We have measured the pressure dependence of a single phonon sheet and the interaction of two such sheets, in pure liquid ${}^4\mathrm{He}$, from $0\text{to}21\text{bar}$ and show it is dominated by three phonon processes (3pp). Pressure affects the 3pp scattering by changing the shape of the dispersion curve. The scattering varies from very strong at $P=0$ to zero at $P=19\text{bar}$. The 3pp is small angle scattering at $P=0$ and, as pressure is increased, the angles decrease further and eventually become zero. We find that the signal from a single phonon sheet increases considerably with pressure to a maximum at $P=7.5\text{bar}$ and then decreases to a minimum at $\sim 15\text{bar}$, and becomes independent of pressure at $>19\text{bar}$. We discuss this behavior in terms of the creation of high-energy phonons and the expansion of the phonon sheet. The signal from the collision of two sheets, at 8.8° to each other, depends on the pressure dependences of the energy density in the individual sheets and of the 3pp. This gives direct evidence that the interaction between two phonon sheets is caused by 3pp scattering. Theory relevant to this experiment is given in the paper following this one, see Adamenko et al., Phys. Rev. B 72, 054507 (2005).

• Received 29 April 2004

DOI:https://doi.org/10.1103/PhysRevB.72.054506