Collision point process

A typical cascade process. A fast atom or ion collides with surface molecules, sharing its momentum and causing the struck molecules to move faster. The resulting fast-moving particles then strike others, setting up a cascade of collisions until all the initial momentum has been redistributed. The dots ( ) indicate collision points, tons or atoms (o) leave the surface. 

This work provides accurate potential energy curves as well as coupling matrix elements for the B2+/H and B4+/ He systems. From the molecular point of view, it appears important to involve all levels correlated to the entry channels in the collision dynamics and, in particular, to take into account rotational effects, which might be quite important. The results concerning the double electron capture process in the (B4+ + He) collision point out the limitations ofthe potential approach model, especially to account for open shell levels, for which more elaborate calculations are necessary. 

This is formally true only for interactions between particles involving hard-sphere potentials. In fact, under these circumstances, the interacting particles perceive each others presence only at the point of contact. When the interactions are governed by a smooth potential, theoretically collisions should not be treated as point processes. Very often, however, even in these cases collisions are described as discontinuous processes occurring at the shortest distance between interacting particles, as in the case of the Maxwell molecules, as explained in the original work of Maxwell (1867). Eor more details readers are referred to Chapter 6. 

For second-order point processes such as hard-sphere collisions, the total number of particles remains unchanged. However, the number of particles with a specific phase-space vector will always increase or decrease. 

Recently Ladanyi has extended the work on N2 and CO2 by examining the induced terms given by a site-site DID model. This model allows for the distribution of polarizable matter within the molecule (c.f the discussion of section 2) by representing the molecular polarizability by an isotropic point polarizability on each interaction site and taking all orders of intra-molecular DID interactions into account. For COo her results are appreciably different from Frenkel and McTague s. In particular there is an enhanced projection of the induced terms along and a better timescale separation between the allowed and collision-induced processes so that the total spectrum resembles the reorientational spectrum more closely. 

All the theory developed up to this point has been limited in the sense that translational motion (the continuum degree of freedom) has been restricted to one dimension. In this section we discuss the generalization of this to three dimensions for collision processes where space is isotropic (i.e., collisions in homogeneous phases, such as in a... 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

In the case of weak collisions, the moment changes in small steps AJ (1 — y)J < J, and the process is considered as diffusion in J-space. Formally, this means that the function /(z) of width [(1 — y2)d]i is narrow relative to P(J,J, x). At t To the latter may be expanded at the point J up to terms of second-order with respect to (/ — /). Then at the limit y -> 1, to — 0 with tj finite, the Feller equations turn into a Fokker-Planck equation... 

An important point is that these advances have been complemented by the concomitant development of innovative pulse-characterisation procedures such that all the features of femtosecond optical pulses - their energy, shape, duration and phase - can be subject to quantitative in situ scrutiny during the course of experiments. Taken together, these resources enable femtosecond lasers to be applied to a whole range of ultrafast processes, from the various stages of plasma formation and nuclear fusion, through molecular fragmentation and collision processes to the crucial, individual events of photosynthesis. 

---