Three-body processes

The phase space theory in its present form suffers from the usual computational difficulties and from the fact it has thus far been developed only for treating three-body processes and a limited number of output channels. Further, to treat dissociation as occurring only through excitation of rotational levels beyond a critical value for bound vibrational states is rather artificial. Nevertheless, it is a useful framework for discussing ion-molecule reaction rates and a powerful incentive for further work. 

A steady-state test similar to that described above can be applied to the three-body process thus the value of kz required to explain Green s experimental data would be given by ... 

In Eq. (3.4), the contributions of both the nuclei and the electrons are considered. The maximum energy transfer for electrons is (l/4)mv2, but since their contribution to the loss cross section is small, no great error is committed in taking the maximum energy transfer as 2mv2 for all ionizations represented in Eq. (3.4). Electron capture is a three-body process best visualized as ionization of a molecule of the medium with the ejected electron having a speed v at least equal to that of the incident ion, followed by capture of that electron in an orbit around the impinging ion. Mozumder et al. (1968) modified an earlier formula of Bohr (1948) and wrote the capture cross section as... 

The O atoms so produced may be in excited states, too. Unless the pressure is very low, the electron invariably attaches to 02in a three-body process, e + 202— 02 + 02, and neutralization occurs through the reaction 02+ + 02—-20 + 02. 

Clustering should be proportional to the square of the pressure at low pressures (three-body process) and proportional to the pressure at high pressures (two-body process). 

Reaction 2-2 is actually a three-body process, in that another molecule (Af), usually nitrogen or oxygen, is necessary to carry off the energy released in the newly formed bond. These two reactions then form a mechanism for ozone formation in the atmosphere. They would not be complete without the additional reaction,... 

Besides this intercollisional interference process, there are other three-body processes which at elevated densities affect the observable spectra over a much wider range of frequencies, virtually at all frequencies at which absorption may be observed. With increasing density, one will be able to discern binary, ternary, and perhaps higher-order spectral contributions (even if cvxi2 1). These are caused by the dipoles induced in systems consisting of N interacting atoms or molecules, with N > 2. 

At the lowest temperatures, the three-body moments are relatively strong, Table 6.4. A density of only 10 amagat will modify the observed moments by roughly 10%. The strong temperature dependence of the three-body moments at low temperature may be quite important for some applications, for example for the spectroscopic modeling of planetary atmospheres. It seems to be related to the formation of dimers and, consequently, to monomer-dimer interactions which are three-body processes by our definition. Of course, at 45 K, quantum corrections are substantial and the numbers quoted must be considered rough estimates. Nevertheless, the general trend of the temperature dependence seems clear. 

The HSCC equations have been solved for various Coulomb three-body processes, such as photoionization and photodetachment of two-electron systems and positronium negative ions [51, 105-111], electron or positron collisions [52, 112-115], ion-atom collisions [116-119], and muon-involving collision systems [103, 114, 120-125]. Figures 4.6, 4.7, 4.8, 4.9, and 4.10 are all due to HSCC calculations. Figure 4.12 illustrates the good agreement between the results of HSCC calculations [51] and the high-resolution photoionization experiment on helium [126]. See Ref. [127] for further detailed account of the comparison between the theory and experiment on QBSs of helium up to the threshold of He+(n = 9). 

In direct gap GaAs, an excited electron at the bottom of the conduction band can relax spontaneously back into a hole in the valence band by emitting a photon at the band gap energy. This electron-hole radiative recombination process can only occur in Si if momentum is conserved, i.e., the excited electron wave vector must be reduced to zero. This, in pure Si, occurs via the transfer of momentum to a phonon that is created with equal and opposite wave vector to that of the initial state in the conduction band. Such a three-body process is quite inefficient compared with direct gap recombination.1218 This is why Si is such a poor light emitter. 

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, Aha, and the catalytic coefficient for the proton-transfer reaction, HA. Figure I shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bronsted Catalysis Law (Bronsted and Pedersen, 1924) shown in equation (9). The quantities p and q are, respectively, the number of... 

In all cases, however, a pronounced increase in the rate of recombination occurs with increasing pressure, corresponding to a three-body process of rate coefficient a,. As opposed to the close similarity of the (Xj values, the values of a, were found to increase by two orders of magnitude in going from iso pentane to water vapor. The magnitude of a, could in fact be directly related to the efficiency of the different molecules at exchanging energy with electrons while within the coulomb well, which results in closed rather than open orbits. 

The fact that Iq depends on the nature of the carrier gas indicates that the chemiluminescent reactions take place in three body processes. The whole range of phenomena may then be explained by postulating an initial termolecular combination to an excited state of CO2, followed at a later stage by the emission of radiation or by collisional quenching to form CO2 in the ground electronic state, viz. 

The mechanisms proposed for the chemiluminescent reaction can be broadly classified in terms of two-body or three-body processes. The argument centres around the pressure dependence of the emission. Harteck et could find no pressure effect down to 3 (i, nor could they observe a variation in intensity with several different inert gases present. They therefore concluded that the reaction involved a two-body process. The majority of workers ° however,... 

Reaction (67a) would not be expected to contribute materially to the formation of ZT. The R" involved in Reaction (67b) is either accelerated toward the surface of the plasma or toward the trapping potential plates this step is an ion-ion reaction in which the necessary excitational energy may be provided the Z species. Reaction (68) is a three body process that involves electron attachment to the excited sin y-charged negative ion to form the T species observed. In Reaction (68) the T species is indicated as formed in an excited state with a relatively long lifetime. 

Finally, we mention that there are certain reactions, which to our opinion must be with no doubt described as three-body processes . Among them, first of all, are... 

It was assumed that the yield of OCM products could be enhanced by increasing the efficiency of CH3 recombination, which competes with reaction (35). Since the recombination of methyl radicals is a three-body process (see Section III.D), its efficiency can be increased by increasing total pressure, or by introducing an additional inert surface, which can play a role of third body. Indeed, it was demonstrated that the increase of inert gas (He or Ar) pressure at constant pressures of methane and oxygen leads to a substantial increase of OCM selectivity and yield (Sinev et al., 1996). Moreover, the addition of a 10-fold amount of various solid materials possessing a very low activity under the same conditions (quartz, fused MgO, Mg phosphate) to a relatively efficient OCM catalyst (Nd/MgO) led to a drastic increase (up to twofold) in the yield of OCM products (Sinev et al., 1997a, b). 

Loss Terms (a) Homogeneous gas-phase atom recombinations are three-body processes with rate constants near 10 32 cm.6 molecule"1 sec. 1... 

In our laboratory a microwave discharge was generated in helium by a 100 watt Raytheon microtherm generator and sampled through a pinhole leak at the apex of a conical probe into a quadrupole mass filter. Typical variations in the intensities of He+ and He2+ with pressure are given in Figure 1. If the He2+ is formed by the three-body process (Equation 11) the rate constant would have to be about 10"28 cc.2/mole-cule2/sec. which far exceeds the measured value (84). We conclude then that the diatomic ion is formed principally by the chemi-ionization process (Equation 10). 

These atoms may recombine in a three body process ... 

Another important stratospheric nitrogen containing species is HNO3. This molecule, which introduces an interaction between nitrogen and hydrogen compounds, is formed by the three body process ... 

The association process is only detectable below 600 K. For this reaction, branching fractions could not be measured directly in most apparatuses since both products of the reaction react rapidly with H2 to produce CHs". At the time the measurements were made, we could not study branching fractions directly either. Therefore, the two and three-body processes were separated by studying the reactions as a function of pressure. The rate constants for the H2 reaction at 400 K are shown in Figure 8 as a function of the helium concentration. The overall measured rate constant is as low... 

The advantages of the use of an electron accelerator for production of ionization in studies of electron reactions is evident from the preceding example. Preliminary experiments with NoO and with N20 in propane show that electron capture by N20 occurs in a way which also depends on the total pressure and so is apparently also a three-body process. The success of these experiments at pressures as high as 200 torr illustrates the relevance to radiation chemistry as compared with other methods such as mass spectrometry which only operate at much lower pressures. 

The three-body electron attachment can be a principal channel for electron losses when electron energies are not high enough for the dissociative attachment, and when pressure is elevated (usually more than 0.1 atm) and the third-order kinetic processes are preferable. In contrast to the dissociative attachment, the three-body process is exothermic and its rate coefficient does not depend strongly on electron temperature. Electrons are usually kinetically less effective as a third body B because of a low degree of ionization. 

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