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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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Analysis of collision processes in quantum mechanics using Siegert states
Konvalinka, Matěj ; Mašín, Zdeněk (advisor) ; Houfek, Karel (referee)
The main task of the work is to analyze the interaction of a particle with a spherically symmetric field in quantum mechanics using so-called Siegert states. In the first chapter we solve the scattering problem analytically for square well. Then we describe Siegert states and we demonstrate their influence on observable quantities (scattering cross of the interaction) using the analytic approach. In the second chapter we implement the numerical resolution of Schrödinger equation using the R-matrix method in the B-spline basis. In the third chapter we present results of the numerical method and validate it by comparison with the analytic solution obtained earlier. The main output of this work is implementation and verification of a numerical method enabling manipulation and analysis of S-matrix poles in simple radial scattering problems.
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor)
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.
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Electron attachment to proton in transmission through graphene.
Ondrašek, Matúš ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In the presented thesis we study the proton neutralization in transmission through graphene. In this transmission, the proton either captures one electron and produces a neutral hydrogen atom, or captures two electrons to form a hydrogen anion or passes through without capture. The aim of this work is theoretically to describe this process by means of quantum mechanics, to calculate the reduction of the proton's kinetic energy in transmission through graphene and to determine the probability of the proton transmission without capture, the probability of the proton catching one electron and the dependence of these probabilities on proton energy and various parameters model. In the work we will introduce and then compare two models - first a simple model that assumes motionless graphene and a constant energy of the proton and then a more complicated model that allows us to determine the change of the proton energy in addition to the probability of capture.
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Collisions of electrons with diatomic molecules
Matoušek, Mikuláš ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
For succesfully carrying out R-matrix calculations, a good description of the excited states of the neutral molecule around the equilibrium is needed, obtained by an ab-initio method in a relatively small basis. It is also neccesary to have potential curves of the neutral molecule and the anion that are consistent with the experimentally obtained values for the molecule and are used to set up the initial parameters of these calculations. In this work we are trying to find a description of the excited states and to obtain reference curves in order to perform R-matrix calculations for two molecules, BeH and OH. For BeH we propose a description of the excited states by the SA-CASSCF method with an active space of 6,2,2,0 and in the aug-cc-pVDZ basis. Similarly for OH a description by the SA-CASSCF method with an active space of 6,2,2,0 or 7,3,3,0 and an in an aug-cc-pVDZ basis should be used, where we have also found a setting of the weights of the states in the SA-CAS-SCF method significantly improving the shape of the curves. We have not yet been able to perform the R-matrix calculations because of insufficient time. 1
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Classical and quantum chaotic dynamics in reactive scattering of atoms and molecules.
Trnka, Jiří ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
The thesis deals with quantum reaction dynamics of three-particle systems. The thesis summarizes main theoretical results about three-body problem in quantum mechanics. A simple two dimensional model of three-particle system corresponding to atom-diatom collision was studied as a part of this thesis. The model allows for vibrational excitation and reaction processes. Solution based on distorted-wave method and Schwinger variational principle is proposed to solve the model. Proposed method of solution is then applied to a system of three coupled Morse potential energy surfaces. Probabilities of possible proces- ses depending on energy of incoming particle were calculated using the proposed method of solution for two variants of coupled Morse PESs. 1
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Two-dimensional model of dissociative recombination
Hvizdoš, Dávid ; Houfek, Karel (advisor)
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.
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Astrophysically important processes in collisions of electrons with hydrogen atoms
Benda, Jakub ; Houfek, Karel (advisor) ; Stelbovics, Andris (referee) ; Zamastil, Jaroslav (referee)
Jakub Benda Astrophysically important processes in collisions of electrons with hydrogen atoms This thesis focuses on calculations of the cross sections and other scattering quantities that characterize the outcome of collisions of electrons with hydro- gen atoms. For the chosen energy range and atomic transitions the scattering process is solved within the non-relativistic quantum mechanics by discretiz- ation of the Schr¨odinger equation in the basis of B-splines, which transforms the equation into a linear-algebraic problem. The thesis discusses the boundary conditions, methods of solution of the linear system, preconditioning of the sys- tem and interpretation of results, including several original ideas that proved to be very beneficient for the calculations. The calculated data are provided by means of graphs at the end of the thesis. Also, a custom web-based scattering database containing the results has been set up, freely available to the expected audience of this project. 1
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