Thermodynamics of an interacting Fermi system in the static fluctuation approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so-called far-distance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high-density limit 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 calculate terms of the respective order r _s and r _s ². It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r _s .