The Debye-Waller Factor in solid 3He and 4He

TL;DR

This study calculates the Debye-Waller factor and atomic displacements in solid helium isotopes using Path Integral Monte Carlo, revealing quantum-classical crossover, non-Gaussian effects, and agreement with experimental data.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the Debye-Waller factor in solid helium, highlighting non-Gaussian corrections and finite-size scaling behaviors.

Findings

Finite-size scaling shows quantum-classical crossover.

Temperature dependence follows T^3, deviating from harmonic theory.

Anisotropic k^4 term indicates non-Gaussian density distribution.

Abstract

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 K and 35 K, and densities between 38 nm^(-3) 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 T^3, different than expected from harmonic theory. An anisotropic k^4 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.