Ab initio theory of many-body interaction and phonon frequencies of rare-gas crystals under pressure in the model of deformable atoms

Ab initio calculations of phonon frequencies of compressed rare-gas crystals have been performed taking into account the many-body interaction in the model of deformable atoms. In the short-range repulsive potential, along with the previously considered three-body interaction associated with the overlap of the electron shells of atoms, the three-body forces generated by the mutual deformation of the electron shells of the nearest-neighbor atoms have been investigated in the dipole approximation. The relevant forces make no contribution to the elastic moduli but affect the equation for lattice vibrations. At high compressions, the softening of the longitudinal mode at the points $L$ and $X$ is observed for all the rare-gas crystals, whereas the transverse mode $T_1$ is softened in the direction $\Sigma$ and at the point $L$ for solid xenon. This effect is enhanced by the three-body forces. There is a good agreement between the theoretical phonon frequencies and the experimental values at zero pressure.