Lattice Dynamics of hepHe3andHe4at High Pressures

Abstract

Calculations of the vibrational properties of hcp solid ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ at 0\ifmmode^\circ\else\textdegree\fi{}K have been carried out. The harmonic coupling parameters for first and second neighbors have been evaluated for four molar volumes in the range 10.0 ${\mathrm{cm}}^{3}$ to 16.0 ${\mathrm{cm}}^{3}$ using the harmonic ground-state wave function and the self-consistent method of Koehler. The dispersion relations and sound velocities were evaluated for the symmetry directions $\ensuremath{\Sigma}$, $T$, and $\ensuremath{\Delta}$. Frequency distribution functions and Debye temperatures at 0\ifmmode^\circ\else\textdegree\fi{}K have also been obtained for both solids in the hcp phase. A comparison with experiment indicates that the calculated Debye temperatures are too high, the agreement with experiment being best at the highest density examined. The ratio of the ${\mathrm{He}}^{3}$ Debye temperature to the ${\mathrm{He}}^{4}$ Debye temperature $\frac{{\ensuremath{\bigominus}}_{3}}{{\ensuremath{\bigominus}}_{4}}$ at 0\ifmmode^\circ\else\textdegree\fi{}K is found to be approximately 1.23 as compared with the classical value of 1.154 and the experimental value of 1.18.