Padé Approximations for the Thermodynamic Functions of Weakly Interacting Coulombic Quantum Systems

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Abstract
A weakly interacting system of electrons (e) and ions (i) is considered. Based on analytical formulae in the limiting regions of both weak and strong degeneration of the e4‐contribution and a few computer calculated points in the intermediate region n Λ3 ≈ 1 (n electron density, Λ thermal wavelength, Λ2 = 2πβh2/me, β = (kBT)−1, me electron mass) Padé‐approximations for the thermodynamic functions are constructed which are valid in the entire temperature–density plane. The temperature dependence of the exchange and correlation contribution to the chemical potential is taken into account here for the first time. In the framework of an unsymmetrical electron–hole model of germanium, a phase transition occurs with a critical point at Tc = 8 K and nc = 1.0 × 1017 cm−3.