# Why do excitonic absorptions have small bandwidth?

Below is an image of the optical density (proportional to the absorption coefficient) of KBr crystal at low temperature. Indicated at 6.6 ev and 7.7 eV are the absorption by excitons. As you can see, it has a small width. Can you explain why?

Source:Theory of Excitons, Robert S Knox, 1954

-

We can invert a bit the situation. You have that $\Delta E\Delta t \ge \frac{\hbar}{2}$. Thus for narrow energy spread $\Delta E$ it means that the lifetime $\Delta t$ is large.
Now the question is why $\Delta t$ is large. In this case, this must be mostly because a rather small interaction of such excitation with its environment (most probably phonons being the most relevant) letting them live long and then having narrow energy spread.