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Multichannel models of Siegert states in electron collisions with molecules
Konvalinka, Matěj ; Mašín, Zdeněk (advisor) ; Čížek, Martin (referee)
This thesis uses the phenomenon of the Siegert states and the R-matrix approach to analyze quantum scattering. The main task of the work is to implement the multichannel R-matrix method and test it on model potentials before applying it to ab initio scattering calculations. I follow up on my bachelor thesis where we described the Siegert states and their influence on the cross section and did the analysis for a short-range potential in one channel. In this work, we implement the multichannel approach within the one-particle R-matrix method. The method is tested for multichannel potentials and the long-range dipole and Coulombic potentials. Then we implement our approach into the multi-electron R-matrix UKRmol+ codes and apply our method to real molecular systems. We analyze the results of electronically elastic and inelastic calculations. 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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Time evolution of resonant collisions of electrons with molecules
Mašín, Zdeněk ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
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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1D model of laser-assisted potential scattering
Tesař, Tomáš ; Mašín, Zdeněk (advisor) ; Kolorenč, Přemysl (referee)
The aim of this thesis is to investigate the effect of strong ultrashort electric fields on scattering of a particle by a short range potential, using a simple one-dimensional model. The interaction potential has the form of a simple potential step. The transmission amplitude is calculated using Fourier analysis of the scattered wavefunction. The scat- tered wavefunction is obtained by solving numerically the time-dependent Schrödinger equation combining the finite difference spatial representation with the Crank Nicholson method to approximate the evolution operator. We validate and test the method on the analytically solvable problem of scattering by a potential barrier without the presence of the external field. Finally, we apply the method to calculation of laser assisted trans- mission through the potential barrier and find that transmission through the barrier can be strongly enhanced or suppressed depending on the choice of the field parameters. We provide elementary clues on interpretation of our findings. 1
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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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Calculations of photoelectron spectra of small water clusters using the independent molecule model
Šklíba, Pavel ; Mašín, Zdeněk (advisor) ; Čížek, Martin (referee)
The aim of this thesis is to investigate theoretically photoelectron spectra of small water molecular clusters. This work is motivated by the recent experimental results of Hartweg et al [Phys. Rev. Letters 118, 103402, 2017] which showed that with an increasing number of constituent molecules in the water cluster the asymmetry parameter characterizing the photoelectron angular distribution converges to a universal shape. At the moment there are no theoretical calculations to support this finding. Therefore, we have developed a very simple model of photoionization of molecular clusters based on the use of photoionization data for a single molecule. We have found that the results of our model are sensitive to the different conformations of the clusters. Some of our results for the photoelectron angular distribution exhibit trends observed in the experiment. Nevertheless, the validity of our model will have to be studied in the future with the help of accurate calculations before the results can be conclusively interpreted.
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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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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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