The single atom kinetic energy $\mathbf{\kappa }$ of high purity solid hcp ${}^4\mathrm{He}$ has been measured by neutron Compton scattering, at temperatures between 0.07 and 0.4 K and a pressure of 40 bar. Within statistical error of $\sim 2\%$ no change in $\mathbf{\kappa }$ was observed. The values of $\mathbf{\kappa }$ at $\sim 0.07\mathrm{K}$ were the same in a single crystal and a polycrystalline sample and were also unaffected (within statistical error) by the addition of 10 ppm of ${}^3\mathrm{He}$. The lattice constant was also found to be independent of temperature to within 1 part in 2000. These results suggest that the supersolid transition in ${}^4\mathrm{He}$ has a different microscopic origin to the superfluid transition in the liquid.

• Received 22 September 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.085301