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Modeling atomic nuclei using supercomputers for precision tests of the Standard model
Rojik, Matúš ; Dytrych, Tomáš (advisor) ; Knapp, František (referee)
One of the most important problems of modern theoretical nuclear physics is to accu- rately determine the structure of atomic nuclei. To obtain results that are in agreement with experimental data, one needs to solve the nuclear many-body problem with high enough precision. Ab initio methods address this problem by trying to solve the emergent Schrödinger equation for all nucleons with a realistic interaction. Until recently, they were applicable only to light nuclei because of the high computational demands. In this work, we briefly present the theory behind the symmetry-adapted no-core shell model, which allows for truncation of the model space based on innate symmetry of nuclei that leads to reduction of the Hamiltonian matrix dimensions, while the convergence of the full space is conserved. We explore its predictive power by studying beta decays of various nuclei and discuss possible applications of the symmetry-adapted no-core shell model for the study of physics beyond the Standard Model. 1
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Many-body methods within the nuclear Lipkin model
Folprecht, Radek ; Knapp, František (advisor) ; Kvasil, Jan (referee)
Title: Many-body methods within the nuclear Lipkin model Author: Radek Folprecht Institute: Institute of Particle and Nuclear Physics Supervisor: Mgr. František Knapp Ph.D., Institute of Particle and Nuclear Physics Abstract: The subject of the present thesis is the Lipkin model, a two- level degenerated quantum system enhanced by two-body interactions. The exact solutions and properties of the model are reviewed and summarized. Several many-body methods common in nuclear physics are used to solve the eigenvalue problem of the time-independent Schrödinger equation. The many-body methods applied to the Lipkin model in the present thesis are the Hartree-Fock mean-field method, the random phase approximation, the Tamm-Dancoff approximation, and the Bardeen-Cooper-Schrieffer method. We propose an instructive iterative extension to the random phase approxi- mation method. For the listed methods, we provide a comprehensive com- parison of the approximation quality for either the ground state energy or excited state energies. Keywords: Lipkin model, Hartree-Fock mean-field method, random phase approximation, Bardeen-Cooper-Schrieffer method 1
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Gigantické rezonance v atomových jádrech
Repko, Anton ; Kvasil, Jan (advisor) ; Knapp, František (referee)
Skyrme functional is commonly used for the description of ground-state and dynamical properties of atomic nuclei. To describe the dynamical properties in the microscopic self-consistent way, we employed Separable Random Phase Approximation (SRPA) based on Skyrme functional. This work describes theory of Skyrme Hartree-Fock and SRPA and presents numerical calculation of E1 and M1 giant resonances in spherical nuclei Ca-40 - Fe-56. There is some evidence for non-zero ground-state deformation of the nucleus Fe-56, so it is treated also with such assumption. The results obtained for various parametrizations are compared to the experimental data.
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Regular and chaotic collective motions of atomic nuclei
Hruška, Petr ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
This thesis deals with quantum chaos in the geometric collective model of atomic nuclei (GCM). The rst and second chapters introduce the derivation and analysis of basic aspects of the GCM. Two ways of quantization are introduced for zero rotations of the nucleus. The rst one takes into account only the vibrational degrees of freedom and does not correspond to real nuclei. The second way reects both vibrational and rotational degrees of freedom and leads to the standard GCM. The third chapter includes analytical calculations of matrix elements of the GCM in the harmonic oscillator basis. Some measures of chaos are described in the fourth chapter, including the method based on Peres lattices. Numerical results for both quantization methods are presented in the form of Peres lattices, which are compared with some adopted results of other measures of chaos.
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Quantal and thermal phase transitions in atomic nuclei
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
In this bachelor work phase transitions in atomic nuclei are studied. The main attention is paid to quantal phase transitions between nuclear ground states of different symmetry. First, the interacting boson model in its simplest version, IBM-1, is introduced. The correspondence between the IBM and the geometric model of nuclei is indicated and possible shapes of the nucleus in the ground state are introduced. In the next step, critical and degenerated critical points of the potential derived from the IBM-1 are investigated in detail, especially their dependence on parameter values of the potential. Degenerated critical points are classified using the catastrophe theory. The special values of potential parameters are found for which phase transitions of the first and second order occur. Finally, the possibility of substitution of the potential by canonical catastrophic functions in a vicinity of degenerated critical points is discussed.
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Photon strength functions in 162Dy from two-step gamma cascade measurement
Chudoba, Petr ; Krtička, Milan (advisor) ; Knapp, František (referee)
Photon strength functions quantities, which describe deexcitation of nucleus by emiting gamma rays within statistical model of the nucleus. Information about these quantities can be gained from study of two-step gamma cascades. The thesis is focused on processing of experimental data from measurement of these cascades in 162Dy nucleus. Data were acquired using experimental set-up istalled on the research reactor in Řež near Prague. In the experiment the 161Dy targed was bombarded by thermal neutrons. Following gamma deexcitation of 162Dy nucleus was measured by coincident spectrometer composed of two semi-conductor detectors. The aim of the thesis is to perform energy and efficiency calibration and to process experimental data into the form of two-step gamma cascades spectra. In adition, a comparsion of the two-step cascades spectra with the outcome of simulations of a few basic models of photon strength functions is made.
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Analysis of residual correlations in nuclear masses after application of Garvey-Kelson relations
Mičo, Samuel ; Stránský, Pavel (advisor) ; Knapp, František (referee)
This thesis is focused on the analysis of residual correlations bet- ween deviations of nuclear masses from Garvey-Kelson relations, which are local algebraic relations connecting masses of neighbouring nuclei. Properties of the correlation matrix determined by the deviations from Garvey-Kelson relations and by the calculated spectral correlations are consistent with the hypothesis formulated beforehand, that it is possible to understand the deviations as statis- tically independent fluctuations in a good agreement. Therefore, the masses of nuclei cannot be described by a global function of the number of protons and neutrons with an accuracy greater than the size of the deviations, i.e. with an accuracy better than an order of 100 keV. Principal component analysis shows that the largest residual correlations are located (i) in the area of magic numbers and (ii) between strongly deformed heavy nuclei.
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Microscopic nuclear models for open-shell nuclei
Herko, Jakub ; Knapp, František (advisor)
Title: Microscopic nuclear models for open-shell nuclei Author: Jakub Herko Institute: Institute of Particle and Nuclear Physics Supervisor: Mgr. František Knapp, Ph.D., Institute of Particle and Nuclear Physics Abstract: Since the nucleus is a quantum many-body system consisting of con- stituents whose mutual interaction is not satisfactorily known, it is necessary to use approximate methods when describing the nucleus. Basic approximate approaches in the microscopic theory of the nucleus are the Hartree-Fock the- ory, Tamm-Dancoff approximation and random phase approximation. They are described in the first chapter of this thesis. The main aim was to develop mi- croscopic models for open-shell nuclei with two valence particles or holes. They are described in the second chapter, which contains detailed derivations of the relevant formulae. These methods have been numerically implemented. The re- sults of the calculations of the nuclear spectra and the electromagnetic transition probabilities are presented in the third chapter. Keywords: Tamm-Dancoff approximation, random phase approximation, open- shell nuclei, nuclear spectra, electromagnetic transition probabilities ii
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