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Elementary atomic collision processes in early Universe
Dvořák, Jan ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
Práce se zabývá kvantovou teorií rozptylu aplikovanou na reaktivní dvou- částicové srážky atom· a iont· v lokální aproximaci. Takovéto reakce vý- znamně ovlivnily vývoj raného vesmíru. Konkrétně jsou zde uvedeny vypočí- tané neelastické účinné pr·řezy dvou reakcí asociativního odtržení Li − a H, resp. Li a H − . Křivky potenciální energie byly získány z programového balíku pro kvantově chemické výpočty MOLPRO. Při řešení radiální Schrödinge- rovy rovnice s lokálním komplexním potenciálem byla použita Numerovova metoda. Účinné pr·řezy byly spočítány z komplexního fázového posunutí určeného z navázání numerického řešení na asymptotické řešení.
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Semiclassical Monte-Carlo method in three particle scattering.
Trnka, Jiří ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
The thesis discusses semiclassical Monte carlo method in three particle scattering. The basic procedure for calculating cross sections of reactions of a single atom with a diatomic molecule is summarized. For the purpose of testing the method, the cross sections of exchange reactions in system H2+H represented by Karplus Porter potential energy surface were calculated. The thesis also deals with chaotic behaviour of threeparticle scattering in a simple model system of coupled Morse potentials. The model system was expanded by incorporating the process of associative detachement, which was studied in combination with long chaotic trajectories. Powered by TCPDF (www.tcpdf.org)
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Particle interaction with atoms in optical lattice
Vozáb, Filip ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
The thesis discusses description of associative detachment of electron in the iont interaction with neutral atoms in optical lattice. This is given by combination of the model for interaction of particles in optical lattice, given by periodic potential, and of the model for associative detachment of electron, describe by imaginary component of the potential. In thesis is stated form of Schrödinger's equation for periodic potential, and subsequent solution of such equation in case of general complex and non hermitian Hamiltonian (because of imaginary component of potential). I specifically compute complex energetic levels one-dimensional model with numeric method from software package EISPACK for non hermitian Hamiltonian decomposed into finite base. Powered by TCPDF (www.tcpdf.org)
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Low-energy processes in H + H- collision
Eliášek, Jiří ; Čížek, Martin (advisor) ; Čurík, Roman (referee) ; Skála, Lubomír (referee)
In this work we generalize existing theory of low-energy collisions of atomic hydrogen with its anion. We extend the non-local resonance model for this system by adding new discrete state and two continua that are coupled with it. We calculate numerically cross sections for associative electron detachment process that is important for models of early universe. We add cross section for collision detachment and show spectra of outgoing electrons. We show how the isotopic effect is involved in studied collision. We also calculate charge transfer, elastic scattering cross sections, and reaction rates for hydrogen collisions with deuterium anion. We compare our results with recent experiments and we discuss their reliability. Powered by TCPDF (www.tcpdf.org)
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Analysis of the Stieltjes imaging method for the calculation of resonance widths
Votavová, Petra ; Kolorenč, Přemysl (advisor) ; Čížek, Martin (referee)
Title: Analysis of the Stieltjes imaging method for the calculation of resonance widths Author: Petra Votavová Department: Institute of Theoretical Physics Supervisor: RNDr. Přemysl Kolorenč, Ph.D., Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague Abstract: This thesis deals with the moment problem in the context of the resonance widths. The moment problem was solved by the Stieltjes imaging method and proposed alternative method based on the direct decomposition into the orthogonal basis. Three different basis derived from the Legendre polynomials were chosen. The properties of these methods were studied by analytical function. Eventually, both methods were applied to the calculation of resonance width of the metastable ion CH3F(2s-2 )2+ . Keywords: moment problem, Gaussian quadrature, orthogonal polynomials, resonance widths, decay of metastable ions
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Difraction of particle on slit with internal structure
Hudec, Matěj ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In this thesis we study the difraction of a particle on a slit, focusing on the resonance effects. The two-dimensional model containing a delta-function barrier with variable height which represents the slit is solved on a belt with periodic boundary condition. In most cases we use the numerical solution of the problem using our program. The results are compared with elastic approximations. We study the characteristics of the resonances in detail, the dependence of their existence, energy and height on the parameters of the slit, and the relation between resonances and bound states. The last chapter is devoted to the problem of spreading the belt in order to get the results that describe the scattering process on the whole plain. We suggest two ap- proaches of description of this process and demonstrate that the appearance of the resonances is not limited to the given boundary condition. 1
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Multimode vibrational dynamics of electron scattering from molecule
Táborský, Jiří ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
In the present work we study vibrational excitation of a generally polyatomic molecule by electron impact. We proceed from the theory of discrete state in continuum and the nonlocal resonance model and we approximate the molecule using two-dimensional harmonic oscillator. We have written numerical procedures in Fortran which compute a cross section of these collisions. The correctness of a transition from 1D model to 2D has been verified. We have performed several computations using different initial parameters and have studied the effect of changing selected parameters on the cross section depending on the energy of the incoming electron. Powered by TCPDF (www.tcpdf.org)
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Reactions of Hydrogen Molecules with Ions and Recombination of H+3 Ions with Electrons at Cryogenic Temperatures
Hejduk, Michal ; Glosík, Juraj (advisor) ; Čížek, Martin (referee) ; Votava, Ondřej (referee)
We studied how distribution of nuclear-spin states of H+ 3 ions or H2 molecules influence rate coefficients of H+ 3 -electron recombination or reactions of H2 with N+ or H+ , with regard to kinetic and internal temperatures of the reactants. Experiments were carried out in plasma environment or in an ensemble of ions in an ion trap. Main diagnostic methods were the Langmuir probe diagnos- tics, laser absorption- and mass spectroscopy. The distribution of nuclear spin states (para and ortho) was varied using a specially constructed para-hydrogen generator. We performed pioneer measurements of the rate coefficients for the nuclear-spin-state-selective binary and ternary H+ 3 -electron recombination in thermalised plasma. We performed studies of N+ + para/ortho-H2 reaction with high accuracy and interpreted the results as dependent on fine structure states of N+ ions. We measured a temperature dependence of the rate coeffi- cients for radiative and ternary channels of H+ + para/ortho-H2 association. 1
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Study of analytic behavior of scattering quantities in the nonlocal resonance model
Bednařík, Lukáš ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In the presented thesis we study analytical behavior of vibrational excitation cross sections and probability flux density in nonlocal resonance model. An analytical formula for determining the shape of Wigner cusps from three complex parameters is derived. The results of this formula are compared to numerical calculations with complex scaling method and interpreted within Feynman approach to quantum mechanics. Furthermore, we derive nonlocal continuity equation and show how it implies the multichannel optical theorem. Detail analysis of fluxes in the nonlocal resonance model is used to accelerate the convergence of formula for the dissociative attachment cross section and we present a simple model describing boomerang oscillations. A program in Fortran language is attached to this work. The program allows calculation of vibrational excitation and dissociative attachment cross sections, flux divergences and other quantities specified in this text.
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