High-density two-level radiative cooling

When collisions thermalize an optically thin two-level atom, the upper fraction is $f_u=g{e}^{-\theta /T}/(1+g{e}^{-\theta /T})$ and the emitted power per atom is $A_{21}\Delta E{f}_u$. Its logarithmic temperature slope is $(\theta /T)(1-f_u)>0$. Radiative cooling still occurs, but collision frequency no longer sets the emitted power as in the low-density limit.