Zero-Point Energy of Rare-Gas Crystals to Orderη4

Expressions are obtained for the anharmonic contributions to the zero-point energy of order ${\eta }^4$, for a crystal in which every atom is on a site of inversion symmetry. The Ludwig approximation has been used to estimate the anharmonic contributions for a nearest-neighbor central-force model of rare-gas crystals. It is found that the ${\eta }^4$ contribution decreases the zero-point energy by about 19% in case of Ne and by less than 0.7% in case of Ar, Kr, and Xe.