^{1,a)}, C. Maul

^{1}, A. I. Chichinin

^{2}and K.-H. Gericke

^{1}

### Abstract

In order to measure the state selective double differential cross section of a reactive collision, the preparation of the reactants with defined initial velocities and quantum states in number densities high enough to achieve an acceptable count rate is most important. At the same time, secondary collisions have to be prevented in order to ensure that the nascent products are not thermalized. Usually, the best way to control the initial conditions is to use crossed molecular beams, but the number density decreases quadratically with the distance from the nozzle orifice which can be a problem, especially if a molecular product with a large number of populated states is to be analyzed state specifically by REMPI spectroscopy. In this contribution we would like to present a method for measuring the quantum state selective differential cross section of a photoinitiated reaction that combines the advantages of the PHOTOLOC technique (high reactant densities) and the parallel beams technique used by the groups of Kitsopoulos, Orr-Ewing, and Suits (defined relative velocity of the reactants). Moreover, an algorithm based on a Bayesian backward reconstruction developed by W. H. Richardson [J. Opt. Soc. Am.62, 55 (1972)] has been derived. Both, one reactant and the precursor of the other reactant, are present in the same molecular beam and the center of mass velocity is selected by shifting the dissociation and the detection laser in time and space. Like in comparable methods, this produces a bias in the measuredvelocity distribution due to the fact that the reaction takes place in the whole volume surrounding the laser beams. This has been also reported by Toomes *et al.* in the case of the parallel beams technique and presents a general problem of probing reaction products by REMPI spectroscopy. To account for this, we develop a general approach that can be easily adapted to other conditions. The bias is removed in addition to deconvolution from the spread in reactant velocities. Using the benchmark system with as the precursor, we demonstrate that the technique is also applicable in a very general sense (i.e., also with a large spread in reactant velocities, products much faster than reactants) and therefore can be used also if such unfortunate conditions cannot be avoided. Since the resulting distribution of velocities in the laboratory frame is not cylindrically symmetric, three dimensional velocity mapping is the method of choice for the detection of the ionized products. For the reconstruction, the distance between the two laser beams is an important parameter. We have measured this distance using the photodissociation of HBr at 193 nm, detecting the H atoms near 243 nm. The collision energy resulting from the 193 nm photodissociation of is . Our results show a preference for backward scattered D atoms with the OH partner fragment in the high vibrational states , in accord with previously published results claiming the growing importance of a linear abstraction mechanism for collision energies higher than 2.4 kcal/mol.

Financial support by the Deutsche Forschungsgemeinschaft and the Alexander von Humboldt foundation is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENTAL

III. DATA ANALYSIS

IV. CALIBRATION OF THE SPATIAL LASER SHIFT

V. RESULTS: D ATOM PRODUCT VELOCITY DISTRIBUTION

VI. CONCLUSION

### Key Topics

- Atomic and molecular beams
- 15.0
- Photodissociation
- 15.0
- Atom scattering
- 13.0
- Velocity measurement
- 13.0
- Dissociation
- 11.0

## Figures

Sketch showing two possible ways to detect forward scattered D atoms with the dye laser (red circle). Here the oxygen precursor is formed by the dissociation laser (blue circle) with a fixed speed and reacts at the time . If the speed is large enough, the ion on path 1 (brown/dashed) can reach the detection laser and will show up in the domain of the forward scattered products.

Sketch showing two possible ways to detect forward scattered D atoms with the dye laser (red circle). Here the oxygen precursor is formed by the dissociation laser (blue circle) with a fixed speed and reacts at the time . If the speed is large enough, the ion on path 1 (brown/dashed) can reach the detection laser and will show up in the domain of the forward scattered products.

Illustration of the relevant coordinate systems. The center of mass system which is defined by the velocity of the atom is transformed into the space fixed laboratory coordinate system by rotating it first about the axis by to coincide z and and then by rotating about the common z-axis by . The axis always lies in the laboratory x,y plane (gray). The measured velocity of a D-atom v is shown as the sum of and u. The components of u in the cm system are constructed by projecting (green dotted lines) u first onto and into the , indicated by the green plane. Finally, is projected onto and .

Illustration of the relevant coordinate systems. The center of mass system which is defined by the velocity of the atom is transformed into the space fixed laboratory coordinate system by rotating it first about the axis by to coincide z and and then by rotating about the common z-axis by . The axis always lies in the laboratory x,y plane (gray). The measured velocity of a D-atom v is shown as the sum of and u. The components of u in the cm system are constructed by projecting (green dotted lines) u first onto and into the , indicated by the green plane. Finally, is projected onto and .

Speed distribution and least square fit of the precursor as inferred from Refs. 76 and 77 used in the simulation.

Speed distribution and least square fit of the precursor as inferred from Refs. 76 and 77 used in the simulation.

Forward simulated laboratory velocity distributions of D atoms for different center of mass velocity distributions. (a) Spatially uniform distribution with . (b) Backward scattering, normal speed distribution with mean of 9000 m/s and . (c) Forward scattering, speed distribution as in (b). The ions detected on the two possible paths shown in Fig. 1 are represented by the respective color. Their numbers are olive (desired): 6405; wine (unwanted): 3595. (d) The same point cloud as in (c) but from a different angle. The lines labeled with dissociation and detection shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Forward simulated laboratory velocity distributions of D atoms for different center of mass velocity distributions. (a) Spatially uniform distribution with . (b) Backward scattering, normal speed distribution with mean of 9000 m/s and . (c) Forward scattering, speed distribution as in (b). The ions detected on the two possible paths shown in Fig. 1 are represented by the respective color. Their numbers are olive (desired): 6405; wine (unwanted): 3595. (d) The same point cloud as in (c) but from a different angle. The lines labeled with dissociation and detection shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Reconstruction of the simulated data in Fig. 4. [(a)–(c)] Backward scattered D atoms for different iteration index. (d) Forward scattered D atoms for 150 iterations. (e) Spatially uniform D atom velocity distribution

Reconstruction of the simulated data in Fig. 4. [(a)–(c)] Backward scattered D atoms for different iteration index. (d) Forward scattered D atoms for 150 iterations. (e) Spatially uniform D atom velocity distribution

Comparison of the DCSs and speed distributions (black, solid) of the simulated distribution in Fig. 4(a) before (left) and after (right) the reconstruction with the ideal functions used in the simulation (red, dashed). One clearly sees that the bias in the speed distribution has been removed successfully and the bias in the DCS was not very large before the reconstruction anyway. This is due to the fact that the biases from forward and backward scattered products cancel each other out. Note that the noise magnification is quite low, too.

Comparison of the DCSs and speed distributions (black, solid) of the simulated distribution in Fig. 4(a) before (left) and after (right) the reconstruction with the ideal functions used in the simulation (red, dashed). One clearly sees that the bias in the speed distribution has been removed successfully and the bias in the DCS was not very large before the reconstruction anyway. This is due to the fact that the biases from forward and backward scattered products cancel each other out. Note that the noise magnification is quite low, too.

Comparison of the DCSs and speed distributions (black, solid) of the simulated distribution in Fig. 4(c) before (left) and after (right) the reconstruction with the ideal functions used in the simulation (red, dashed). The bias has been removed successfully from both the angular and the speed distribution. The Gaussian fit (blue, dash-dotted) gives a hint of the remaining broadening due to the spread in reactant velocities (see text).

Comparison of the DCSs and speed distributions (black, solid) of the simulated distribution in Fig. 4(c) before (left) and after (right) the reconstruction with the ideal functions used in the simulation (red, dashed). The bias has been removed successfully from both the angular and the speed distribution. The Gaussian fit (blue, dash-dotted) gives a hint of the remaining broadening due to the spread in reactant velocities (see text).

Doppler sliced 3D velocity map of H atoms emerging from the photodissociation of HBr at 243 nm [two rings with opposite for the and the channel, respectively] and 193 nm shifted perpendicular to the z-axis (dots on the right hand side of the outer ring). The H atoms are detected by at 243 nm. The arrows labeled with the dissociation and detection wavelengths shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Doppler sliced 3D velocity map of H atoms emerging from the photodissociation of HBr at 243 nm [two rings with opposite for the and the channel, respectively] and 193 nm shifted perpendicular to the z-axis (dots on the right hand side of the outer ring). The H atoms are detected by at 243 nm. The arrows labeled with the dissociation and detection wavelengths shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Raw data of D atom laboratory velocities and meridian plot of the reconstructed center of mass velocity distribution after background correction. The lines labeled with dissociation and detection in the lower panel shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Raw data of D atom laboratory velocities and meridian plot of the reconstructed center of mass velocity distribution after background correction. The lines labeled with dissociation and detection in the lower panel shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Upper panel: DCS of the D-atoms emerging from the reaction of ; middle panel: speed distribution; lower panel: speed distribution decomposed into forward and backward scattering (black/solid: backward hemisphere; red/dashed: forward hemisphere).

Upper panel: DCS of the D-atoms emerging from the reaction of ; middle panel: speed distribution; lower panel: speed distribution decomposed into forward and backward scattering (black/solid: backward hemisphere; red/dashed: forward hemisphere).

Collision energy distribution and O atom precursor velocity distribution from a Monte Carlo simulation assuming a Gaussian center of mass speed distribution of D atoms with 9000 m/s as the center and a standard deviation of 2800 m/s using the experimental parameters and . The lines labeled with dissociation and detection in the lower panel shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

Collision energy distribution and O atom precursor velocity distribution from a Monte Carlo simulation assuming a Gaussian center of mass speed distribution of D atoms with 9000 m/s as the center and a standard deviation of 2800 m/s using the experimental parameters and . The lines labeled with dissociation and detection in the lower panel shall serve as a help for orientation only. The exact velocity values associated with them have no meaning of their own.

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