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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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A model of resonant collisions of electrons with molecules and molecular ions
Váňa, Martin ; Houfek, Karel (advisor) ; Cejnar, Pavel (referee) ; Mašín, Zdeněk (referee)
A two-dimensional model of the resonant electron-molecule collision processes with one nuclear and one electronic degree of freedom introduced by Houfek, Rescigno and McCurdy [Phys. Rev. A 73, 032721 (2006)] and a similar two- dimensional model of the dissociative recombination with potential proposed by Hamilton [Ph.D. thesis, University of Colorado, (2003)] are formulated within the time-dependent framework and solved numerically using the finite-element method with the discrete variable representation basis, the exterior complex scaling method and the generalized Crank-Nicolson method. On the model of electron-molecule collisions we illustrate how the time-dependent calculations can provide a deep insight into the origin of oscillatory structures in the vibrational excitation cross sections if one evaluates the cross sections not only at sufficiently large time to obtain the final cross sections, but rather at several characteristic times which are given by the evolution of the system. With use of the time- dependent calculations we demonstrate the complex nature of the dissociative recombination model dynamics and we propose the interpretation of the recom- bination process mechanism. We also propose few techniques for the explanation of the sharp structures in the dissociative recombination cross sections...
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Numerical determination of the scattering length for atomic collisions
Basler, Ondřej ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
The goal of this bachelor thesis is to compare numerical methods designed for the determination of scattering length for atomic collisions. We compare nume- rical solutions calculated by the method of direct integration of the Schrödinger equation, the variable phase equation, the Riccati equation for the scattering length and the method of exterior complex scaling. Methods are tested on the exponential potential and the empirical potential of the Cs-Cs dimer. Calculated scattering lengths are further compared with results from other autors. 1
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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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