We solve the problem of the transmission and reflection of phonons and rotons at the interface between superfluid helium and a solid for all angles of incidence and in both directions. A consistent solution of the problem is presented, which allows us to rigorously describe the simultaneous creation of phonons and $R^{-}$ and $R^{+}$ rotons in helium by either a phonon from the solid or a helium quasiparticle incident on the interface. The interaction of all $\text{He}\text{II}$ quasiparticles with the interface, as well as their transmission, reflection, and conversion into each other, is described in a unified way. The angles of propagation and the probabilities of creating quasiparticles are obtained for all of the cases. The Andreev reflection of helium phonons and rotons is predicted. Energy flows through the interface due to phonons and $R^{-}$ and $R^{+}$ rotons are derived. The small contribution of the $R^{-}$ rotons is due to the small probability of an $R^{-}$ roton being created by a phonon in the solid, and vice versa. This explains the failure to directly create beams of $R^{-}$ rotons before the experiments of Tucker and Wyatt in 1999 [Science 283, 1150 (1999)]. Experiments for creating $R^{-}$ rotons by beams of high-energy phonons are suggested.

• Received 17 December 2007

DOI:https://doi.org/10.1103/PhysRevB.77.174510