Investigations of the wave vector dependence of theoretical phonon frequencies of neon, argon, krypton, and xenon, deduced by invoking a six constant Clark, Gazis, and Wallis model, reveal that they satisfy a relation,Mngr;2lsqb;sin(pgr;zgr;/p)rsqb;n=Fgr;(r), a constant which depends on individual rare gas solid withp=1 or 2 andn=minus;2.018plusmn;0.038 at all polarizations except lsqb;110rsqb;Lalong the principal symmetry directions and hence their dependence on wave vectorqcould be separated from that on nearest neighbor distance,r. It is shown that the latter is adequately represented at all wave vectors and polarizations in the Brillouin zone by a homologous relation,Mngr;2ragr;=dgr;(q), a constant with agr;=minus;2.818plusmn;0.127 in the case of argon, krypton, and xenon and could be exploited to determine the zero point energy which destroys the homology in the case of neon. The physical significance of these empirical relations, the degree of homology that exists among these rare gas solids, influence of zero point energy on their dispersion relations, as well as the accuracy of scaling factors in the evaluation of zero point energy are discussed.
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