Abstract
Long range interactions between the atoms in a rare gas crystal are developed in a many-body multipole series formalism. The various interaction terms are expressed as the product of a geometric part, which depends only upon the lattice structure, and a multipole interaction constant appropriate to the atomic species. The interaction constants for Neon, Argon, Krypton and Xenon are calculated by means of time-dependent Brueckner-Goldstone perturbation theory and provide results of a higher expected accuracy than previous calculations and in many cases provide results previously unavailable. Lattice summations are performed for the geometric part of the interactions. To overcome the slow convergence of the tripledipole lattice summation, the finite summation range is extended, and and extrapolation to infinite range is accomplished analytically by means of a continuum model for the crystal. The contributions to the various properties of the rare gas crystals of three-body multipole long range interactions are calculated. In particular the lattice energy, the harmonic zero point vibrational energy, the elastic constants C[11], C[12] and C[44] and the bulk modulus are evaluated for each of the rare gas crystals at the absolute zero. The effects of the high order multipole terms are shown to be not negligible. The quantity delta = (C[44] - C[12])/C[12], which is always positive when calculated with only two-body forces, is reduced when three-body interactions are included. In the cases of A, Kr and Xe, delta in fact becomes negative. For the only experimental data available delta is found to be negative for Argon providing strong evidence for the existence of three-body forces. In the final chapter a number of points arising from the thesis are discussed and some indication is given of the possible direction of future developments in this area of research.