Abstract
Near the melting point liquid alkali metals show positive dispersion, which can be described within generalized hydrodynamics as a visco-elastic reaction of the simple liquid. To understand an upward bending of the dispersion relation at small momentum transfer, treatment of pseudopotential theory on liquid potassium is performed at different temperatures in entire liquid regime. In the present study, we used the modified empty core potential due to Hasegawa et al. along with a local field correction due to Ichimaru-Utsumi (IU) to explain an electron-ion interaction. The potential used is composed of a full electron-ion interaction and a repulsive delta function to incorporate 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 for longitudinal phonon frequencies, and thus derived sound velocities and elastic modulii are compared with recent inelastic X-ray scattering experiment. It is found sufficient to carried temperature effect into the description only via the damping factor, keeping the volume of normal melting.
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