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Báze vlnových balíků v popisu rezonančního rozptylu
Lukeš, Petr ; Kolorenč, Přemysl (advisor) ; Houfek, Karel (referee)
Title: Wave-packet basis in the description of the resonance scattering Author: Petr Lukeš Institute: Institute of Theoretical physics Supervisor: RNDr. Přemysl Kolorenč, Ph.D., Institute of Theoretical Physics Abstract: A common approach towards the solution of problems of particle scattering problems is the approximation of the wavefunctions with some set of square integrable functions. A new type of such basis is assessed in this work. The vectors of the basis are obtained by integration of eigenvectors of free Hamiltonian over finite intervals of energies. This basis is called the wave- packet basis. This basis is used to compute values of resonance width and resonant energy for two simple cases and the results are compared to benchmark data known from other works. The results serve to evaluate the properties of this basis. Also this work contains a proposal of how could this basis be applied in computations of quantum scattering. Keywords: potential scattering, wave-packet basis, resonance width, resonant energy.
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Computing resonance widths using square integrable basis
Votavová, Petra ; Kolorenč, Přemysl (advisor) ; Houfek, Karel (referee)
Four different non-orthogonal basis sets are studied and compared in order to obtain the resonance properties of a model scattering problem. In particular, two types of Gaussian basis sets, one B-spline basis set and one hybrid Gaussian - B-spline basis set. Their ability to represent the scattering continuum is investigated along with their numerical properties. Particular attention is paid to the energy range within which each basis set gives reasonably accurate values of the phase shift and the decay width. The radial Schrödinger equation is solved by the Löwdin's symmetric orthogonalization method and the decay width is extracted by the Stieltjes imaging procedure. The R-matrix method within the framework of Feshbach-Fano projection operator formalism with polynomial basis set is utilized as a numerically exact reference method.
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Resonant collisions of electrons with diatomic molecules
Alt, Václav ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
This work aims at calculating the cross sections for vibrational excitation of the oxygen molecules by collisons with electrons. Potential energy curves are obtained with standard quantum chemistry methods and the R-matrix method with good agreement with measurable molecular properties, the cross sections are calculated within the local complex potential approximation. It was shown that the results obtained with different, but seemingly satisfactory settings can vary by a significant degree. Comparison with experimental data then point out the insufficiency of the local complex potential approximation. Powered by TCPDF (www.tcpdf.org)
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Investigation of quantum reaction dynamics using semiclassical method.
Táborský, Jiří ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In the presented thesis we study quantum reaction dynamics of H2O- using semiclassical method. Using ab initio quantum potential evaluated on a fine grid we derive analytical formula for potential energy surface, which is used for solving classical equations of motion. A reaction path is analyzed using contour plots with a focus on a saddle point area. Reaction dynamics analysis is focused on properties of interaction probability and cross section depending on impact parameter, collision energy and initial vibrational state of interacting molecule. Final results are compared with experimental data.
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor) ; Čurík, Roman (referee)
The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H$_2^+$ by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics. Powered by TCPDF (www.tcpdf.org)
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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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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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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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Model průchodu dvojitou bariérou s anharmonickými vibracemi
Gráf, Lukáš ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In the presented thesis we study the electron scattering off a molecular junction with anharmonic vibrations. This junction we simulate by a double barrier in- cluding the cosine dependence on the vibrational coordinate. The electron trans- mission through the barrier can be viewed as movement of the electron on the surface of infinitely long cylinder with zero potential energy everywhere except for a finite region where it is described by delta function terms. We solve this 2D problem employing the transfer matrix method and we present also the scat- tering theory approach to the problem. Using our own program we compute the numerically exact transmission probability and we investigate its dependence on parameters characterizing the model. We compare particular parametric regimes with various approximations which can be used for given settings. The elastic scattering is approximated by one-dimensional and Chase approximations where- as in case of vibrational excitation we employ the LCP approximation. Resulting graphs affirm that these approximation methods often used in molecular physics work very well.
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