For reference: http://arxiv.org/abs/astro-ph/9912312" [Broken]

The paper linked above notes in the introduction:

The authors are performing this calculation for an isotropic electron distribution. However, for my work, I am considering an electron population with a relativistic macroscopic bulk flow. That is, the electrons are considered to be isotropic in their frame, but they are all moving in a (generally) single direction in the lab frame.

It seems intuitive to me that the Doppler factor, as above, would modify the mean free path of a photon in the electron flow. So, if a photon is traveling in the same direction as the electrons, it would have a longer mean free path, whereas if the photon is traveling against the electron bulk flow, it would have a shorter mean free path and scatter sooner.

Please correct me if I'm wrong (or confirm this if I'm right) and explain your reasoning. Thanks in advance.