|
|
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.
|
|
| |
|
|
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.
|
|
|
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.
|
|
| |
|
|
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.
|
|
|
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.
|
|
|
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.
|
|
| |
|
|
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
|
guest ::
