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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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Violation and Conservation of Symmetries in Atomic Systems
Uhlířová, Tereza ; Zamastil, Jaroslav (advisor) ; Čížek, Martin (referee) ; Pittner, Jiří (referee)
This thesis focuses on the three pillars of any high-precision ab initio calculation: on the Hartree-Fock (HF) model, on the choice of a suitable basis set, and on the inclusion of electron correlation. We start with a study of singular properties of the HF model. Specifically, we sys- tematically investigate the stability of all atomic closed-shell systems up to xenon using a symmetry-adapted Thouless stability matrix. To obtain a global view on the stability of a particular isoelectronic sequence, we employ high-order perturbative method and then analyze the obtained series. This allows us to determine onsets of spin and orbital symmetry breaking. In addition, we also propose a physical meaning of the instabilities. In the next part of this thesis, we focus on the use of the Sturmian basis set for relativistic calculations. We propose a numerically stable algorithm for the evaluation of one- and two-electron matrix elements. Thus we defeat the major impediment of a wider use of this basis set in precise atomic structure calculations. The use of the proposed method and its significance is illustrated on a series of calculations. For instance, we evaluate the so-called parity non-conserving amplitude for cesium; this is a second-order property and thus greatly depends on the accuracy of the used wave...
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Influence of intra-molecular vibrational modes on excitation energy transfer in molecular aggregates
Herman, Daniel ; Mančal, Tomáš (advisor) ; Zamastil, Jaroslav (referee)
The energy transfer in molecular aggregates is generally hard to describe in a simple yet effective manner. There is often a trade-off between the accuracy of simulated results and the level of understanding of the underlying physics. To understand the evolution of a system with electronic degrees of freedom, understanding the influence of the system's evolution on the evolution of the bath is also required. To obtain an insight into the bath evolution, we introduce an exact factorization of the density matrix elements representing an entangled state of the bath and the system. We leverage this factorization to derive iterative quantum master equations. Iterative treatment of bath evolution is then used to derive corrected memory kernel with correlation functions in a local basis with the assumption of linear harmonic oscillators as modes of the bath. This approach attempts to improve existing perturbative master equations in a regime of weak interaction between the system and the bath. To judge the improvement achieved, we apply the theory to systems with the finite bath of small size. 1
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Účinné průřezy srážek elektronů s atomy vodíku
Benda, Jakub ; Houfek, Karel (advisor) ; Zamastil, Jaroslav (referee)
Although the collisions of electrons and atomic hydrogen has been studied for several decades, there is still neither a complete database of scattering data, nor a universal method that would let generate such data. For astronomical and other purposes the cross sections of electron-hydrogen collisions are necessary, in a broad range of energies - from tenths of electronvolt to millions of electronvolts. In this work the author concentrates on several established approaches to electron-atom scattering and confronts results of his own implementations of these methods against the published data and results of freely available computer codes. A special attention is given to the overlaps of different methods, so that in the end a database with easy user interface can be offered for common practical usage of scattering data in applied fields.
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Astrophysically important processes in collisions of electrons with hydrogen atoms
Benda, Jakub ; Houfek, Karel (advisor) ; Stelbovics, Andris (referee) ; Zamastil, Jaroslav (referee)
Jakub Benda Astrophysically important processes in collisions of electrons with hydrogen atoms This thesis focuses on calculations of the cross sections and other scattering quantities that characterize the outcome of collisions of electrons with hydro- gen atoms. For the chosen energy range and atomic transitions the scattering process is solved within the non-relativistic quantum mechanics by discretiz- ation of the Schr¨odinger equation in the basis of B-splines, which transforms the equation into a linear-algebraic problem. The thesis discusses the boundary conditions, methods of solution of the linear system, preconditioning of the sys- tem and interpretation of results, including several original ideas that proved to be very beneficient for the calculations. The calculated data are provided by means of graphs at the end of the thesis. Also, a custom web-based scattering database containing the results has been set up, freely available to the expected audience of this project. 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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