Abstract
Liquid alkali metals show, near the melting point, an upward bending of the dispersion relation at small momentum transfer values. This so-called positive dispersion can be described within generalized hydrodynamics as a visco-elastic reaction of the liquid. There is a speculation that long-living clusters could be the physical reason behind this phenomenon. To shed light on this question a treatment of pseudopotential theory on liquid sodium was performed at different temperatures starting at the melting point. In the present study, we used the modified empty core potential due to Hasegawa et al. (J. Non-Cryst. Solids, 117/118 (1990) 300) along with a local field correction due to Ichimaru-Utsumi (IU) to explain electron-ion interaction. The potential used is composed of a full electron-ion interaction and a repulsive delta function, which represents the orthogonalisation effect due to the s core states. The temperature dependence of pair potential is calculated by using the damping term exp(-πkBTr/2kF). While the expression for phonon dispersions are derived within the memory function formalism. Results thus obtained are well compared with the other theoretical and experimental results.
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