Transmission and reflection of phonons and rotons at the superfluid helium-solid interface

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, $R^-$, and $R^+$ rotons in helium by either a phonon from the solid or a helium quasiparticle incident on the interface. The interaction of all $HeII$ quasiparticles with the interface, and 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 cases. Andreev reflection of helium phonons and rotons is predicted. The energy flows through the interface due to phonons, $R^-$, 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 prior to the experiments of Tucker and Wyatt in 1999. New experiments for creating $R^-$ rotons, by beams of high-energy phonons (h-phonons), are suggested.