Resonances in Three-Body Systems
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Three particles interacting via Coulomb forces represent a fundamental problem in quantum mechanics with no known exact solution. We have investigated resonance states composed of three particles interacting via Coulombic and more general potentials in non-relativistic quantum mechanics, using the complex scaling method. Our calculations have been applied to three different systems.
(i) An investigation of resonances in the positron-alkali (Li, Na, K) systems has been conducted. Some calculations have previously been reported on the resonances in positron-alkali systems; however, most of the work was limited to the lower partial wave, such as S-wave resonances. In this thesis, we have extended the calculations to higher partial waves and extracted the resonance positions and widths using the more accurate complex scaling method. A dipole series of resonances has been found under positronium n = 2 threshold, for natural parity and n = 3 threshold for unnatural parity states. Furthermore, these resonances were found to agree well with an analytically derived scaling law. This series in the positron-alkali system are caused by the attractive potential formed by the dipole moment of positronium (the bound state of an electron and a positron). This dipole moment is a hydrogen-like system, and hence its energy levels are degenerate with respect to orbital angular momentum. We have also predicted several new resonances.
(ii) A calculation of resonances in positron-hydrogen scattering, which shows that we can represent this system with the accuracy needed for future scattering calculations. Such cross sections are of interest since this is a way to form anti-hydrogen.
(iii) A search for possible resonances in the pµe system, which has been suggested as a possible reason for unexpected results from a recent measurement of the proton radius in muonic hydrogen. We have ruled out the possibility of such resonances.
In all calculations we used the Couple Rearrangement Channel Method, where the wave function is represented by Gaussians expressed in Jacobi coordinates. Thus effects due to mass polarization are automatically.
Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2016. , 44 p.
Atom and Molecular Physics and Optics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:su:diva-128860ISBN: 978-91-7649-408-0OAI: oai:DiVA.org:su-128860DiVA: diva2:917244
2016-05-27, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Kino, Yasushi, Associate Professor
Jonsell, Svante, Associate professor
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Submitted. Paper 6: Submitted.
List of papers