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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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Jaderné kolektivní stupně volnosti a Skyrme funkcionál
Božík, Daniel ; Kvasil, Jan (advisor) ; Cejnar, Pavel (referee)
Title: Energy functional theories in nuclear physics Author: Daniel Božík Department: Institute of Particle and Nuclear Physics of Charles University Supervisor: prof. RNDr. Jan Kvasil, DrSc. Supervisor's e-mail address: kvasil@ipnp.troja.mff.cuni.cz Abstract: In the present work we study the giant resonances of the chain of even-even samarium nuclei 144−154 Sm. The numerical calculations are provided by a chain of numer- ical codes. Mean field is calculated by the HFB method for the Skyrme density functional and the residual interaction is included by the separable RPA method, which was devel- oped at IPNP MFF UK and JINR Dubna. The studied resonances are E1, E2 and M1. A special interest is paid to pygmy and scissor modes. The dependence of the pygmy modes on the deformation of nuclei is studied. The linear dependence of the integral scissor mode strength on the square of the nuclear deformation is verified within our microscopic model. Keywords: Skyrme functional, separable RPA, electric and magnetic giant resonances
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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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Statistical aspects of nuclear collective dynamics
Macek, Michal ; Cejnar, Pavel (advisor) ; Kvasil, Jan (referee) ; Mareš, Jiří (referee)
The current PhD thesis presents a collection of selected articles related to the theoretical and numerical study of low-energy collective dynamics of atomic nuclei. The articles were published or recently submitted to international physics journals and were authored or co-authored by the author of the thesis. The eects in collective dynamics have been studied within the framework of two common models-the interacting boson model (IBM) and to a lesser extent the geometric collective model (GCM). The "statistical aspects" in the title relate predominantly to the interplay of ordered and chaotic behavior observed in properties of quantum eigenstates as well as in the classical limits of the models. The main attention was devoted to correlations between the measures of regularity/chaos and the presence of exact and approximate dynamical symmetries. An important subject of the studies were also the relationships between the properties of the classical and quantum solutions of the models both in the integrable regime as well as in the mixed regime containing elements of regularity and chaos simultaneously.
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Hypernuclear production in K--stopped reactions
Krejčiřík, Vojtěch ; Cieplý, Aleš (advisor) ; Kvasil, Jan (referee)
The thesis focuses on -hypernuclear production induced by K meson stopped at an atomic orbit. Calculations are performed within the framework of the distorted wave impulse approximation. We use a microscopic model based on chiral perturbation theory for the description of the elementary kaon-nucleon process. The use of the microscopic model is one of the assets of the present work. Another novelty is a proper treatment of the pion distortion in the eective nucleon density available for the reaction. We consider several kaon-nucleus and pion-nucleus potentials. We study various eects on the capture rate of the reaction. We compare our results with experimental data and with previous calculations. Although our results are closer to the experimental values then the results of previous authors, the agreement with experiment is still unsatisfactory.
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Study of exotic hypernuclei
Posolda, Petr ; Mareš, Jiří (advisor) ; Kvasil, Jan (referee)
The thesis focuses on the study of properties of exotic hypernuclei, particularly of beryllium, carbon, oxygen and neon isotopes with and hyperons. Calculations were performed in the framework of the relativistic mean field theory (RMF) where a (hyper)nucleus is treated as a system of Dirac spinors (nucleons, hyperons) interacting via (mean) meson fields. The exotic hypernuclei were considered as axial symmetric. Up to now, hypernuclear calculations have been performed under assumption of spherical symmetry. This work thus extends hypernuclear calculations to the region of exotic, generally deformed systems. For the above nuclei, the numerical calculations of the binding energies and root mean square radii were performed. Moreover, we studied influence of the tensor interaction between meson and hyperon on the spin-orbit splitting. The results confirmed that the presence of the hyperon increases values of the binding energy of a system and on the contrary, it decreases its root mean square radius. We studied the possibility of the existence of the hyperon bound states in a nucleus. For the above isotopes, no bound states were found for the + hyperons. On the other hand, weekly bound states of the - hyperon are predicted for several isotopes.
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Analysis of dijet events in diffractive ep interactions with tagged leading proton at the H1 experiment
Polifka, Richard ; Kvasil, Jan (advisor)
Title: Analysis of dijet events in diffractive ep interactions with tagged leading proton at the H1 experiment Author: Richard Polifka Department: Institute of Particle and Nuclear Physics Supervisor: RNDr. Alice Valkárová, DrSc. Supervisor's e-mail address: avalkar@mail.desy.de Abstract: An inclusive dijet production in diffractive deep-inelastic scattering is measured. The diffractive selection is based on tagging of the leading proton in the Forward Proton Spectrometer. The statistics of events obtained during the HERA II running period (integrated luminosity of 156.7 pb−1 ) enables the measurement of jet final states with leading proton for the first time. The data cover the phase space of xIP < 0.1, |t| ≤ 1.0 GeV2 and 4 ≤ Q2 ≤ 110 GeV2 . The dijet data are compared with the next to leading order predictions of the quantum chromodynamics (QCD). The phase space of diffractive dijets is in this analysis by factor of 3 in xIP larger than in previous measurements. The QCD predictions based on the DGLAP parton evolution describe the measured data well even in a non-DGLAP enriched phase space where one on the jets goes into the region close to the direction of the outgoing proton. The measured single-differential cross sections are compared to several Monte Carlo models with different treatment of...
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Microscopic nuclear models for open-shell nuclei
Herko, Jakub ; Knapp, František (advisor) ; Kvasil, Jan (referee)
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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