Three-body scattering

We continue with the full description in three-dimensional space and consider first, as an introduction to reactive scattering, elastic two-body scattering, and then generalize to reactive (three-body) scattering [14]. 

We consider now, briefly, the generalization to three-body scattering that is required in order to describe chemical reactions, i.e.,... 

R. A. Broucke, On the role of the moment of inertia in three-body scattering, in From Newton to Chaos (A. Roy and B. Steves, eds.) Plenum Press, New York (1995). 

The role of resonances was in some sense verified by a study prototype three-body scattering reaction F + H2 — HF(v, J) + H problem[8]. Recent experimental as well as theoretical results indicate that resonances play a very important role in this reaction [9]. We have previously developed methods by which scattering cross sections can be computed from the properties associated with resonant states[19, 28, 29, 30]. Problems like the fluorine hydrogen collision encourage us to come back and combine these methods with our current 3-D finite element method in order to study the influence of intermediate resonant states FH2 (v, J, K) in... 

The Efimov trimers influence the three-body scattering properties. When an Efimov state intersects the continuum threshold for a < 0 three-body recombination loss is enhanced [79,80], as the resonant coupling of three atoms to an Efimov state opens up fast decay channels into deeply bound dimer states plus a free atom. Such an Efimov resonance has been observed in an ultracold, thermal gas of Cs atoms [77]. For fl > 0 a similar phenomenon is predicted, namely an atom-dimer scattering resonance at the location at which an Efimov state intersects the atom-dimer threshold [81,82]. Resonance enhancement of P has been observed in a mixture of Cs atoms and Cs2 halo dimers [78] see Figure 9.15. The asymmetric shape of the resonance can be explained by the background scattering behavior, which here is a linear increase as a function of a. 

Figure 4. Intermediate scattering function ( c(t F(k,t) and dynamic structure factor (right), S(k,(o), computed from MCY with and without three-body corrections.

Material bodies scattered throughout Plane P have neither zero thickness nor are they infinitely small. They have, instead, a very small, finite thickness, and this is formed by superimposed atoms or molecules. This thickness is not suspected by the Plat Men [or inhabitants of a wholly imaginary, two-dimensional Flat Land ], for whom there is only a bed of atoms and for whom groupings of atoms constituting the molecules are all formed within Plane P. This hypothesis does not, however, deny the possibility, if one prefers, of considering some identical bodies to be like slices [tranches] within the three-dimensional body of our Universe.. . . ... 

F. Barocchi, M. Neri, and M. Zoppi. Derivation of three-body collision induced light scattering spectral moments for argon, krypton, xenon. Molec. Phys., 34 1391, 1977. 

Because the orbital angular momentum of the positron-hydrogen system is zero for s-wave scattering, the total wave function is spherically symmetric and depends only on the three internal coordinates which specify the shape of the three-body system. The kinetic energy operator... 

The scattering process can now be considered as a three-body problem, rather similar to positron scattering by atomic hydrogen but with the important difference that, because the ionization energy of an alkali atom is less than the binding energy of positronium, 6.8 eV, the positronium formation channel is open even at zero positron energy. 

When the constituent two-body interactions in a three-body system produce an s-wave scattering length a of much larger magnitude a than... 

Three-body (and many-body) quasi-classical scattering is formulated and the numerical evaluation of the reaction probability is described. 

The two-body dynamics described in the preceding section has been useful in introducing a number of important concepts, and we have obtained valuable insights concerning the angular distribution of scattered particles. However, there is obviously no way to faithfully describe a chemical reaction in terms of only two interacting particles at least three particles are required. Unfortunately, the three-body problem is one for which no analytic solution is known. Accordingly, we must use numerical analysis and computers to solve this problem.7... 

A problem of great practical importance is the three-body problem with non-Keplerian forces and a repulsive core. The triatomic problem has widespread applications in reactive scattering and triatomic isomerization. There are many studies dealing with experiments and theory. The principal problem for reactive scattering has always been the calculation of a reliable potential function on which the triatomic dynamics takes place. However, quantum dynamics on those... 

While relative equilibria and relative TS might occur in bound motion (isomerization with nonzero J, we restrict ourselves to scattering situations in all that follows. A generalization of the isomerization for the three-body system, for instance, is still lacking. Also, the very important case of three-body (and four-body) reactive scattering, with angular momentum, is only treated in the literature without explicitly resorting to a TS concept [73-75]. 

N. N. Choi, M.-H. Lee, and G. Tanner, Private communication. The poster presentation in this conference entitled Electron-positive hehum ion scattering as a three-body Coulomb problem, 2003 N. N. Choi, M.-H. Lee and G. Tanner, Phys. Rev. Lett. 93 054302 (2004). 

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