**Физика Низких Температур: ***Том ***33**, Выпуск **6-7** (Июнь 2007), c. 719-727
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### Many-body interactions and high-pressure equations of state in rare-gas solids

**Yu.A. Freiman and S.M. Tretyak**

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61103, Ukraine

*Received December 18, 2006*

**Аннотация**

The *T* = 0 K equations of state (EOS) of rare-gas solids (RGS) (He, Ne, Ar, Kr, and Xe) are calculated in
the experimentally studied ranges of pressures accounting for two- and three-body interatomic forces. Solid-state corrections to the pure two-body Aziz et al. potentials included the long-range Axilrod–Teller three-body interaction and short-range three-body exchange interaction. The energy-scale and length-scale parameters of the latter were taken as adjustable parameters of theory. The calculated *T* = 0 K EOS for all
RGS are in excellent agreement with experiment in the whole range of pressures. The calculated EOS for Ar,
Kr, and Xe exhibit inflection points where the isothermal bulk moduli have non-physical maxima indicating that account of only three-body forces becomes insufficient. These points lie at pressures 250, 200, and 175 GPa (volume compressions of approximately 4.8, 4.1, and 3.6) for Ar, Kr, and Xe, respectively. No such points were found in the calculated EOS of He and Ne. The relative magnitude of the three-body contribution to the ground-state energy with respect to the two-body one as a function of the volume compression was found to be non-monotonic in the sequence Ne–Ar–Kr–Xe. In a large range of compressions, Kr has the highest value of this ratio. This anomally high three-body exchange forces contributes to the EOS so large negative pressure that the EOS for Kr and Ar as a function of compression nearly coincide. At compressions higher approximately 3.5, the curves intersect and further on the EOS of Kr lies lower than that of Ar.

PACS: 64.60.Cn Order-disorder transformations; statistical mechanics of model systems;

PACS: 67.80.–s Solid helium and related quantum crystals;

PACS: 67.90.+z Other topics in quantum fluids and solids; liquid and solid helium.

**Ключевые слова: **rare-gas solids, equations of state, two and tree-body interatomic forces.