Mean free path through randomly oriented disc absorbers (source code)

= Mean free path through randomly oriented disc absorbers
{title2=$\ell^{-1}=n_{\rm com}(1+z)^3\pi R_d^2/2$}

For an unclustered population of fully covering circular disc absorbers, the inverse <mean free path> is proper number density times mean projected area. A comoving number density must first be multiplied by $(1+z)^3$. The incidence then constrains the proper radius; covering factor and multiplicity of detectable lines can change the inference.