On the Validity of the Master Equation for Internal Relaxation at High Densities

The validity of the collisional master equation for the relaxation of molecular internal degrees of freedom in a high-density reservoir of inert particles is examined using the generalized master equation for this system. When the hypotheses of the “Markovian approximation” to this equation are examined, it is found that they are invalidated by correlated collision processes which occur at elevated reservoir densities. At densities where the mean free time is long compared to a characteristic frequency of the internal states and the duration of a collision, the usual multiple collision theory master equation is shown to hold.