NO-N₂ Bi-molecular Crossbeam Scattering

The rotationally inelastic scattering dynamics of NO and N₂ was studied in a crossed molecular beam with polarized 1+1' REMPI probing and ion imaging detection. The angular correlation of the NO recoil velocity and angular momentum with the relative velocity vector of the collision are measured for the NO(X ²Π_1/2) product.

For NO-N₂ scattering both collision partners have rotational degrees of freedom that can be energetically accessed. When probing one rotational state of the NO the coincident rotational state of the N₂ is also obtained in the ion image by conservation of energy. The experiment also reveals changing preferences for NO rotational orientation as higher coincident N₂ rotational states are accessed. For example, in a given deflection direction, NO may be rotating clockwise at corresponding low N₂ rotational states, and counterclockwise at high N₂ rotational states. Also, for a given NO product rotational state the DCS changes from strongly forward scattered to nearly isotropic as the N₂ rotational state increases.

We have recently shown (Science 293, 2063 (2001)) that preferred senses of rotation in NO can be created as a result of rotationally inelastic scattering with rare gas atoms. In the present experiments our interest is in the rotationally excited product NO after inelastic collision with a diatomic (N₂). Figure 1 is a simple cartoon showing how specific senses of rotation can be generated by an inelastic collision with an Ar atom. To the upper right of the cartoon are ion images of the molecular beams (j'=1/2, no scattering) with Newton diagrams overlayed. To the lower right of this cartoon is an ion image of the NO-Ar system (previous work) obtained when detecting the scattered j'=8.5 NO product. The NO is initially traveling to the left while the Ar is traveling to the right. With these initial velocities, the left side of the ion image images represents forward scattered NO product and the right side back scattered NO product. The top and bottom of the images show side scattered NO.

At a well-defined collision energy, the scattering dynamics of an NO-atom system are simple in that the product NO has only one recoil velocity associated with a specific NO rotational energy. For the NO-N₂ system, there are multiple N₂ rotational degrees of freedom that are energetically accessible, creating a distribution of possible translational recoil velocities coincident with a particular j'_NO rotational state. The collision energy in these experiments to low to excite vibration in either the NO or the N₂. Figure 2 is a cartoon depicting the NO-N₂ scattering process as well as the corresponding Newton diagrams.

After the scattering occurs, we REMPI ionize the rotationally state selected NO and then ion image this product NO. The ion images clearly show the differential cross section (DCS) of the scattered NO. By using circularly polarized REMPI detection to probe the NO, we can also detect preferences for the sense of rotation (angular momentum orientation) of the scattered NO.

The experiments are done using the cross beam apparatus at Sandia National Laboratories. This apparatus has two collimated molecular beams intersecting perpendicularly in the interaction region defined by the velocity mapping ion optics. The collider beam is comprised of pure N₂ while the target beam is ~5% NO seeded in He.

The interaction region is then probed with a 1+1' resonance enhanced multiphoton ionization (REMPI) scheme. To measure the orientation of the product NO, the probe laser beam must intersect the interaction region normal to the plane of the detector. The ionization beam then intersects the probe beam perpendicularly, bifurcating the molecular beam angle. The polarization of the probe beam is either right or left circularly polarized, labeled RCP or LCP respectively. By changing the polarization of the probe beam, we can distinguish between product NO molecules that are rotating clockwise or counterclockwise. The ionization beam is unpolarized. Individually, neither laser beam produces NO ions. Only together do they induce ionization. This gives us confidence that we are not saturating the NO A²Σ ← X²Π transition, which would obscure orientation effects.

The product NO, after it is ionized by the REMPI scheme, is accelerated to the imaging detector by velocity-mapping ion optics. Great care was taken to ensure that the detector was protected from the probe beam. This was accomplished by using a ``pick-off'' optic that deflected the beam shortly before impact with the detector. Figure 3 shows the experimental setup.

The ion-image results for the NO-N₂ scattering system are shown below in Figure 4. The difference between the NO-N₂ data and previous data (NO-Ar and NO-Ne) is compared in Figure 5. Compared to the atom scattering, the NO-N₂ images are less sharp due to multiple recoil velocities and are tilted due to the change in Newton diagram for this system.

In past experiments the extraction of the DCS and generation of a simulated image was a fairly straight forward process because we were imaging a single scattering sphere. Now that both scattering partners have rotational degrees of freedom, introducing a distribution of recoil velocities for a specific NO rotational state, a new processing scheme must be used so as to extract the individual scattering spheres.

The processing scheme begins with a scattering image (i.e. NO-N₂ j'=11.5) with both the RCP and LCP summed together giving a 'sum' image. This sum image is insenstive to NO rotational orientation.

This summed image from the NO-N₂ system can be thought of a series of scattering spheres inside of each other much like the famous Russian "Matryoshka" dolls. These different scattering sphere radii can be calculated knowing the initial beam velocities and masses of the beam constituents. These calculated rings can also be overlayed onto the ion image to show the location of recoil velocities for different NO states. This is shown in Figure 8.

The simulation process starts with a calculation of the NO recoil velocities at a particular rotational state. These velocities are used when generating the simulated scattering images.

In simulating the NO-N₂ system we utilize a program written by K. Thomas Lorenz and Michael Westley that takes an input file consisting of several experimental parameters and generates a simulated scattering image (Phys. Chem. Chem. Phys., 2000, 2, 481-494). The program has been modified by Michael S. Elioff and James W. Barr to accept variables such as the laser orientation (Elioff) and recoil velocities (Barr) to mimic the experimental conditions.

The first concern in simluating images is that the experimental resolution is not sufficient to resolve individual scattering rings. To account for the limited resolution the image is divided into six regions covering the same recoil velocity increment. Each of these regions is simulated as if it were a single NO recoil velocity, even though a multitude of states are actually embedded in the ring. This is illustrated in Figure 9.

The outer-most ring is simulated first. This is done by creating an image using an isotropic DCS and then comparing this image to the experimental image. The differences are then accounted for in a correlation function that corrects the isotropic DCS to one that generates a more accurate simulated image. This is repeated iteratively three times. Figure 10 story-boards the process.

The isotropic DCS, correlation function (C (Θ), and new DCS are plotted in Figure 11. This shows how quickly the iterations converge on the experimental DCS that is extracted from the ion image.

After the outer-most ring is simulated, it is subtracted from the experimental image so that its inner image component is removed leaving the inner scattering rings unmarred by the outer rings. The next step is to simulate the second ring from the outer-most region. This process is continued until all six rings are simulated. Figure 12 shows the six simulated rings individually and then summed into a total image.

There are obvious gaps in between the six simulated rings. To account for these gaps we generate each of the 20+ NO coincident ion images and then sum them together to fill in the gaps. To do this, the extracted DCS for each of the six simulated rings is divided by the number of NO states that are incorporated into the ring. As an example, the NO-N₂ j'=11.5 image is divided in the following way: Ring 1 (16 states), Ring 2 (5 states), Ring 3 (4 states), Ring 4 (2 states), Ring 5 (1 state), and Ring 6 (1 state). It follows that Ring 1 is then divided by 16 so that the DCS intensity is distributed evenly among the states incorporated in that ring. After each ring is generated, they are summed together to create a new image that is less disjointed and similar to the experimental image. The result is shown in Figure 13.

The DCS's from the six simulated rings can be plotted as a surface showing the change in DCS as a function of the recoil velocity of the NO. This surface plot is shown in Figure 14.

This surface plot shows that at high NO recoil velocities (low N₂ rotational states) the recoil NO is primarily forward scattered. As the interior rings are analyzed a trend can be seen where lower NO recoil velocities, higher N₂ rotational states, become less forward scattered. The contour plot beneath the surface plot illustrates this more clearly by the contour lines as the intensity is distributed from its initial peak to a more leveled intensity.

The same process was used to analyze the NO-N₂ j'=18.5 system. Figure 15 shows the six rings that will be simulated.

The six rings are simulated using the method described in Figures 10 and 11 with the resulting six simulated rings shown in Figure 16.

The DCS for each of the simulated rings is then extracted and new rings are simulated for each of the coincident N₂ rotational states. Again, this is done to fill in the gaps between the six simulated rings to create a smooth simulated image. The result for the NO-N₂ j'=18.5 system is shown in Figure 17.

The DCS's from the six simulated rings can be plotted as a surface showing the change in DCS as a function of the recoil velocity of the NO. This surface plot is shown in Figure 18.

Orientation measurements of the recoil NO are also possible in the NO-N₂ system. Figure 19 shows the previous work of the NO-Ar system and the recent work of the NO-N₂ system. The normalized difference images show the preference for the NO orientation. The negative intensity (blue) is indicative of counter-clockwise rotation while the positive intensity (red) is clockwise rotation. The NO-N₂ system is similar to the NO-Ar system in that the orientations or the NO are of the same sense.

The rotational orientation of the recoiling NO in the forward scattered region is very similar for the Ar and the low j product N₂ collider. This would suggest that the scattering dynamics giving low j N₂ is similar to the NO collision dynamics with atoms.

For backscattered NO products there are significant differences in rotational orientation between the atomic colliders and N₂. The NO-Ar system shows multiple alternations in the preferred sense of rotation as a function of deflection angle. In contrast, the NO-N₂ system shows at most one alternation in the preferred orientation. For atomic colliders, we know that interferences among multiple scattering pathways into the same final state and deflection angle account for the orientation oscillations. Perhaps these multiple pathways are not as important in diatom-diatom scattering.

In the side and back scattered regions, the NO-N₂ images show that the preferred sense of rotational orientation changes with the coincident N₂ rotational state. The reasons for these changes in the orientation of the NO in the NO-N₂ system are not understood at this time. Future statistical and dynamical state distribution calculations will interpret this data.

The difference image for NO-N₂ j'=11.5 shows an interesting features in the upper right hand quadrant. These rings are reproducible over multiple experimental measurements and gives some indication of the coincident N₂ rotational state resolution in the experimental data.

Ion images have been collected for several states of the NO-N₂ system. A method has been used to forward convolute the experimental parameters of the experiment into a simulated ion image. Previous work done by K. Thomas Lorenz and Michael Westley has been the foundation for this simulation and hence expounded upon so that multiple states can be generated by way of defining the recoil velocity of the NO. These individual states (corresponding to coincident N₂ rotational states) are then summed together to create a somewhat accurate simulation of the entire ion image. Several assumptions are made during this process that must be taken due to the resolution of the individual states.

Although this method produces somewhat similar images it is not perfect. The population distribution of the N₂ rotational states is not clearly defined for each individual state. There is also concern that since the states are intertwined with each other there is no clear cut way to disassemble the image to then simulate a ring. The best we can do at this time is to divide the image into the six rings that cover a distribution and not single rings. At this point we have only a crude representation of the population distribution because of our resolution limitations. This allows us to report trends in the data, trends in the dynamics, and not specific quantities as was reported with the NO-Ar system.

It is clear from the data fitting that the DCS varies in with the N₂ rotational state. As higher rotational states of the N₂ are accessed the DCS becomes less intense in the front scatter region and more isotropic. It is also shown that the lowest N₂ rotational states are more highly populated than the high N₂ rotational states.

The overall trends in DCS are similar to those measured in the NO-Ar system. There are still several things in the images that must be measured and quantified. Better simulation programs are needed as well. Statistical and dynamical calculations are needed to interpret this data. Other systems with coincident collision partners accessible to greater degrees of freedom are possible to interpret and able to be measured.