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Rezonanční srážky elektronů s molekulami
Formánek, Martin ; Houfek, Karel (advisor) ; Kolorenč, Přemysl (referee)
In the present work we study different approaches for solving the nuclear dy- namics of resonant electron molecule collisions. Namely, we review two methods addressing this phenomenon which are a local complex potential (LCP) approxi- mation and a nonlocal resonance model (NRM). We briefly discuss a numerical implementation of these methods. We show how to derive model parameters for both of them from fixed-nuclei scattering calculations and we implement them in the time independent picture of quantum mechanics. We compare their vibrational excitation cross sections for the diatomic molecule CO. Then we generalize the non- local resonance model for systems with more nuclear degrees of freedom. Output of our work is a computer code producing the vibrational excitation cross sections for systems with two degrees of freedom. We aim to use this code for studying a threshold behavior of the low-energy electron collisions with the CO2 molecule and therefore we review a current state of understanding for this phenomenon. Mea- nwhile we test the functionality of the code by comparing results with those of the LCP approximation on a simple 2D model system.
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Účinné průřezy srážek elektronů s atomy vodíku
Benda, Jakub ; Houfek, Karel (advisor) ; Zamastil, Jaroslav (referee)
Although the collisions of electrons and atomic hydrogen has been studied for several decades, there is still neither a complete database of scattering data, nor a universal method that would let generate such data. For astronomical and other purposes the cross sections of electron-hydrogen collisions are necessary, in a broad range of energies - from tenths of electronvolt to millions of electronvolts. In this work the author concentrates on several established approaches to electron-atom scattering and confronts results of his own implementations of these methods against the published data and results of freely available computer codes. A special attention is given to the overlaps of different methods, so that in the end a database with easy user interface can be offered for common practical usage of scattering data in applied fields.
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Časově závislé řešení dvourozměrných rozptylových problémů v kvantové mechanice
Váňa, Martin ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
The scope of this thesis is in the time-dependent formulation of the two dimensional model of resonant electron-diatomic molecule collisions in the range of low energies. In its time independent form the model was previously numerically solved without the Born-Oppenheimer approximation with use of modern tools such as the finite element method with discrete variable representation (FEM-DVR) or exterior complex scaling (ECS). Within the scope of this model we numerically solve the evolution problem, with use of the Crank-Nicolson method and the Padé approximation. Later we evaluate the cross section of the elastic and some inelastic processes with the correlation function approach. At last we make a comparison of the evolution and the cross sections to time dependent formulation of the local complex potential approximation of the electron-molecule collisions.
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Description of narrow resonances using two-potential formula
Bednařík, Lukáš ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
In the presented thesis we study tunneling problems with projection formalism and two potential approach. We apply this approximative method proposed by S.A. Gurvitz in [4] to two new potentials with a quasistationary state. In the next chapter we generalize this method to one-dimensional nonsymmetric potential. A new formula is found and used for calculation of energy width. We compare our results with a numerical method of complex scaling. Finally, we discuss three-dimensional potential. One axis of symmetry is assumed and we derive relatively simple formula for energy width.
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Time evolution of resonant collisions of electrons with molecules
Mašín, Zdeněk ; Čížek, Martin (referee) ; Houfek, Karel (advisor)
In the present work we study an alternative formulation of the so called nonlocal resonant model, which describes collisions of electrons with molecules. In our approach we solve a system of differential equations describing time-dependent nuclear dynamics of the collision process instead of solving a standard equation with nonlocal potential. The goal of this work was to find a suitable numerical method for solution of those equations, test it on a model problem and on the problem of resonant collision of electron with molecule H2. Obtained results are in very good agreement with reference results from the standard calculations.
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