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Influence of relativistic effects on atomic spectra
Kasáček, Štěpán ; Zamastil, Jaroslav (advisor) ; Patkóš, Vojtěch (referee)
In this thesis we investigate solution of Dirac equation in spherically symmetric po- tential. The potential consist of Coulomb field of the nucleus and average potential of all other electrons in atom. We expand the solution of Dirac equation in finite Sturmian basis set. For this finite basis we introduce and investigate corresponding Foldy-Wouthuysen transformation. We apply the theory to the case of cesium atom. We find that non- relativistic energies are monotonically decreasing with increasing basis set. However, relativistic corrections cause oscillatory behaviour of energies present in fully relativistic case. 1
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Algebraic calculation of atomic integrals
Anderle, Vít ; Patkóš, Vojtěch (advisor) ; Zamastil, Jaroslav (referee)
The objective of this thesis is the examination of a novel method for the calculation of spectra of helium-like ions. In the helium atom, the electron-electron interaction is difficult to account for as it often leads to numerical instabilities. A reformulation of this problem is proposed. A purely algebraic approach is then taken, yielding exact formulas for the atomic integrals. A numerically stable procedure is eventually employed, recovering back the physical Coulomb interaction. 1
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Radiation corrections to atomic spectra
Patkóš, Vojtěch ; Zamastil, Jaroslav (advisor) ; Skála, Lubomír (referee)
Main aim of this work is calculation of contribution of the selfenergy of electron to atomic spectra. We derive relation for improved Bethe logarithm and perform non-relativistic limit. Then we derive relation for non-relativistic oscillator strengths and recurrence relations for them. This we will use for calculation of Bethe logarithm. Then we derive solution to Dirac equation for electron in Coulomb potential as linear combination of functions whose radial part is similar to non-relativistic hydrogen wave functions. Finally we perform numerical calculation of improved Bethe logarithm for 1s, 2s and 2p states.
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Radiation corrections to atomic spectra
Patkóš, Vojtěch ; Zamastil, Jaroslav (advisor) ; Hořejší, Jiří (referee) ; Čurík, Roman (referee)
Title: Radiation corrections to atomic spectra. Author: Vojtěch Patkóš Department: Department of chemical physics and optics Supervisor: doc. Mgr. Jaroslav Zamastil, Ph.D., KCHFO Abstract: In present time accuracy of spectroscopic measurements achieved fan- tastic accuracy 1 part in 10 to the power 14. If these measures are followed by theoretical calculations of similar accuracy we can test quantum electrodynamics and part of the standard model responsible for parity violating weak forces by comparing theory and experiment and set some of the basic physical constants like Rydberg constant, mass and radius of nucleus, constant of fine structure and it's variation in time etc. For achieving this kind of accuracy of calculations one must take into account so called radiation corrections. This thesis focus is on accurate calculation of the most important of them, the self-energy of electron in one-loop aproximation. Keywords: Quantum electrodynamics, radiation corrections, self-energy of elec- tron.
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Radiation corrections to atomic spectra
Patkóš, Vojtěch ; Skála, Lubomír (referee) ; Zamastil, Jaroslav (advisor)
Main aim of this work is calculation of contribution of the selfenergy of electron to atomic spectra. We derive relation for improved Bethe logarithm and perform non-relativistic limit. Then we derive relation for non-relativistic oscillator strengths and recurrence relations for them. This we will use for calculation of Bethe logarithm. Then we derive solution to Dirac equation for electron in Coulomb potential as linear combination of functions whose radial part is similar to non-relativistic hydrogen wave functions. Finally we perform numerical calculation of improved Bethe logarithm for 1s, 2s and 2p states.
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