Early opaque universe - why little proton-photon scattering?

[Lapidus]

I read many times that the early universe was opaque foremost because of the scattering of photons off free electrons (Thomson scattering). Why is the scattering off free protons not equally important?

Btw, the same they say about stars. Photons within stars need a very long time to get out of the star because of scattering off the free electrons. Again, why not protons?

thanks!

 

[bapowell]

The Thomson scattering cross section is proportional to $m^{-2}$, and so scattering off the much heavier protons is suppressed by a factor of a million relative to scattering off electrons.

 

[Lapidus]

Thanks!

And why is that so? Is there a simple physical argument behind this (curious) effect that photons scatter off particle with less mass with higher probability than they do with more massive particles?

My guess is that in Compton scattering the virtual particle in the Feynman graph is massive (an electron). So the more massive the propagator particle, the smaller the amplitude. Wrong?

 

[Lapidus]

OR is it simply because the Compton wavelength is much smaller for protons than for electrons?

 

[bapowell]

It's best to think about Thomson scattering as a classical phenomenon, in which instead of photons bouncing of particles, one has a charged particle being accelerated by incident electromagnetic radiation and in turn radiating electromagnetic energy -- the scattered light. The power emitted is proportional to the time-averaged squared acceleration of the particle, which is itself proportional to $m^{-2}$ from Newton's 2nd law. This makes sense: electrons are more vigorously jiggled than protons by the electromagnetic radiation.