The independent binary collision IBC model

Consider first the assumption that those oscillator-bath encounters that lead to vibrational relaxation can be described as uncorrelated binary collisions. It is sufficient to focus on the rate expression (13.17) 

Further reading J. Chesnoy and G. M. Gale, Adv. Chem. Phys. 70, 298-355 (1988). 

In the second line of (13.44) and in (13.45)/(r) denotes the force between the relaxing coordinate and a single bath atom at distance r away and/(Z r,p) is the same force, a time t later, given that the initial momentum of the bath atom was p. All bath atoms are assumed identical and their bulk density is denoted p. g(r) is the 

The important feature in the final result (13.45) is the fact that all the needed dynamical information is associated with the time course of a single collision event. To calculate the correlation function that appears here it is sufficient to consider a single binary collision with thermal initial conditions. The result is given in terms of the function B, a two-body property that depends only on the relative position of the particles (the initial configuration for the collision event) and the temperature. The host structure as determined by the V-body force enters only through the configurational average that involves the pair distribution g(r). 

Within the IBC approximation the result (13.45) is general, ft is particularly useful for interpretation of vibrational relaxation in pure liquids, because it can be related immediately to measurement of the same property in the corresponding low pressure gas phases. To show this define 

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