collision energy forthe reactions by means of the EQM (dark solid line), QWP (light solid line), SQM (dashed line), and QCT (dotted-dashed line) methods. As in Fig. 5, the theoretical distributions are compared with the state-to-state experimental cross sections reported by Song *et al.* (Ref. 3) (shown in solid squares with solid line). The insets show a magnification of the angular range between 20° and 140°.

Same as Figure 6 but for the reactions.

Same as Figure 6 but for the reactions.

Kinetic energy spectra for the , 17°, and 24° laboratory angles at collision energy. Experimental results (dark solid line) and simulations obtained by using the EQM (solid line), SQM (dashed line), QCT (dotted line), and QWP (light solid line) results. The position of the different rotational states of reactively scattered and inelastically scattered are shown in the bottom of each panel.

Kinetic energy spectra for the , 17°, and 24° laboratory angles at collision energy. Experimental results (dark solid line) and simulations obtained by using the EQM (solid line), SQM (dashed line), QCT (dotted line), and QWP (light solid line) results. The position of the different rotational states of reactively scattered and inelastically scattered are shown in the bottom of each panel.

Same as Fig. 8 but for , 42°, and 52°.

Same as Fig. 8 but for , 42°, and 52°.

Opacity function or reaction probability in terms of the total angular momentum calculated at collision energy for the reaction by means of the EQM (full squares with solid line), QWP (gray full triangles and solid line), SQM (empty circles and dashed line), and QCT (solid line) approaches.

Total differential cross section (in ) calculated at collision energy for the reaction using the EQM (grey solid line), QWP (dashed-dotted line), SQM (dashed line), and QCT (solid line) methods.

Total differential cross section (in ) calculated at collision energy for the reaction using the EQM (grey solid line), QWP (dashed-dotted line), SQM (dashed line), and QCT (solid line) methods.

Rotationally state resolved differential cross sections (in ) calculated at collision energy for the reactions by means of the EQM (grey solid line), QWP (dashed-dotted line), SQM (dashed line), and QCT (solid line) methods. The inset in the top panel shows a magnification of the backward region for the reaction yielding .

Rotationally state resolved differential cross sections (in ) calculated at collision energy for the reactions by means of the EQM (grey solid line), QWP (dashed-dotted line), SQM (dashed line), and QCT (solid line) methods. The inset in the top panel shows a magnification of the backward region for the reaction yielding .

## Tables

Total and vibrationally state selected integral cross sections (in ) calculated at for the reaction using the different theoretical methods employed in the present work, i.e., EQM, QWP, SQM, and QCT.

Total and vibrationally state selected integral cross sections (in ) calculated at for the reaction using the different theoretical methods employed in the present work, i.e., EQM, QWP, SQM, and QCT.

Total and vibrationally state selected integral cross sections (in ) calculated at for the reaction using the different theoretical methods employed in the present work, i.e., EQM, QWP, SQM, and QCT.

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