Final state interaction and temperature effects in Compton scattering from lithium
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Date
2001-04-12
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Universität Dortmund
Abstract
In dieser Arbeit wird anhand von Lithium Compton Profilen, gemessen mit einer Impulsraumauflösung von 0.02 a.u. bei einer Primärenergie von 9 keV, der Einfluss der Endzustandswechselwirkung auf das Compton Profil der Valenzelektronen und damit die Gültigkeit der Stossnäherung in der Interpretation dieser Profile untersucht. Darüberhinaus werden Messungen der Temperaturabhängigkeit des Compton Profiles von Lithium bei einer Primärenergie von 30 keV und einer Impulsraumauflösung von 0.10 a.u. gezeigt. Beide Experimente werden im Hinblick auf die bekannte Diskrepanz zwischen gemessenen Compton Profilen und Ergebnissen aus Bandstrukturrechnungen im Rahmen der Lokalen Dichte Näherung diskutiert.
Die bei 9 keV erhaltenen Compton Profile der Valenzelektronen zeigen eine deutliche Asymmetrie. Weiterhin sind die durch die Theorie vorhergesagten scharfen Strukturen in der Nähe des Fermi Impulses trotz der sehr guten Impulsraumauflösung stark verschmiert. Die Asymmetrie wird durch Vielteilchen-Rechnungen, die sowohl Selbstenergie- als auch Vertexkorrekturen der effektiven Polarisationsfunktion berücksichtigen, gut wiedergegeben. Die unerwartete Verschmierung des Valenzprofiles wird auf den Einfluss der spektralen Dichtefunktion des angeregten Zustandes zurückgeführt. Die endliche energetische Breite der spektralen Dichtefunktion des angeregten Zustandes begrenzt die effektive Impulsraumauflösung in Messungen von Compton Profilen bei niedrigen Primärenergien. Unter diesen experimentellen Bedingungen versagt die Stossnäherung.
Die temperaturabhängigen Messungen der Lithium Compton Profile zeigen eine Verbreiterung des Valenzprofiles mit fallender Temperatur. Das Compton Profil der Rumpf-Elektronen weist keine Temperaturabhängigkeit auf. Der Temperatureffekt wird anhand von temperaturabhängigen Jellium- und Pseudopotential-Rechnungen diskutiert. In den Pseudopotential-Rechnungen wird ein empirisches lokales Pseudopotential benutzt und die Temperaturabhängigkeit über den Debye-Waller Faktor berücksichtigt. Durch den Vergleich zwischen den experimentellen Ergebnissen und den Rechnungen lässt sich der Temperatureffekt zum einen auf die Änderung der Gitterkonstante und zum anderen auf die Reduktion des Beitrages der Hochimpulskomponenten zum Valenzprofil mit steigender Temperatur zurückführen.
This thesis presents measurements of lithium Compton profiles with an incident energy around 9 keV and a momentum space resolution of 0.02 a.u. to investigate the effect of final state interaction and thus to test the validity of the impulse approximation in interpreting the valence electron Compton profile. Furthermore, the temperature dependence of the lithium Compton profile is studied at 30 keV incident energy and 0.10 a.u. momentum space resolution. Both experiments are discussed with respect to the well known discrepancy between experimentally found lithium Compton profiles and results from bandstructure calculations in local density approxiamtion. The valence Compton profiles measured at 9 keV show an asymmetric shape and the predicted sharp features at the Fermi break which should be resolved with the highly improved momentum space resolution are drastically smeared out. The asymmetry agrees well with calculations using a many-particle scheme including self-energy and vertex corrections of the proper polarization function. The additional broadening of the Compton profile is mainly attributed to the finite width of the spectral density function of the excited particle resulting in an intrinsic resolution limit for Compton profile measurements at low incident energies. Under these experimental conditions the application of the impulse approximation is not justified. The temperature dependent measurements of the lithium valence Compton profiles exhibit a narrowing of the valence electron Compton profile with increasing temperature. The Compton profile measured at 95 K is above the room temperature profile around the Fermi momentum and below at the Compton peak. No temperature dependence of the core electron contribution to the Compton profile is detected. The temperature effect is confronted with a temperature dependent jellium calculation and with computations utilizing an empirical local pseudopotential, where in the pseudopotential calculation the influence of temperature is considered via the Debye-Waller factor. With respect to the calculations the temperature effect is attributed to the lattice expansion and to the diminishing of the high momentum component contribution to the Compton profile with increasing temperature.
This thesis presents measurements of lithium Compton profiles with an incident energy around 9 keV and a momentum space resolution of 0.02 a.u. to investigate the effect of final state interaction and thus to test the validity of the impulse approximation in interpreting the valence electron Compton profile. Furthermore, the temperature dependence of the lithium Compton profile is studied at 30 keV incident energy and 0.10 a.u. momentum space resolution. Both experiments are discussed with respect to the well known discrepancy between experimentally found lithium Compton profiles and results from bandstructure calculations in local density approxiamtion. The valence Compton profiles measured at 9 keV show an asymmetric shape and the predicted sharp features at the Fermi break which should be resolved with the highly improved momentum space resolution are drastically smeared out. The asymmetry agrees well with calculations using a many-particle scheme including self-energy and vertex corrections of the proper polarization function. The additional broadening of the Compton profile is mainly attributed to the finite width of the spectral density function of the excited particle resulting in an intrinsic resolution limit for Compton profile measurements at low incident energies. Under these experimental conditions the application of the impulse approximation is not justified. The temperature dependent measurements of the lithium valence Compton profiles exhibit a narrowing of the valence electron Compton profile with increasing temperature. The Compton profile measured at 95 K is above the room temperature profile around the Fermi momentum and below at the Compton peak. No temperature dependence of the core electron contribution to the Compton profile is detected. The temperature effect is confronted with a temperature dependent jellium calculation and with computations utilizing an empirical local pseudopotential, where in the pseudopotential calculation the influence of temperature is considered via the Debye-Waller factor. With respect to the calculations the temperature effect is attributed to the lattice expansion and to the diminishing of the high momentum component contribution to the Compton profile with increasing temperature.
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Keywords
Röntgenstreuung, Compton Streuung, Lithium, Li, Compton Profil, Dynamischer Strukturfaktor, Elektronen Impulsdichte, Stossnäherung, Polarisationsfunktion, Korrelationseffekte, Vertexkorrektur, Selbstenergie, Spektrale Dichtefunktion, Endzustandseffekte, Fermi break, Renormalisierungskonstante, Reziproker Formfaktor, Temperatureffekte, Gitterausdehnung, Hochimpulskomponenten, Umklapp-Prozess, Debye-Waller Faktor, Bandstrukturrechnungen, Lokale Dichte Näherung, LDA, x-ray scattering, compton scattering, lithium, Li, Compton profil, dynamic structure factor, electron momentum density, impulse approximation, polarization function, correlation effects, vertex correction, self-energy, spectral density function, final state effects, fermi break, renormalization constant, reciprocal form factor, temperature effects, lattice expansion, high momentum components, Umklapp-process, Debye-Waller faktor, bandstructure calculation, local density approximation, LDA