Electron and nuclear pressures in electron-nucleus mixtures

Chihara, Junzo*; Yamagiwa, Mitsuru

For a solid metal with frozen nuclei, the density-functional theory provides a unique definition of the electron pressure in an electron-nucleus mixture, and the total pressure of this mixture is represented as the sum of the electron and nuclear pressures. This fact leads to definitions of the electron and nuclear pressures on the basis of the virial theorem in terms of the wall potentials confining the electrons and nuclei. These definitions take a general form applicable without use of the adiabatic approximation. In this situation, we show that Janak's definition of the electron pressure in terms of the nuclear virial term is inappropriate; a similar statement holds for the definition of the stress tensor in this mixture. It is also demonstrated that both the electron and nuclear pressures become zero individually for a metal in vacuum, in contrast to the conventional understanding, according to which zero pressure is realized as a result of a cancellation of the electron and nuclear pressures. On the basis of these facts, a simple equation of state for liquid metals is derived, and it is examined numerically for the case of liquid alkaline metals by use of the quantum hypernetted chain equation and the Ashcroft model potential.