Englert-Schwinger Functional in Quantum Statistical Model for Finite Temperature Equation of State of Electrons in Plasmas

The main aim in this paper is to present a temperature-dependent version of the Englert-Schwinger functional, within the quantum statistical model, for computing the finite temperature equation of state of electrons in plasmas. Schwinger and co-workers originally derived the functional for the case of isolated atoms at zero temperature, and applied it to compute the electronic properties. After deriving the extension to finite temperatures, a new algorithm is developed to solve the finite temperature Englert-Schwinger model. With the introduction of corrections to the density of strongly bound electrons, the model automatically takes into account the effects of these electrons in all the thermodynamic properties. Furthermore, the approach reduces the order of the nonlinear differential equation to two, in lieu of four in the quantum statistical model. Thus, at much less computing efforts, the model would be useful in high-energy-density physics applications of equation of state theory. Numerical results obtained for Cu and Al are compared with those of the original quantum statistical model. Good agreement is found for pressure and energy of electrons. The Appendix provides a derivation of the stationary property of the finite temperature free energy functional, and details of the new algorithm.