Lattice Dynamics of hepHe3andHe4at High Pressures

Calculations of the vibrational properties of hcp solid ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ at 0°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 $\Sigma$, $T$, and $\Delta$. Frequency distribution functions and Debye temperatures at 0°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 $\frac{{\ominus }_3}{{\ominus }_4}$ at 0°K is found to be approximately 1.23 as compared with the classical value of 1.154 and the experimental value of 1.18.