Strong collision limit

The density matrix p describes a pure state, as seen from the equality p2 = p, while p does not. The transition described by (2.37) corresponds to the strong collision limit in which the particle is completely localized. In the more general case, the off-diagonal elements may not completely vanish. This, however, does not affect the qualitative picture. 

Fig. 1.19. Populations during low pressure dissociation, model for k(Ej E described in Fig. 1.18. a = strong collision limit, b = intermediate case, c = weak collision limit.

The expression (1.51) derived for the overall rate constant k shows that most details of individual collision processes are lost by thermal averaging. However, two averaged quantities of collisional transitions at the bottle-neck near q, i.e. (Ttot( o) and (A ( o)), enter into the rate constant. From low pressure dissociation studies one can thus derive information on the product fftot(Po)(A ( o)) at the weak collision limit or fftot( o) at the strong collision limit. Little use has yet been made of this source of information on collision processes. 

Since equation (1.47) is valid at the strong collision limit for all possible values of k f, we can perform a simple expansion around this limit. The integral equation (1.42) can be solved by iteration - it... 

While nonequilibrium effects at the weak collision limit or for intermediate cases have been treated only recently, the strong collision limit was discussed much earlier. The relation with these earlier theories is reviewed briefly. At the strong collision limit k is given by... 

When using the temperature dependence of the nuclear spin-spin or nuclear spin-lattice relaxation rate to study molecular motion, as is the case with the surface diffusion we are dealing with here, there exist soolled strong and weak collision limits. Different mathematical relationships are needed to describe these limits. Consider the nuclear spin-spin relaxation rate (1 / T2) as measured by a conventional Hahn-echo pulse sequence, and suppose that Aa> is the amplitude of the local field fluctuation responsible for relaxation. Also assume that r is the correlation time for the motion, say a jump, which causes the local field to fluctuate. The strong collision limit is defined such that... 

In the strong collision limit, the time taken for the transition from Cl to Cl is negligible in comparison with the residence time, r, spent by the molecule... 

Similarly, the spectral densities for the phenyl deuterons of 5CB may be calculated. The strong collision limit is used to describe internal ring rotation about its para axis and the following is obtained [8.26] ... 

This aspect has been discussed in the weak and strong collision limits[l2,13], and for systems with many internal degrees of freedom it is certain that this reduction in dimensionality occurs at bath densities where the reaction rates... 

In the automaton, collisions, both non-reactive and reactive, are local events that occur at the nodes of the lattice. Elastic collisions are treated in the strong collision limit so that each collision completely randomizes the velocities of the particles at a node. There is a number of ways that one can carry out velocity randomization and all will be denoted by the operator R. Here we briefly describe one scheme that is used in simulations reported below. 

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