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LECTRONIC PROPERTIES OF SOLID

Thermodynamics of an Interacting Fermi System in the Static Fluctuation Approximation1 R. R. Nigmatullin, A. A. Khamzin, and I. I. Popov Theoretical Physics Department, Kazan (Volga Region) Federal University, Kazan, 420008 Russia email: [email protected] Received April 19, 2011

Abstract—We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermigas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the socalled fardis tance 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 manybody system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the highdensity limit were obtained. All expres sions are given in the units of rs, where rs determines the ratio of a mean distance between electrons to the 2

Bohr radius a0. In these expressions, we calculate terms of the respective order rs and r s . 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 rs. DOI: 10.1134/S1063776112010050 1

1. INTRODUCTION TO THE STATIC FLUCTUATION APPROXIMATION METHOD The calculation of the correlation energy of the ground state in the absence of external fields for the strongly degenerated electron gas constitutes the cen tral problem in solid state physics, in particular, the physics of metals. In the pioneering works of Gell Mann and Brueckner [1] and Wigner [2], the first ana lytic results for the highdensity and lowdensity elec tron gas were obtained. In those papers, an expression for the ground state energy was obtained in the terms of the dimensionless parameter rs = r0/a0, where r0 = 3

3/4πn is the mean distance between electrons, n is the electron gas density, and a0 determines the con ventional Bohr radius. For the highdensity limit (rs < 1), the ground state energy has the form [2] E 0.916 0 = ⎛ 2.21  –  + 0.0622 ln r s – 0.094⎞ Ry. (1) ⎝ r2 ⎠ N rs s

The first term corresponds to the kinetic energy and the second term determines the contribution of the exchange energy. The last two terms in Eq. (1) describe the correlation energy Ecorr . We note that another numerical coefficient before the logarithmic term was obtained in [3]: E corr (2)  = ( 0.0570 ln r s – 0.094 )Ry. N 1

The article is published in the original.

Besides this observation, we note papers [4–6], where the different numerical values for the constant term in Eq. (2) are presented. Therefore, the problem of the correct evaluation of the expression for the correlation energy remains open. The second task is related to the problem of the accurate (erro