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Resonances in Three-Body Systems
Stockholm University, Faculty of Science, Department of Physics. (Theoretical Atomic physics)
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.
National Category
Atom and Molecular Physics and Optics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-128860ISBN: 978-91-7649-408-0 (print)OAI: oai:DiVA.org:su-128860DiVA: diva2:917244
Public defence
2016-05-27, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Submitted. Paper 6: Submitted.

 

Available from: 2016-05-02 Created: 2016-04-06 Last updated: 2017-02-24Bibliographically approved
List of papers
1. A search for resonances in the p mu e system
Open this publication in new window or tab >>A search for resonances in the p mu e system
2014 (English)In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 47, no 17, 175003Article in journal (Refereed) Published
Abstract [en]

The charge radius of the proton has recently been determined from 2s-2p spectroscopy of muonic hydrogen, giving a result which significantly deviates from earlier measurements. One hypothesis is that this discrepancy could arise because a metastable p mu e state is formed under the p mu (2s) threshold. We search for such a state by considering the three-body pex and p mu x systems, where x is a particle with charge -e and a mass which is varied between the electron and muon mass. We identify a new class of resonances, which extends the mass range allowing formation of resonances compared to an earlier work. We conclude that no p mu e resonances relevant for 2s-2p spectroscopy in muonic hydrogen can exist.

Keyword
proton radius, muonic hydrogen, three-body systems, resonances
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-108371 (URN)10.1088/0953-4075/47/17/175003 (DOI)000341976100003 ()
Note

AuthorCount:2;

Available from: 2014-10-24 Created: 2014-10-22 Last updated: 2017-12-05Bibliographically approved
2. Natural and unnatural parity resonance states in positron-hydrogen scattering
Open this publication in new window or tab >>Natural and unnatural parity resonance states in positron-hydrogen scattering
2014 (English)In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 47, no 22, 225001Article in journal (Refereed) Published
Abstract [en]

We present an investigation of resonances with natural and unnatural parities in positron scattering with atomic hydrogen. The complex scaling method has been used. Resonance states for natural parity pi=(-1)(J) with total angular momenta J = 0 - 2 and unnatural parity pi = (-1)(J+1) with J = 1, 2 are calculated. Resonance energies and widths are reported and compared with other theoretical calculations.

Keyword
positron-hydrogen scattering, positronium, resonances
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-110530 (URN)10.1088/0953-4075/47/22/225001 (DOI)000344499200002 ()
Note

AuthorCount:2;

Available from: 2014-12-16 Created: 2014-12-16 Last updated: 2017-12-05Bibliographically approved
3. Resonances with natural and unnatural parities in positron-sodium scattering
Open this publication in new window or tab >>Resonances with natural and unnatural parities in positron-sodium scattering
2015 (English)In: Physical Review A, ISSN 2469-9926, Vol. 92, 012706Article in journal (Refereed) Published
Abstract [en]

We present an investigation of resonances in positron-sodium scattering using the complex scaling method. For the target sodium atoms, the interaction between the core and outer electron is treated using two different types of analytical model potentials. Explicitly correlated Gaussian wave functions are used to represent the correlation effects between the outer electron, the positron, and the Na+ core. S-, P-, and D-wave resonances with natural parity have been calculated for energies extending up to the positronium n = 2 formation threshold. Resonance states for unnatural parities Pe and D0 have been calculated for energies extending up to the positronium n = 3 threshold. Below both positronium thresholds we have for each symmetry identified a dipole series of resonances, with binding energies scaling in good agreement with expectations from an analytical calculation. The presented results are compared with other theoretical calculations.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-124120 (URN)10.1103/PhysRevA.92.012706 (DOI)
Available from: 2015-12-14 Created: 2015-12-14 Last updated: 2016-04-11Bibliographically approved
4. Resonances in positron-potassium ($e^{+}$-K) system with natural and unnatural parities
Open this publication in new window or tab >>Resonances in positron-potassium ($e^{+}$-K) system with natural and unnatural parities
2016 (English)In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 49, no 1, 015004Article in journal (Refereed) Published
Abstract [en]

We present an investigation of resonances with natural and unnatural parities in the positron-potassium system using the complex scaling method. A model potential is used to represent the interaction between the core and the valence electron. Explicitly correlated Gaussian wave functions are used to represent the correlation effects between the valence electron, the positron and the K+ core. Resonance energies and widths for two partial waves (S- and P-wave) below the K(4p, 5s, 5p, 4d, 4f) excitation thresholds and positronium n = 2 formation threshold are calculated for natural parity. Resonance states for P-e below the K(4d) excitation threshold and positronium n = 2, 3 formation thresholds are calculated for unnatural parity which has not been previously reported. Below both positronium thresholds we have found a dipole series of resonances, with binding energies scaling in good agreement with exceptions from an analytical calculation. The present results are compared with those in the literature.

Keyword
resonances, positronium, three-body system, dipole series
National Category
Atom and Molecular Physics and Optics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-124121 (URN)10.1088/0953-4075/49/1/015004 (DOI)000367153800009 ()
Available from: 2015-12-14 Created: 2015-12-14 Last updated: 2017-12-01Bibliographically approved
5. Positronium-dipole induced resonances in e$^{+}$-H and e$^{+}$-alkali systems
Open this publication in new window or tab >>Positronium-dipole induced resonances in e$^{+}$-H and e$^{+}$-alkali systems
(English)In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455Article in journal (Refereed) Submitted
National Category
Atom and Molecular Physics and Optics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-128703 (URN)
Available from: 2016-03-31 Created: 2016-03-31 Last updated: 2017-11-30Bibliographically approved
6. Resonances in a positron-lithium (e(+)-Li) system
Open this publication in new window or tab >>Resonances in a positron-lithium (e(+)-Li) system
2016 (English)In: Physical Review A, ISSN 2469-9926, Vol. 93, no 5, 052707Article in journal (Refereed) Published
Abstract [en]

The method of complex scaling is used to calculate S- and P-wave resonance energies and widths below the Li(3s, 3p, 4s, 4p) excitation thresholds and positronium n = 2 formation threshold in the positron-lithium system. We use two different types of model potentials to determine the interaction between the core and the valence electron. Explicitly correlated Gaussian basis functions are used to represent the correlation effects between the valence electron, the positron, and the Li+ core. A dipole series of resonances are found under the positronium n = 2 threshold. Furthermore, these resonances are found to agree well with an analytically derived scaling law. The present results are compared with those in the literature.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-131492 (URN)10.1103/PhysRevA.93.052707 (DOI)000376239900008 ()
Available from: 2016-06-21 Created: 2016-06-20 Last updated: 2017-02-01Bibliographically approved

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