Rate Kernel via Pair Theory

Before concluding this section on the implications of the pair kinetic theory for configuration space descriptions, we show that the kinetic equation may also be used to obtain the kinetic theory result for the rate kernel. This can be accomplished by projecting out the position and velocity dependence of the pair phase-space correlation function ab,ab( 2 1 2 /) to obtain an equation for 

This result is the same as that in (8.9) except that the propagator involving Ln is somewhat more elaborate than G g(12 z) because the effects of the triple fields have been explicitly included. To avoid proliferation of notation, we also let (j b(12 z) denote this more general propagator. 

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