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Vícekanálové modely Siegertových stavů v atomech a molekulách
Thesis title in Czech: Vícekanálové modely Siegertových stavů v atomech a molekulách
Thesis title in English: Multi-channel models of Siegert states in atoms and molecules
English key words: Scattering theory|S-matrix|Riemann surface|R-matrix theory|resonance|virtual state
Academic year of topic announcement: 2021/2022
Type of assignment: diploma thesis
Thesis language: čeština
Department: Institute of Theoretical Physics (32-UTF)
Supervisor: Mgr. Zdeněk Mašín, Ph.D.
Author: hidden - assigned by the advisor
Date of registration: 14.04.2022
Date of assignment: 14.04.2022
Familiarization with the basic theory of multi-channel scattering in non-relativistic quantum mechanics. Implement a numerical method for finding Siegert states in a multi-channel system. Apply the theory to model various types of resonances and virtual states in atoms and molecules, e.g.: Feshbach resonances in short-range multi-channel systems, Siegert states in a realistic (i.e. non-spherical) model of dipolar systems and their motion on physical and non-physical sheets of the Riemann surface, application of the method of pole removal to study the effect of resonances in electron collisions with HNCO molecule and singly ionized Xenon atom.
R.G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (1982).
V.I. Kukulin, V.M. Krasnopolsky, J.Horáček, Theory of resonances: principles and applications, (1989).
L.A. Morgan and P.G. Burke, J. Phys. B: At. Mol. Opt. Phys. 21, 2091 (1988).
H. Estrada and W. Domcke, J. Phys. B: At. Mol. Opt. Phys. 17, 279 (1984).
D. B. Milosevic et al, J. Phys. B: At. Mol. Opt. Phys. 43 015401 (2010).
Chen et al, Physical Review A 91, 032503 (2015).
Preliminary scope of work in English
In quantum mechanics of collision processes the basic quantity that is obtained in experiments is the scattering cross section which is a measure of the strength of interaction between the incoming particle and the target. The scattering cross section depends on the energy of the incoming particle and can have a complicated shape depending on the processes that take place during the collision.

For example the process of electron-atom collision can be strongly influenced by formation of so called virtual and resonant states of the electron during the collision. However, an unambiguous identification of these states may be difficult especially in collisions where more channels (such as electronic excitation of the atom) are open. The resonant and virtual states are special cases of so called Siegert states which are solutions of the Schrodinger for complex momenta (energies).

In this work we will focus on development of analytic and numerical methods for direct computation of the Siegert states in simple models of quantum mechanical systems. This work will result in the development of a general methodology for a detailed analysis of computed scattering cross sections. This work can be extended by implementation of this approach into sophisticated ab initio codes for studying electron collisions with atoms and molecules.
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