^{1}, Harold Linnartz

^{2}and Steven Stolte

^{3,a)}

### Abstract

The dependent differential collision cross sections of with fully state selected (, , ) NO have been determined at a collision energy of about . The collisionally excited NO molecules are detected by resonance enhanced multiphoton ionization combined using velocity-mapped ion-imaging. The results are compared to He–NO scattering results and tend to be more forward scattered for the same final rotational state. Both for collisions of the atomic He and the molecular with NO, scattering into pairs of rotational states with the same value of yields the same angular dependence of the cross section. This “parity propensity rule” remains present both for spin-orbit conserving and spin-orbit changing transitions. The maxima in the differential cross sections—that reflect rotational rainbows—have been extracted from the and the He–NO differential cross sections. These maxima are found to be distinct for odd and even parity pair number . Rainbow positions of parity changing transitions ( is odd) occur at larger scattering angles than those of parity conserving transitions ( is even). Parity conserving transitions exhibit—from a classical point of view—a larger effective eccentricity of the shell. No rainbow doubling due to collisions onto either the N-end or the O-end was observed. From a classical point of view the presence of a double rainbow is expected. Rotational excitation of the molecules has not been observed.

The authors congratulate Yuan Lee on his 70th birthday and thank him for his pioneering and inspiring work in the field of molecular dynamics. The Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged for financial support through CW and FOM. The authors are very grateful to Professor A. W. Kleyn for his experimental support.

I. INTRODUCTION

II. EXPERIMENT

III. RESULTS AND DISCUSSION

A. Differential cross sections and parity pairs

B. Rotational rainbows

IV. CONCLUDING REMARKS

### Key Topics

- Parity
- 47.0
- Anisotropy
- 8.0
- Molecule scattering
- 7.0
- Atomic and molecular beams
- 6.0
- Forward scattering
- 5.0

## Figures

(Color) Set of raw experimental ion images for spin-orbit conserving scattering. The images for are collected using the spectroscopic branch. The majority of the images for are collected via the branch; those labeled with a star are from the combined branch that exhibits more asymmetry with respect to the . This is due to the combination of collision-induced alignment and the residence time of the molecules in the detection region. For a and branch transition the effects of alignment and residence time nearly cancel, while for branch transitions these add, yielding very asymmetric ion images. The images are plotted such that two images above each other relate to the same parity pair . The missing image for , could not be collected due to overlapping spectral lines.

(Color) Set of raw experimental ion images for spin-orbit conserving scattering. The images for are collected using the spectroscopic branch. The majority of the images for are collected via the branch; those labeled with a star are from the combined branch that exhibits more asymmetry with respect to the . This is due to the combination of collision-induced alignment and the residence time of the molecules in the detection region. For a and branch transition the effects of alignment and residence time nearly cancel, while for branch transitions these add, yielding very asymmetric ion images. The images are plotted such that two images above each other relate to the same parity pair . The missing image for , could not be collected due to overlapping spectral lines.

The rotational levels of the NO molecule are labeled with their rotational quantum number and symmetry index . Recall that parity and relate as . The parity pair numbers in this figure relate to the experimental case where the incoming state is given by , . Parity pairs are observed for both spin-orbit conserving as for spin-orbit changing transitions, but the differential cross sections of a parity pair for spin-orbit conserving transitions does not correspond to that of the same pair for a spin-orbit changing collision. The energy differences are taken arbitrarily and are not scaled to the actual values.

The rotational levels of the NO molecule are labeled with their rotational quantum number and symmetry index . Recall that parity and relate as . The parity pair numbers in this figure relate to the experimental case where the incoming state is given by , . Parity pairs are observed for both spin-orbit conserving as for spin-orbit changing transitions, but the differential cross sections of a parity pair for spin-orbit conserving transitions does not correspond to that of the same pair for a spin-orbit changing collision. The energy differences are taken arbitrarily and are not scaled to the actual values.

Differential cross sections for scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral . The differential cross section for , is plotted separately in Fig. 5.

Differential cross sections for scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral . The differential cross section for , is plotted separately in Fig. 5.

Differential cross sections for scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral . The differential cross section for , is plotted separately in Fig. 5.

Differential cross sections for scattering into the highest observed rotational state of the lower component of the doublet . Note that the differential cross section for , has a strong sideways scattered contribution. From a simple classical model this cannot be understood. A similar, but even more pronounced effect has been observed for He–NO collisions (Ref. 18).

Differential cross sections for scattering into the highest observed rotational state of the lower component of the doublet . Note that the differential cross section for , has a strong sideways scattered contribution. From a simple classical model this cannot be understood. A similar, but even more pronounced effect has been observed for He–NO collisions (Ref. 18).

Differential cross sections for (He–NO) scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral .

Differential cross sections for (He–NO) scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral .

Differential cross sections for (He–NO) scattering into . The differential cross sections are plotted per parity pair and normalized such that the integral .

The positions of the rotational rainbows for each parity pair are plotted for both and He–NO scattering. The upper panel shows the rainbow maxima for spin-orbit conserving collisions, while the lower panel shows the rainbow maxima for spin-orbit changing collisions. The results are averaged over both components of the pairs. To guide the eyes, the points for He–NO and are connected via lines. The dotted line in the upper panel follows from a fit of parameters and of Eq. (9) to the data points.

The positions of the rotational rainbows for each parity pair are plotted for both and He–NO scattering. The upper panel shows the rainbow maxima for spin-orbit conserving collisions, while the lower panel shows the rainbow maxima for spin-orbit changing collisions. The results are averaged over both components of the pairs. To guide the eyes, the points for He–NO and are connected via lines. The dotted line in the upper panel follows from a fit of parameters and of Eq. (9) to the data points.

Schematic representation of a hard ellipsoid NO shell colliding with a molecule. The incoming linear momentum is decomposed into a component parallel and one perpendicular to the hard shell. The parallel component is conserved during collision, while the perpendicular one is partly transferred into rotation.

Schematic representation of a hard ellipsoid NO shell colliding with a molecule. The incoming linear momentum is decomposed into a component parallel and one perpendicular to the hard shell. The parallel component is conserved during collision, while the perpendicular one is partly transferred into rotation.

Experimental He–NO rainbow maxima from Fig. 8 are compared to values from CC calculations (Ref. 18). Results for spin-orbit conserving transitions are found in the upper panel, while the lower panel shows results for spin-orbit changing transitions. The maxima for parity changing transitions are at larger scattering angles than those for parity conserving transitions . To elucidate this, separate lines are drawn that connect the data points for both cases. The filtering of the data causes a slight underestimation of the scattering angle with maximum differential cross section when it is close to 180°.

Experimental He–NO rainbow maxima from Fig. 8 are compared to values from CC calculations (Ref. 18). Results for spin-orbit conserving transitions are found in the upper panel, while the lower panel shows results for spin-orbit changing transitions. The maxima for parity changing transitions are at larger scattering angles than those for parity conserving transitions . To elucidate this, separate lines are drawn that connect the data points for both cases. The filtering of the data causes a slight underestimation of the scattering angle with maximum differential cross section when it is close to 180°.

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