Angular momentum and energy relaxation

Though Kj(t) decays from 1 to 0 it is in general non-exponential relaxation. Its conventually defined correlation time 

If the rotational energy reaches its equilibrium value (e) =kT exponentially as in Eq. (5.29) then the times are the same  

As we shall see, it is approximately true only in the high-temperature limit. 

Using corrected operators in Eq. (5.11) and Eq. (5.15) and substituting their solutions into Eq. (5.31) and Eq. (5.32), we bring them into the 

Performing power series expansion of the exponents and using formulae (5.30) and (5.28) respectively we obtain 

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