# A dispersion relation for simple metals

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## Abstract

In this thesis, the role of simple interactions in metals is investigated. This is done by first building a theoretical dispersion relation for simple metals and then applying it to the fee metals aluminum and copper, assuming appropriate forms for the ion-ion Interaction and for the electron-ion interaction. For the purpose of this work, the lon-ion interaction Is represented by the sum of a Coulomb Interaction and a non-Coulombic short range interaction due to the overlap of core electron wave functions of different Ions, and the electron-ion interaction is taken to be simply an attractive Coulomb Interaction. In addition, the self-consistent-field Hartree dielectric constant is used in the screening terms. For each of the metals, calculations of Ionic frequencies consist of two parts. In the first part, the short range interaction is neglected, and ion frequencies for the (1,0,0) symmetry direction are calculated. In the second part, the short range Interaction is Included by giving it the form of a Yukawa interaction, treating the strength and the range as parameters to force the best possible agreement between theory and experiment. Dispersion curves for the three symmetry directions (1,0,0), (1,1,0), and (1,1,1) are calculated in this part. The calculations reveal that aluminum is characterized by long range forces and that copper is characterized by short range forces. In the case of copper, excellent agreement is obtained with experimental dispersion curves for all three symmetry directions.