Impact processes with finite collision time

7 Impact processes with finite collision time 

In impact theory the gas density is restricted by the criterion for the validity of the binary collision approximation. Roughly speaking, the time between collisions must be greater than their duration 

However, only the left-hand side of the inequality has a clear, although qualitative, physical meaning. As far as collision time tc is concerned, its evaluation as p/ v) in Eq. (1.58) is rather arbitrary. Alternatively, it may be defined as the correlation time of the collisional processes which modulate the rotation. Using the mechanical equation of motion 

The above reasoning applies also to the correlation function of the torque. It follows from the stationarity of the random processes J(t) and M(t) that their correlation functions depend solely on difference of times arguments 

Owing to this, d/dt = —d/dt, and Eq. (1.62) turns into a simple and general relation which connects Kj to Km- 

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