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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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