  We suggest a new method of calculation of the equilibrium correlation
functions of an arbitrary order for the interacting Fermi-gas model in the
frame of the static fluctuation approximation (SFA) method. This method based
only on the single and controllable approximation allows to obtain the
so-called far-distance equations (FDEs). These equations connecting the quantum
states of a Fermi particle with variables of the local field operator contains
all necessary information related to calculation of the desired correlation
functions and basic thermodynamic parameters of the many-body system
considered. The basic expressions for the mean energy and heat capacity for
electron 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 of
a mean distance between electrons to the Bohr radius a_0. In these expressions
we calculated the terms of the order r_s and r_s^2, correspondingly. It was
shown also that the SFA allows to find the terms related with high orders of
the decomposition with respect to the parameter r_s.
