A single-particle model in which the wave functions are spherically symmetric about each lattice site was used to calculate the ground-state energy $E_0$ of solid He. The self-consistent Hartree equations (which yielded the best such wave functions) were solved numerically to an accuracy of better than 1%. The results were worse than could have been expected a priori: At the observed densities, the calculated values of $E_0$ were approximately +34 and +14 cal/mole for ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$, respectively, as compared with experimental values of -4.5 and -12 cal/mole. Previous calculations are discussed in the light of our results. In addition, we calculated $E_0$ for the crystals of the other noble gas elements. The results for Ar, Kr, and Xe are within experimental error whereas ${\mathrm{E}}_0$ for Ne is definitely outside this error (being about 5% higher than experiment).

• Received 6 June 1962

DOI:https://doi.org/10.1103/PhysRev.128.546