Huth, Frank Lukas (2018)
Local interactions and
shell-model interactions from
chiral effective field theory.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung
Kurzbeschreibung (Abstract)
The strong force is a vital contribution to both, nucleon-nucleon interactions as well as complicated nu- clear many-body systems. The theory of the strong interactions is quantum chromodynamics (QCD), but it is nonperturbative in the low-energy region of interest to us. Chiral effective field theory (EFT) pro- vides a systematic framework to derive low-energy few-body interactions and currents, based on, and consistent with all relevant symmetries of QCD. Short-distance physics is not resolved explicitly and gets absorbed in contact terms with so-called low-energy constants (LECs), which are adjusted to experimen- tal data. A power counting scheme sorts the different contributions according to their importance and a regularization scheme removes high-momentum modes which may otherwise lead to divergences. The resulting interactions are widely used in ab initio many-body calculations of nuclei and nuclear matter. Recently, efforts have been directed towards the development of local interactions from chiral EFT that can be applied directly in Quantum Monte Carlo calculations. Thus, this enables one to investi- gate chiral interactions in this powerful and statistically exact many body methods. In the first half of this thesis, we construct and analyze local two-body interactions from chiral EFT. In particular, we construct soft local interactions at leading order (LO), next-to-leading order (NLO), and next-to-next-to- leading order (N 2 LO) by enlarging the coordinate-space cutoff. Afterwards, we present first applications of the soft local interactions in 16 O– 16 O nucleus-nucleus scattering from double-folding potentials. In ad- dition, we investigate regulator and cutoff artifacts of local chiral interactions. We study effects from the violated Fierz-rearrangement freedom on phase shifts, nuclear matter calculations, and the 4 He ground-state energy. For this, we vary different LO-operator combinations for interactions at LO and NLO. Furthermore, the large-cutoff behavior of local interactions at LO on phase shifts is explored for dif- ferent functional forms of the regulator and for different operator combinations over a wide range of the inverse coordinate-space cutoff. We find that the broken Fierz-rearrangement freedom has sizable con- sequences at LO, but it is restored to a great extend at NLO, where subleading contact interactions enter. For a particular choice of those operators, nucleon-nucleon phase shifts and the deuteron ground-state energy converge to cutoff-independent plateaus. Those plateaus are at the same values, independent of the functional form of regulators we investigate. Even though, this does not imply that the power counting scheme is renormalizable, it allows the construction of harder interactions. In the second half, we construct valence-space Hamiltonians for shell-model calculations. The residual two-body interaction is based on symmetry principles and the low-momentum expansion from chiral EFT. We adjust the LECs to ground-state and excitation energies in the valence space. In addition to the usual free-space contact interactions, we also include novel center-of-mass–dependent operators that arise due to the Galilean invariance breaking by in-medium effects. We construct interactions up to fourth order (N 3 LO) for the sd and sd + 0 f 7/2 valence space. In the sd shell, at N 3 LO, we obtain a root-mean- square deviation to experiment of 0.16 MeV which is similar to that obtained with the phenomenological universal sd -shell interactions USDA and USDB. Even though the precision of our interactions in the sd + 0 f 7/2 valence space deteriorates, they provide interesting predictions for the one-neutron dripline of isotopes from oxygen to sodium. All our interactions lead to natural LECs and show promising predictions for ground-state energies and excitation spectra, which are not considered in the data set.
| Typ des Eintrags: | Dissertation | ||||
|---|---|---|---|---|---|
| Erschienen: | 2018 | ||||
| Autor(en): | Huth, Frank Lukas | ||||
| Art des Eintrags: | Erstveröffentlichung | ||||
| Titel: | Local interactions and shell-model interactions from chiral effective field theory | ||||
| Sprache: | Englisch | ||||
| Referenten: | Schwenk, Prof. Ph.D Achim ; Braun, Prof. Dr. Jens | ||||
| Publikationsjahr: | 2018 | ||||
| Ort: | Darmstadt | ||||
| Datum der mündlichen Prüfung: | 11 Juli 2018 | ||||
| URL / URN: | http://tuprints.ulb.tu-darmstadt.de/7645 | ||||
| Kurzbeschreibung (Abstract): | The strong force is a vital contribution to both, nucleon-nucleon interactions as well as complicated nu- clear many-body systems. The theory of the strong interactions is quantum chromodynamics (QCD), but it is nonperturbative in the low-energy region of interest to us. Chiral effective field theory (EFT) pro- vides a systematic framework to derive low-energy few-body interactions and currents, based on, and consistent with all relevant symmetries of QCD. Short-distance physics is not resolved explicitly and gets absorbed in contact terms with so-called low-energy constants (LECs), which are adjusted to experimen- tal data. A power counting scheme sorts the different contributions according to their importance and a regularization scheme removes high-momentum modes which may otherwise lead to divergences. The resulting interactions are widely used in ab initio many-body calculations of nuclei and nuclear matter. Recently, efforts have been directed towards the development of local interactions from chiral EFT that can be applied directly in Quantum Monte Carlo calculations. Thus, this enables one to investi- gate chiral interactions in this powerful and statistically exact many body methods. In the first half of this thesis, we construct and analyze local two-body interactions from chiral EFT. In particular, we construct soft local interactions at leading order (LO), next-to-leading order (NLO), and next-to-next-to- leading order (N 2 LO) by enlarging the coordinate-space cutoff. Afterwards, we present first applications of the soft local interactions in 16 O– 16 O nucleus-nucleus scattering from double-folding potentials. In ad- dition, we investigate regulator and cutoff artifacts of local chiral interactions. We study effects from the violated Fierz-rearrangement freedom on phase shifts, nuclear matter calculations, and the 4 He ground-state energy. For this, we vary different LO-operator combinations for interactions at LO and NLO. Furthermore, the large-cutoff behavior of local interactions at LO on phase shifts is explored for dif- ferent functional forms of the regulator and for different operator combinations over a wide range of the inverse coordinate-space cutoff. We find that the broken Fierz-rearrangement freedom has sizable con- sequences at LO, but it is restored to a great extend at NLO, where subleading contact interactions enter. For a particular choice of those operators, nucleon-nucleon phase shifts and the deuteron ground-state energy converge to cutoff-independent plateaus. Those plateaus are at the same values, independent of the functional form of regulators we investigate. Even though, this does not imply that the power counting scheme is renormalizable, it allows the construction of harder interactions. In the second half, we construct valence-space Hamiltonians for shell-model calculations. The residual two-body interaction is based on symmetry principles and the low-momentum expansion from chiral EFT. We adjust the LECs to ground-state and excitation energies in the valence space. In addition to the usual free-space contact interactions, we also include novel center-of-mass–dependent operators that arise due to the Galilean invariance breaking by in-medium effects. We construct interactions up to fourth order (N 3 LO) for the sd and sd + 0 f 7/2 valence space. In the sd shell, at N 3 LO, we obtain a root-mean- square deviation to experiment of 0.16 MeV which is similar to that obtained with the phenomenological universal sd -shell interactions USDA and USDB. Even though the precision of our interactions in the sd + 0 f 7/2 valence space deteriorates, they provide interesting predictions for the one-neutron dripline of isotopes from oxygen to sodium. All our interactions lead to natural LECs and show promising predictions for ground-state energies and excitation spectra, which are not considered in the data set. |
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| Alternatives oder übersetztes Abstract: |
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| URN: | urn:nbn:de:tuda-tuprints-76458 | ||||
| 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 > Kern- und Hadronenphysik 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik > Kerne und Materie an den Extremen 05 Fachbereich Physik > Institut für Kernphysik > Theoretische Kernphysik > Starke Wechselwirkung und ultrakalte Atome |
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| Hinterlegungsdatum: | 05 Aug 2018 19:56 | ||||
| Letzte Änderung: | 05 Aug 2018 19:56 | ||||
| PPN: | |||||
| Referenten: | Schwenk, Prof. Ph.D Achim ; Braun, Prof. Dr. Jens | ||||
| Datum der mündlichen Prüfung / Verteidigung / mdl. Prüfung: | 11 Juli 2018 | ||||
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