Debye-Waller factor in solid ³He and ⁴He

The Debye-Waller factor and the mean-squared displacement from lattice sites for solid ³He and ⁴He were calculated with path-integral Monte Carlo at temperatures between 5 and 35 K, and densities between 38 and 67 nm^-3. It was found that the mean-squared displacement exhibits finite-size scaling consistent with a crossover between the quantum and classical limits of N^-2/3 and N^-1/3, respectively. The temperature dependence appears to be T³, different than expected from harmonic theory. An anisotropic k⁴ term was also observed in the Debye-Waller factor, indicating the presence of non-Gaussian corrections to the density distribution around lattice sites. Our results, extrapolated to the thermodynamic limit, agree well with recent values from scattering experiments.