Debye-Waller factor in solid He-4 at sub-Kelvin temperatures

The recent observation by Kim and Chan [Science 305 (2204) 1941] of a transition at low temperatures ($\sim $ 200 mK) in the hcp-phase of solid helium has re-opened interest in the old question of supersolidity. The nature of the low-temperature phase remains in question, and to investigate this in more detail, we have measured the density distribution of He-4 nuclei in crystals of He-4 with a molar volume of 21.3 cm$^{3}$ down to 140 mK. We find no evidence for any changes in the vicinity of the transition. Treating the material as a traditional crystal, we have extracted the mean square displacement for the nuclei and find anisotropy between the in- and out-of-plane motions. Our values are in agreement with previous work at higher temperatures.