High-Pressure Behavior of Solid ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{Ne}}^{20}$

The failure of the harmonic approximation for the lattice dynamics of solid ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{He}}^3$, and ${\mathrm{He}}^4$ at densities corresponding to pressures below the order of ${10}^3$ atm is well known. We present evidence that the equation of state for solid ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{Ne}}^{20}$ at high densities may, however, be calculated successfully in the harmonic approximation. Equation-of-state curves at high density for ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{Ne}}^{20}$ (all for the fcc phase at $T=0\mathrm{}$ °K) are given and compare well with results from Monte Carlo or cluster-expansion treatments using a Jastrow wave function. The comparison with experiment shows good agreement in the high-density range for ${\mathrm{He}}^3$, ${\mathrm{He}}^4$, and ${\mathrm{Ne}}^{20}$. For ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ the theoretical results agree closely with each other at high densities, but not so well with the experimental data of Stewart in that region, suggesting inadequacy either of the potential or of the experimental data. For the Lennard-Jones and Buckingham potentials used for pressures ranging from a few thousand to several million bars the Domb-Salter approximation gives an accurate result for the zero-point energy of the harmonic crystal. Our results lead us to conclude that for good high-density computations the necessary short range correlations are adequately accounted for in the harmonic approximation.