Simplified Quantum Statistical Model for Electron Equation of State of Materials

The main aim in this paper is to present a simplified (temperature-dependent) version of the quantum statistical model for computing the equation of state of electrons in materials. For this purpose, the Englert-Schwinger approximation scheme within the quantum statistical model is extended to finite temperatures. This procedure leads to a modified Thomas-Fermi-Dirac model. Schwinger and co-workers had originally demonstrated this procedure for the case of zero-temperature, and applied it to compute the electronic properties of cold free atoms. In this paper, a new algorithm is developed to solve the modified Thomas-Fermi-Dirac model, and the numerical results obtained for Cu and Al are compared with those of the exact quantum statistical model. Good agreement is found particularly for thermal component of electron equation of state. The present approach, at much less efforts, would be useful in high-energy-density physics as thermal component of electron properties alone are needed in equation of state theory. Derivation of explicit expressions of different contributions (viz. kinetic, gradient, exchange and exchange-correlation terms) to the free energy functional, its stationary property, finite-temperature corrections to energy of strongly bound electrons, and (iv) details of the new algorithm are provided in the Appendix.