What is the specific photon-particle interaction by which momentum is transferred in radiation pressure? Updated Preface (in response to comments).
Per the title, this question is focused on understanding "the specific photon-particle interaction by which momentum is transferred in radiation pressure".
In the original question I included a preface which gave an example of what I meant by "radiation pressure":  solar sails.  That was for an example only.  The question is not about solar sails, and not about the classical theory of how to calculate radiation pressure.  "Solar sails" are mentioned only as orientation and evidence that there is a real macroscopic phenomena involved that does not have an obvious description at the detailed level of specific photon-particle interaction. My apologies if that mention has been misleading.
The information I seek is a description of what happens at the level of specific photon-particle interaction to generate radiation pressure.
What follows is the original post, verbatim:
In this question "radiation pressure" means the term as used in describing the behavior of light sails.
"specific photon-particle interaction" means exactly what particles the photons interact with to impart momentum to the impacted object.
There are formulas to calculate radiation pressure, however, they do not describe the photon-particle interaction that produces the pressure.
There are the photon-electron interactions of reflection and refraction, however, these are 100% elastic, meaning no energy is lost or gained, so it is difficult to see how they could transfer the energy of increased momentum to the to the impacted object.
A conjecture is that the photons impact the quarks in the hadrons of the impacted object.  However, I have not seen any obvious (i.e. through googling) papers that describe this.
So the question: what is the specific photon-particle interaction by which momentum is transferred in radiation pressure, and what are links to papers that describe this?
 A: An individual photon carries energy $h \nu$ and momentum $h \nu / c$. When a photon is absorbed by material, the energy and momentum are transferred to the absorber. If a photon is subsequently emitted by any process, then energy and momentum is carried away by the emitted photon. 
If we consider photons in a beam directed at a perfect planar mirror along its normal vector, then in the mirror frame each photon is contributing 2 $h \nu / c$ in momentum to the mirror where $\nu$ is the photon frequency as measured in the mirror frame. This causes the mirror to accelerate.
In the initial rest frame of the mirror, the frequency of the incident photons remains the same, but the reflected beam becomes increasingly redshifted owing to reflection off of the receding mirror. In this way, the photons are transferring both energy and momentum to the mirror. Schematically this is how a solar sail might operate.
None of the above discussion depended on the nature of the absorption or emission processes. As commenters have already indicated, the interaction cross section of photons with electrons is vastly greater than that of their interaction with hadrons. Practically speaking, the hadrons don't make an important contribution to the absorption or emission of the photons.
