Compton scattering on complex materials [Elektronische Ressource] : an investigation on the electronic structure of alkali-metal doped Si-clathrates / vorgelegt von Martin Volmer

Compton Scattering on Complex Materials-an investigation on the electronic structureof alkali-metal doped Si-clathratesDISSERTATIONzur Erlangung des Doktorgrades derNaturwissenschaftendes Fachbereiches Physik der Universit¨at Dortmundvorgelegt vonMartin Volmer2006Table of contents IIIContentsTable of contents IIIIntroduction 11 Theory of Compton scattering 51.1 Inelastic x-ray scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 The non-relativistic double differential scattering cross-section . . . . . 61.3 The dynamic structure factor . . . . . . . . . . . . . . . . . . . . . . . 81.4 Impulse Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 The Compton profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 The free electron gas model . . . . . . . . . . . . . . . . . . . . . . . . 141.6.1 Electron-electron correlation . . . . . . . . . . . . . . . . . . . . 141.7 The asymmetry of Compton profiles and limitations of the ImpulseApproximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.8 Relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Models for the theoretical treatment of Compton profiles 192.1 The Hartree-Fock approximation . . . . . . . . . . . . . . . . . . . . . 192.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 The Khon-Sham equations . . . . . . . . . . . . . . . . . . . . . 212.2.