Differential reaction cross-section

G(ln/ij, u0) State-to-state differential reaction cross section... 

These p, x coordinates have been used in all integral and differential reaction cross-section calculations which include the effect of the geometric phase reported so far [12,36,46-48]. They are closely related to several sets of coordinates described previously [49-54]. 

In conventional, macroscopic chemical kinetics, the rate of a reaction is defined in terms of the change in concmitration with time of a single (reactant or product) chemical entity, and obsm ation of this rate yields the rate constant, ki.T). At the other, microscopic , end of the scale, the ultinute, and still distant, goal in reaction dynamics is to study the scattering between species whose velocities and internal states are all accurately defined and to measure differential reaction cross-sections, o(n n v , 0), for processes that connect fully spedfied reactant and product states (denoted by n and nO in collisions of defined relative velocity, v , where 6 is the scattering angle in the centre-of-mass frame of reference. 

Reaction rate constants cannot be used to describe such detailed processes. Instead the differential reaction cross section, areact ( i, 2, 3, n l, 2 0 ployed, where n, are various quantum numbers and the primed quantities refer to reaction products. Such cross sections represent the effective collision area for reagents with given i, 2, , to give specific products. Rate constants represent the effective average of the product of the cross section with the approach velocity taken over the calculated distribution of reagent quantum states. 

Introduction to reaction dynamics total and differential reaction cross-sections... 

Normally, one assumes that the differential reaction cross-section does not depend on the azimuthal angle. Hence, one takes advantage of the axial symmetry of the collision and works with differential cross-sections integrated over . Thus, one uses the element of sohd angle dm = 27t sin 0 dO ... 

Figure 21.8 Angular differential reaction cross-section distributions of the KI product generated in the...

The images of the D atom provide the differential reaction cross-section, summed over all ro-vibrational states of the HD product. In an ideal experiment, the inversion of the D images should have sufficient resolution to infer the ro-vibrational states of the HD products, but in practice this is not so easy and the rotational resolution is very difficult to obtain. One way to circumvent this difficulty is to apply REMPI detection to the HD product to obtain rotational state-specific differential cross-sections. However, the strong focusing requirements of REMPI schemes substantially reduce the sensitivity, as pointed out earlier. 

In this new VELMl method the conventional grids of the WUey-McLaren TOE spectrometer are simply replaced by open electrostatic lenses and the potentials are adjusted to achieve momentum focusing. Under these conditions, all products with the same initial velocity vector in the plane parallel to the detector are focused to the same point, irrespective of their initial distance from the ion lens axis. Thus, the technique improves quite significantly the low sensitivity of standard REMPl schemes of detection and offers a way to resolve state-specific differential reaction cross-sections in crossed-beam reactions. 

Rulis AM, Bernstein RB. 1972. Molecular beam study of K + CH3I reaction - energy-dependence of detailed differential reaction cross-section . J. Chem. Phys. 57(12) 5497-5515. 

In this connection interest was directed to theoretical calculations of the differential reaction cross section, assuming a certain interaction between reagents. Whatever the kind of interaction — either given by ah initio calculations or by semiempirical methods — the classical or quantum calculation of the cross section requires, in general, the use of modern computers. Consequently, the present development of theory is, to a considerable extent, due to the progress of computational technique [11]. 

Figure 4.14 The complete angular distribution of Kl for the K + I2 and K + CH3I reactions. Plotted is the polar differential reaction cross-section 2x sin 0 /r(0) vs. e. When integrated over 0, this gives directly the reaction cross-section ctr and the result is quoted in the figure [adapted from the experimental results of K.T. Gillen, A. M. Rulis, and R. B. Bernstein, J. Chem. Phys. 54, 2831 (1971) A.M. Rulis and R. B. Bernstein, J. Chem. Phys. 57, 5497 (1972)].

The observable quantity in molecular beam experiments is called the differential reaction cross section danj nr( jO,)/dQ, defined by [7]... 

To illustrate these definitions, we consider a collision between two hard spheres (HS) with radii ri and T2, yielding a total hard sphere radius r = ri -f T2. The HS differential reaction cross section is r /4, independent of scattering angle. The HS integral reaction cross section is Trr, consistent with circular area of radius... 

It should be stressed that these predictions are qualitative in nature and that more detailed quantitative predictions depend on the performance of accurate differential reaction cross section calculations, which, as pointed out in section III are a very difficult goal to achieve and constitute an important theoretical challenge. 

The nonstatistical branching ratios observed in reactions (3), (5), and (6) are a result of the dynamics of the collision complex and cannot be explained by energetics alone. Further information about the collision complex can be extracted from such other dynamical properties as the differential reaction cross section as a... 

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