Abstract
The correlation functions of liquid metals and normal liquids in the zero sound wave range are formulated using the quantum-mechanical two-time Green function method, and the classical formula of Bogolyubov-Sadovnikov and Nelkin-Ranganathan for normal liquids is extended to the quantum-mechanical case. The formula obtained clarifies the relation between the coherent-correlation function and the self-correlation function of a free gas, and becomes the quantum-mechanical extension of Kerr's classical formula for the relation. The effective potential obtained classically by Percus and Zwanzig from the direct correlation function is extended to the quantum-mechanical case, and the relation between the effective potential and S( k, E) is obtained. The effective potential between ions of liquid metals is formulated by taking into account the contribution from the conduction electrons. And the formula obtained by March is improved by taking into account the electron correlation effect together with the exchange interaction.
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