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?