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The lattice dynamics of rare gas crystals has been constructed taking into account the deforma tion of electron shells of the atoms of the dipole and quadrupole types, depending on the displacement of the nuclei. The obtained equations of lattice vibrations have been investigated in the long wavelength approxi mation. The role played by the three body interaction and the deformation of the electron shells in the vio lation of the Cauchy relation has been discussed. The calculated Birch elastic moduli for Xe and deviations from the Cauchy relation are in good agreement with the available experimental data over a wide range of pressures.

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