Feasibility study of resonant antiproton capture by ions and an open system approach to resonance decay

Abstract: The present thesis is based on two different projects. The first part deals withresonant capture of antiprotons by electron excitation in highly charged hydrogenlike ions.The search for this process was mentioned by an experimental group at the Max Planck Institute inHeidelberg (Germany) as a possible future project at the Facility for Low Antiproton andIon Research (FLAIR) at the "Gesellschaft f"ur Schwerionenforschung" (GSI) in Darmstadt (Germany),which motivated the theoretical feasibility study presented in this thesis.Illustrative calculations on the collision of antiprotons in the energyregion $Eapprox 0.13-0.14,{ m keV}$ with hydrogenlike calcium Ca$^{19+}$ have been carried outusing an approach which is common in dielectronic recombination (DR) calculations, justified by the factthat the process ofinterest can formally be seen as the exotic analogon of DR where the incoming electron is replaced byan antiproton.In particular, we investigated the doubly excited resonant electron-antiproton states that can eventually be formedin such a collision and estimated their positions as well as the rates of the possible decay channels. Based on this,first approximate predictions for the cross section of resonant antiproton capture are made.The second part of the thesis is devoted to resonances as well, but in quite a different context. Due to the couplingto the continuum, a quantum system that contains resonances can be treated as an {it open} quantum system. Such an approach,however, is often heuristic to a certain extent, because the theoretical decription of thedissipative interaction of an open system with its environment in many cases requires phenomenological constants that cannotbe determined from the first principles. To investigate whether such constants are connected to known parameters of a resonance(its width, in particular), the unitary time evolution of a model quantum system within the Schr"odinger equation iscompared to the non-unitary time evolution within the Lindblad master equation. For the chosen model potential, good agreementwas achieved and a relation between the resonance width and the phenomenological constants that appear in theLindblad-type equations of motion is suggested.