Solutions of the BBGKI equations in the fourth approximation in the temperature

Solutions of the Bogolyubov-Born-Green-Kirkwood-Ivon equations in the fourth approximation in the temperature are given in a class of generalized functions both for van der Waals and ionic crystals in the case of the so-called taking into account of smoothed correlations. A statistical thermodynamics of strongly anharmonic van der Waals and ionic crystals is constructed. Temperature expansions of the correlative distribution functions and thermodynamic quantities are investigated within the framework of the indicated method. The temperature dependence of cubic order is taken into account in the expression of the isochoric specific heat and the Grüneisen parameter of the listed crystals. It is shown that the temperature expansion for the isochoric specific heat of anharmonic crystals converges well for a value of the reduced temperature 0.33 T_m (T_m is the melting temperature).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 55–59, July, 1981.