Newton spheres

In this section, the relationship between the measured quantity and the desired center-of-mass differential cross-section will be established and a brief description of the data analysis procedure will then be given. First, consider a Newton sphere with a single value of the product velocity v (see Fig. 4). From the Doppler-shift formula, at a given laser wavelength, the Doppler effect selectively ionizes those ions with vz = vcosO in the... 

Now consider a Newton sphere with a distribution of the center-of-mass velocity v. The corresponding signal can be expressed as... 

Fig. 20. A few examples of the Doppler-selected TOF data are exemplified. The TOF spectra have been converted into velocity space and weighted by a term. For each spectrum, the VUV laser frequency is selected to slice through the Newton sphere near the center-of-mass, i.e. wcm- The cap marked on the top corresponds to the (v, j ) state of the co-product F1F for Ec = 1.18kcal/mol. Note the slight tilt of the dashed lines which act as a visual guide for quantum state assignments.

In another Doppler-selective method, the position of the probe laser beam is kept parallel to that of the photolysis laser, but is moved in one dimension with respect to it in order to spatially scan the Newton sphere [102,103]. This method can be considered a two-dimensional version of Reisler s experiment shown in Figure 6. Work by the Valentini group has shown that this method works well for probing the velocity distributions of systems with large kinetic energy release, as in the case of HI dissociation at 266 nm, and also systems with small kinetic energy release, for example, the vibrational predissociation of (HC1)2. 

Figure 23.8 Pair of Newton spheres (spherical coordinates are used, r, 6 and ris not shown). Two events are shown in (a), with equaland opposite momentum. Surface pattern obtained by summing up a large number of events for particle B are shown in (b). Adapted from Parker and Eppink, in Imaging in molecular dynamics, 2003, with permission of Cambridge University Press...

Normally, one draws these Newton spheres in two dimensions instead of three, as shown in Figure 23.9. Suppose we squash the latter figure onto a vertical plane. It will look like a disc with most of the events located on the outside edges, both at the top and bottom of the disc. The ion-imaging method works exactly in this way, as was pointed out earlier. One records 3D Newton spheres, projected onto a 2D surface, where it appears as a partially lilled-in circle. 

Reaction gas-phase collisions should generate Newton spheres with isotropic distributions. However, very often these surface patterns are anisotropic (as the one shown in the figure) due to the existence of some directionality in the process. In photodissociation, this is often due to the use of a linearly polarized laser, which acts as the reference axis. In a bimolecular collision (see below), carried out in a crossed-beam experiment, the relative velocity vector introduces a reference axis to which the directional properties of the reaction products are referenced. 

To each internal state of the products there corresponds a velocity whose mag-nitnde is determined from conservation of energy and whose direction is to be measured. Both experiment and theory can provide such resolution, as shown in Figure 5.12. But this requires a separate plot for each final quantum state. Instead, we represent this information on a single plot in such a way that the major dynamical features of the reaction are immediately evident. We do so in the form of a product flux contour map, a map showing the distribution of the final velocity vectors. We develop the concept of a Newton sphere by means of an example. Consider the elementary reaction... 

Imaging is the term used for a direct mapping of die velocity (vector) of the products. " It captures the Newton sphere, Section 6.3.1, and projects it for viewing in a number of ways, as shown in Figure 7.7. The figiue shows the technique applied to photodissociation but it is equally useful and important for bimolecular collisions and in other instances where an energy-rich species blows up and one wants to monitor the distribution of fragments in velocity space. 

Figure 7.9 Experimental observation of the entire Newton sphere. Section 6.3.1. The sphere of products can be generated by using a linearly polarized light for photodissociation, see Figure 7.6, or from a crossed-beam experiment as in Section 6.3. A second laser ionizes the fragments and this has the advantage that it can be done selectively for different internal states of the products. An electric field allows collection of the ions and produces a 2D image. The cylindrical symmetry of the original sphere allows this collapsed image to be transformed into a 3D contour plot of the intensity of the products [adapted from D. H. Parker, Acc. Chem. Res. 33, 563 (2000)].

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