Dietz, Sebastian (2023)
Continuum structure of few-body systems.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00023025
Dissertation, Erstveröffentlichung, Verlagsversion
Kurzbeschreibung (Abstract)
The focus of this work is on the study of states on the unphysical sheets of the complex energy plane for few-particle systems using potentials derived from leading order pionless effective field theory. The aim is to obtain a statement about the continuum structure of the three-neutron system. For this purpose, various methods are applied. These allow the computation of observables on both, the physical and unphysical sheets. This group of methods is complemented by calculations in finite volume. On the basis of different two-particle test systems, methods for the calculation of the phase shifts and time delays, the analytical continuation in the coupling constant (ACCC) and the analytical continuation of the Lippmann-Schwinger equation to the unphysical sheet are compared with each other by the difficulty and possibilities of their application and the quality of their results. In the following, different three-particle system are considered. First, the method of analytical continuation is applied to a system of three spinless bosons. This offers the possibility to investigate resonances as well as virtual states on both unphysical sheets connected to the physical one. Furthermore, three-particle systems containing spin are considered. First, the phase shift anomaly of the neutron-deuteron system is investigated. Subsequently the three-neutron system is considered. For this purpose, first the phase shifts on the physical sheet are extracted by extrapolation from a bound to the physical dineutron. In the following, the pole structure of the three-neutron system on the unphysical sheet is investigated by analytical continuation. In both cases, no sign of a resonance or a virtual state is found. This result is supported by the calculation of the point production amplitude and its comparison with the predictions of the nonrelativistic conformal field theory. The point production amplitude is further derived for a four-neutron system as well as for the system of the three spinless bosons. The system of the three bosons serves here as a benchmark for the existence of a resonance. Finally, using the Lüscher formalism, the spectra of the dineutron-neutron as well as the dineutrondineutron scattering for unphysically bound dineutrons in finite volume are calculated. In both cases, it is shown that even for an unphysically increased interaction strength neither three- nor four-neutron resonances occur. In summary, this work shows using different methods, that the three-neutron system neither presents resonances nor virtual states. Furthermore, the non-existence of resonances in the four-neutron system is motivated by two methods.
Typ des Eintrags: | Dissertation | ||||
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Erschienen: | 2023 | ||||
Autor(en): | Dietz, Sebastian | ||||
Art des Eintrags: | Erstveröffentlichung | ||||
Titel: | Continuum structure of few-body systems | ||||
Sprache: | Englisch | ||||
Referenten: | Hammer, Prof. Dr. Hans-Werner ; Schwenk, Prof. Ph.D Achim | ||||
Publikationsjahr: | 2023 | ||||
Ort: | Darmstadt | ||||
Kollation: | xii, 175 Seiten | ||||
Datum der mündlichen Prüfung: | 19 Dezember 2022 | ||||
DOI: | 10.26083/tuprints-00023025 | ||||
URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23025 | ||||
Kurzbeschreibung (Abstract): | The focus of this work is on the study of states on the unphysical sheets of the complex energy plane for few-particle systems using potentials derived from leading order pionless effective field theory. The aim is to obtain a statement about the continuum structure of the three-neutron system. For this purpose, various methods are applied. These allow the computation of observables on both, the physical and unphysical sheets. This group of methods is complemented by calculations in finite volume. On the basis of different two-particle test systems, methods for the calculation of the phase shifts and time delays, the analytical continuation in the coupling constant (ACCC) and the analytical continuation of the Lippmann-Schwinger equation to the unphysical sheet are compared with each other by the difficulty and possibilities of their application and the quality of their results. In the following, different three-particle system are considered. First, the method of analytical continuation is applied to a system of three spinless bosons. This offers the possibility to investigate resonances as well as virtual states on both unphysical sheets connected to the physical one. Furthermore, three-particle systems containing spin are considered. First, the phase shift anomaly of the neutron-deuteron system is investigated. Subsequently the three-neutron system is considered. For this purpose, first the phase shifts on the physical sheet are extracted by extrapolation from a bound to the physical dineutron. In the following, the pole structure of the three-neutron system on the unphysical sheet is investigated by analytical continuation. In both cases, no sign of a resonance or a virtual state is found. This result is supported by the calculation of the point production amplitude and its comparison with the predictions of the nonrelativistic conformal field theory. The point production amplitude is further derived for a four-neutron system as well as for the system of the three spinless bosons. The system of the three bosons serves here as a benchmark for the existence of a resonance. Finally, using the Lüscher formalism, the spectra of the dineutron-neutron as well as the dineutrondineutron scattering for unphysically bound dineutrons in finite volume are calculated. In both cases, it is shown that even for an unphysically increased interaction strength neither three- nor four-neutron resonances occur. In summary, this work shows using different methods, that the three-neutron system neither presents resonances nor virtual states. Furthermore, the non-existence of resonances in the four-neutron system is motivated by two methods. |
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Alternatives oder übersetztes Abstract: |
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Status: | Verlagsversion | ||||
URN: | urn:nbn:de:tuda-tuprints-230252 | ||||
Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik | ||||
Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik 05 Fachbereich Physik > Institut für Kernphysik 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik > Starke Wechselwirkung und ultrakalte Atome |
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Hinterlegungsdatum: | 24 Jan 2023 13:11 | ||||
Letzte Änderung: | 31 Jan 2023 08:59 | ||||
PPN: | |||||
Referenten: | Hammer, Prof. Dr. Hans-Werner ; Schwenk, Prof. Ph.D Achim | ||||
Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 19 Dezember 2022 | ||||
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