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We suggest a new method of calculation of the equilibrium correlationfunctions of an arbitrary order for the interacting Fermi-gas model in theframe of the static fluctuation approximation (SFA) method. This method basedonly on the single and controllable approximation allows to obtain theso-called far-distance equations (FDEs). These equations connecting the quantumstates of a Fermi particle with variables of the local field operator containsall necessary information related to calculation of the desired correlationfunctions and basic thermodynamic parameters of the many-body systemconsidered. The basic expressions for the mean energy and heat capacity forelectron gas at low temperatures in the limit of high density were obtained.All expressions are given in the units of r_s,where r_s determines the ratio ofa mean distance between electrons to the Bohr radius a_0. In these expressionswe calculated the terms of the order r_s and r_s^2, correspondingly. It wasshown also that the SFA allows to find the terms related with high orders ofthe decomposition with respect to the parameter r_s.

Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation