The direct correlation function of inhomogeneous quantum liquids

Within the framework of the Kohn-Sham-Mermin scheme (1965), the direct correlation function of inhomogeneous quantum liquids is defined from a thermodynamic argument. In terms of this quantal direct correlation function (QDCF), the WLMB equation derived by Wertheim, Lovett, Mou and Buff (1976) is extended to be applicable to a non-uniform quantum liquid, and the equation of state for inhomogeneous quantum liquids is derived with the use of the QDCF. Also, the definition of the QDCF is extended to the case of a non-uniform mixture, and applied to a liquid metal treated as an electron-ion mixture. As a result, the electron distribution around each ion in a liquid metal is obtained exactly within the neutral pseudo-atom model. Thus, the electrical resistivity and the effective ion-ion potential in the pseudopotential theory are much improved, since the QDCFs in their expressions take account of the non-linear effect properly.