Structure and thermodynamic properties of relativistic electron gases

Relativistic effect is important in many quantum systems but theoretically complicated from both fundamental and practical perspectives. Herein we introduce an efficient computational procedure to predict the structure and energetic properties of relativistic quantum systems by mapping the Pauli principle into an effective pairwise-additive potential such that the properties of relativistic nonquantum systems can be readily predicted from conventional liquid-state methods. We applied our theoretical procedure to relativistic uniform electron gases and compared the pair correlation functions with those for systems of nonrelativistic electrons. A simple analytical expression has been developed to correlate the exchange-correlation free energy of relativistic uniform electron systems.

Figure 1

Effective Pauli potential for a uniform electron gas at different temperatures (ρ = 0.033 77 a.u.).

Figure 2

The radial distribution functions of uniform electron gas at different temperatures (ρ = 0.033 77 a.u.).

Figure 3

Exchange-correlation free energy as a function of the electron density at several temperatures. The lines are calculated from Eq. (23).

Figure 4

Parameter κ versus temperature. It deviates from unity significantly only at high temperature.