Compton scattering in relativistic flow

[dobbykins]

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

The paper linked above notes in the introduction:

...a photon is more likely to suffer a scat-
tering from an electron that is moving toward it, rather
than away from it (the probability of scattering is propor-
tional to the Doppler factor 1 − cos θ v/c, where v is the
electron velocity and θ is the angle at which the photon
and electron encounter).

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.

 

[lippyka]

You are correct. The Doppler factor does modify the mean free path of a photon in an electron flow. When the photon is traveling in the same direction as the electrons, the Doppler effect increases the energy of the photon and thus its interaction cross-section and mean free path. Conversely, when the photon is traveling against the electron bulk flow, the Doppler effect decreases the energy of the photon and thus its interaction cross-section and mean free path.