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Coupled-Cluster Theory for Nuclear Structure

Binder, Sven (2014):
Coupled-Cluster Theory for Nuclear Structure.
TU Darmstadt, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/3946],
[Ph.D. Thesis]

Abstract

Nuclear Hamiltonians constructed within chiral effective field theory provide an unprecedented opportunity to access nuclear phenomena based on low-energy quantum chromodynamics and, in combination with sophisticated many-body methods, allow for an ab initio description of nuclei without resorting to phenomenology. This work focuses on the inclusion of chiral two-, and in particular three-body Hamiltonians into many-body calculations, with emphasis on the formal and computational aspects related to the three-body interactions. Through similarity renormalization group evolutions, the chiral Hamiltonians are transformed into a form in which strong short-range correlations are tamed in order to accelerate the convergence in the subsequent many-body calculations. The many-body method mainly used is an angular-momentum coupled formulation of coupled-cluster theory with an iterative treatment of singly and doubly excited clusters, and two different approaches to non-iteratively include effects of triply excited clusters. Excited nuclear states are accessed via the equation-of- motion coupled-cluster framework. The extension of coupled-cluster theory to three-body Hamiltonians is considered to verify the approximate treatment of three-nucleon interactions via the normal-ordering two-body approximation as a highly efficient and accurate way to include three-nucleon interactions into the many-body calculations, particularly for heavier nuclei. Using a single chiral Hamiltonian whose low-energy constants are fitted to three- and four-body systems, a qualitative reproduction of the experimental trend of nuclear binding energies, from 16O up to 132Sn, is achieved, which hints at the predictive power of chiral Hamiltonians, even in the early state of development they are at today.

Item Type: Ph.D. Thesis
Erschienen: 2014
Creators: Binder, Sven
Title: Coupled-Cluster Theory for Nuclear Structure
Language: English
Abstract:

Nuclear Hamiltonians constructed within chiral effective field theory provide an unprecedented opportunity to access nuclear phenomena based on low-energy quantum chromodynamics and, in combination with sophisticated many-body methods, allow for an ab initio description of nuclei without resorting to phenomenology. This work focuses on the inclusion of chiral two-, and in particular three-body Hamiltonians into many-body calculations, with emphasis on the formal and computational aspects related to the three-body interactions. Through similarity renormalization group evolutions, the chiral Hamiltonians are transformed into a form in which strong short-range correlations are tamed in order to accelerate the convergence in the subsequent many-body calculations. The many-body method mainly used is an angular-momentum coupled formulation of coupled-cluster theory with an iterative treatment of singly and doubly excited clusters, and two different approaches to non-iteratively include effects of triply excited clusters. Excited nuclear states are accessed via the equation-of- motion coupled-cluster framework. The extension of coupled-cluster theory to three-body Hamiltonians is considered to verify the approximate treatment of three-nucleon interactions via the normal-ordering two-body approximation as a highly efficient and accurate way to include three-nucleon interactions into the many-body calculations, particularly for heavier nuclei. Using a single chiral Hamiltonian whose low-energy constants are fitted to three- and four-body systems, a qualitative reproduction of the experimental trend of nuclear binding energies, from 16O up to 132Sn, is achieved, which hints at the predictive power of chiral Hamiltonians, even in the early state of development they are at today.

Divisions: 05 Department of Physics > Institute of Nuclear Physics
05 Department of Physics
Date Deposited: 25 May 2014 19:55
Official URL: http://tuprints.ulb.tu-darmstadt.de/3946
URN: urn:nbn:de:tuda-tuprints-39462
Referees: Roth, Prof. Dr. Robert and Wambach, Prof. Dr. Jochen
Refereed / Verteidigung / mdl. Prüfung: 23 April 2014
Alternative Abstract:
Alternative abstract Language
Nukleare Hamiltonoperatoren die aus chiraler effektiver Feldtheorie abgeleitet werden bieten eine einzigartige Gelegenheit, nukleare Phänomene auf Grundlage niederenergetischer Quantenchromodynamik zu untersuchen. In Verbindung mit fortgeschrittenen Vielteilchenmethoden ermöglicht dies eine ab initio Beschreibung von Atomkernen ohne auf Phänomenologie zurückzugreifen. Die vorliegende Arbeit beschäftigt sich mit der Inklusion chiraler Zwei-, und insbesondere Dreinukleonen-Hamiltonoperatoren in Vielteilchenrechnungen, mit Schwerpunkt auf den formalen und rechnerischen Aspekten der Behandlung der Dreinukleonenwechselwirkungen. Durch Evolution mittels der Similarity Renormalization Group werden die chiralen Hamiltonoperatoren derart transformiert, dass die starken kurzreichweitigen Korrelationen gemildert werden um die Konvergenz in den anschließenden Vielteilchenrechnungen zu beschleunigen. Die hauptsächlich eingesetzte Vielteilchenmethode ist eine drehimpulsgekoppelte Formulierung von Coupled-Cluster-Theorie mit einer iterativen Behandlung von ein- und zweifach angeregten Clustern, sowie einer nicht-iterativen Berücksichtigung dreifach angeregter Cluster. Angeregte Kernzustände werden über die Coupled-Cluster Bewegungsgleichungsmethode bestimmt. Es wird die Erweiterung von Coupled-Cluster-Theorie auf Dreiteilchen-Hamiltonoperatoren betrachtet um die Behandlung von Dreinukleonen-Wechselwirkungen in der Normalordnungsapproximation zu verifizieren als eine hochef- fiziente und akkurate Methode diese Wechselwirkungen näherungsweise in Vielteilchenrechnungen einzubeziehen, insbesondere für schwere Kerne. Ein einzelner Hamiltonoperator dessen Niederenergiekonstanten in Drei- und Vierteilchensystemen bestimmt wurden genügt, um den experimentellen Trend nuklearer Bindungsenergien von 16O bis 132Sn qualitativ zu reproduzieren was, trotz ihres gegenwärtig frühen Entwicklungsstadiums, auf das Potential chiraler Wechselwirkungen hinweist Vorhersagen zu ermöglichen. German
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