Lattice Distortion Due to Isotopes in Solid Helium

Abstract

Observations of the thermal resistivity of solid helium containing ${\mathrm{He}}^3$ isotopes have indicated that the phonon scattering cross section of the isotope is three times larger than the theoretical value obtained by considering only the mass-difference. Using as a model a helium atom in the potential well formed by its neighbors, and taking account of the zero-point energy of that atom and of the strain energy in the surrounding solid when the atomic cell is expanded, it is shown that around a ${\mathrm{He}}^3$ isotope the lattice suffers an outward distortion of about 1-2%. This distortion can account for the discrepancy in the phonon scattering cross section.