Theory of crystallization waves inHe4at finite frequency

We determine the spectrum of crystallization waves and Rayleigh waves at the interface between superfluid and solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, taking into account the effect of elasticity and the finite-growth coefficient of the crystal. For $k\gtrsim {10}^6$ ${\mathrm{cm}}^{-1\mathrm{}}$ the coupling between these two modes significantly changes the entire spectrum.