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Nuclear Matter from Chiral Effective Field Theory

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Nuclear Matter from Chiral Effective Field Theory Nuclear matter from chiral effective field theory Kernmaterie basierend auf chiraler effektiver Feldtheorie Zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Christian Drischler Tag der Einreichung: 17.10.2017, Tag der Prüfung: 15.11.2017 Darmstadt 2017 — D 17 1. Gutachten: Prof. Ph.D. Achim Schwenk 2. Gutachten: Prof. Dr. Jens Braun Fachbereich Physik Institut für Kernphysik Theoriezentrum Nuclear matter from chiral effective field theory Kernmaterie basierend auf chiraler effektiver Feldtheorie Genehmigte Dissertation von Christian Drischler 1. Gutachten: Prof. Ph.D. Achim Schwenk 2. Gutachten: Prof. Dr. Jens Braun Tag der Einreichung: 17.10.2017 Tag der Prüfung: 15.11.2017 Darmstadt 2017 — D 17 Bitte zitieren Sie dieses Dokument als: URN: urn:nbn:de:tuda-tuprints-69845 URL: http://tuprints.ulb.tu-darmstadt.de/id/eprint/6984 Dieses Dokument wird bereitgestellt von tuprints, E-Publishing-Service der TU Darmstadt http://tuprints.ulb.tu-darmstadt.de [email protected] Die Veröffentlichung steht unter folgender Creative Commons Lizenz: Namensnennung – Keine kommerzielle Nutzung – Keine Bearbeitung 4.0 international https://creativecommons.org/licenses/by-nc-nd/4.0/ Abstract Nuclear matter is an ideal theoretical system that provides key insights into the physics of different length scales. While recent ab initio calculations of medium-mass to heavy nuclei have demonstrated that realistic saturation properties in infinite matter are crucial for reproducing experimental binding energies and charge radii, the nuclear-matter equation of state allows tight constraints on key quantities of neutron stars. In the present thesis we take advantage of both aspects. Chiral effective field theory (EFT) with pion and nucleon degrees of freedom has become the modern low-energy approach to nuclear forces based on the symmetries of quantum chromodynamics, the fun- damental theory of strong interactions. The systematic chiral expansion enables improvable calculations associated with theoretical uncertainty estimates. In recent years, chiral many-body forces were derived up to high orders, allowing consistent calculations including all many-body contributions at next-to-next- to-next-to-leading order (N3LO). Many further advances have driven the construction of novel chiral potentials with different regularization schemes. Here, we develop advanced methods for microscopic calculations of the equation of state of homogeneous nuclear matter with arbitrary proton-to-neutron ratio at zero temperature. Specifically, we push the limits of many-body perturbation theory (MBPT) considerations to high orders in the chiral and in the many-body expansion. To address the challenging inclusion of three-body forces, we introduce a new partial-wave method for normal ordering that generalizes the treatment of these contributions. We show improved predictions for the neutron-matter equation of state with consistent N3LO nucleon-nucleon (NN) plus three-nucleon (3N) potentials using MBPT up to third order and self-consistent Green’s function theory. The latter also provides nonperturbative benchmarks for the many-body convergence. In addition, we extend the normal-ordering method to finite temperatures. Calculations of asymmetric matter require in addition reliable fit values for the low-energy couplings that contribute to the 3N forces. This was not the case for N3LO calculations. We present a novel Monte-Carlo framework for perturbative calculations with two-, three-, and four-nucleon interactions, which, including automatic code generation, allows to compute successive orders in MBPT as well as chiral EFT in an efficient way. The performance is such that it can be used for optimizing next-generation chiral potentials with respect to saturation properties. As a first step in this direction, we study nuclear matter based on chiral low-momentum interactions, exhibiting a very good many-body convergence up to fourth order. We then explore new chiral interactions up to N3LO, where simultaneous fits to the triton and to saturation properties can be achieved with natural 3N low-energy couplings. We perform a comprehensive Weinberg eigenvalue analysis of a representative set of modern local, semilo- cal, and nonlocal chiral NN potentials. Our detailed comparison of Weinberg eigenvalues provides various insights into idiosyncrasies of chiral potentials for different orders and partial waves. We demonstrate that a direct comparison of numerical cutoff values of different interactions is in general misleading due to the different analytic form of regulators. This shows that Weinberg eigenvalues also can be used as a helpful monitoring scheme when constructing new interactions. 1 3 3 Furthermore, we present solutions of the BCS gap equation in the channels S0 and P2 F 2 in neutron matter. Our studies are based on nonlocal NN plus 3N interactions up to N3LO as well as− the aforemen- tioned local and semilocal chiral NN interactions up to N2LO and N4LO, respectively. In particular, we investigate the impact of N3LO 3N forces on pairing gaps and also derive uncertainty estimates by taking into account results at different orders in the chiral expansion. In addition, different methods for obtaining self-consistent solutions of the gap equation are discussed. Besides the widely-used quasilinear method we demonstrate that the modified Broyden method is well applicable and exhibits a robust convergence behavior. Zusammenfassung Kernmaterie ist ein ideales, theoretisches System, das zentrale Einblicke in die Physik verschiedener Län- genskalen gewährt. Während ab initio Rechnungen von mittelschweren bis schweren Kerne vor kurzem gezeigt haben, dass realistische Saturierungseigenschaften in unendlicher Materie für die experimentalen Bindungsenergien und Kernradien wichtig sind, erlaubt die Zustandsgleichung von Kernmaterie starke Einschränkungen von Schlüsselgrößen für Neutronensternen. In der vorliegenden Dissertation machen wir uns beide Aspekte zu nutze. Die chirale effektive Feldtheorie (EFT), mit Pionen und Nukleonen als Freiheitsgraden, wurde zum moder- nen, niederenergetischen Zugang zu Kernkräften, basierend auf den Symmetrien der Quantenchromody- namik, der fundamentalen Theorie der Starken Wechselwirkung. Die systematische, chirale Entwicklung ermöglicht verbesserbare Rechnungen mit theoretischen Unsicherheitsabschätzungen. In den letzten Jah- ren wurden chirale Vielteilchenkräfte bis in hohe Ordnungen ausgearbeitet. Konsistente Rechnungen mit allen Vielteilchenbeiträgen auf der sogenannten „next-to-next-to-next-to-leading order“ (N3LO) sind daher möglich. Viele weitere Fortschritte führten zu der Entwicklung von neuen chiralen Potentialen innerhalb verschiedener Regularisierungschemen. Wir entwickeln fortgeschrittene Methoden für mikroskopische Berechnungen der Zustandsgleichung von homogener Kernmaterie mit beliebigem Proton-zu-Neutron-Verhältnis am Temperatur-Nullpunkt. Im Spe- ziellen setzen wir die Maßstäbe für Vielteilchen-störungstheoretische Ansätze zu hohen Ordnungen in der chiralen und der Vielteilchen-Entwicklung. Um die schwierige Einbindung von Dreinukleon-Kräften zu ermöglichen, führen wir eine neue Partialwellen-Methode für die Normalordnung ein, welche die Behandlung dieser Beiträge verallgemeinert. Wir treffen verbesserte Vorhersagen für die Zustandsglei- chung von Neutronenmaterie mit konsistenten N3LO Nukleon-Nukleon- (NN) plus Dreinukleon- (3N) Potentialen bis zur dritten Ordnung in der Vielteilchenstörungstheorie und in der Methode der selbstkon- sistenten Greens-Funktionen. Letztere erlaubt nichtperturbative Vergleichsrechnungen zum Bestimmen der Vielteilchenkonvergenz. Wir erweitern außerdem die Methode zur Normalordnung zu endlichen Temperaturen. Berechnungen von asymmetrischer Materie setzen zusätzlich zuverlässige Fitwerte für die Niederenergie- kopplungen, die zu den 3N Kräften beitragen, voraus. Das war bisher nicht der Fall für N3LO Rechnun- gen. Wir zeigen ein neues Monte-Carlo Framework für perturbative Rechnungen mit Zwei-, Drei- und Viernukleonen-Wechselwirkungen, das es auf effiziente Weise erlaubt (zusammen mit dem automatischen Generieren von Quellcode), verschiedene Ordnungen in der Störungstheorie als auch in der chiralen EFT zu berechnen. Die Leistungsfähigkeit der Methode ist so angelegt, dass sie zur Optimierung von neuen chiralen Potentialen im Sinne von Saturierungseigenschaften benutzt werden kann. Als einen ersten Schritt in diese Richtung, studieren wir Kernmaterie basierend auf evolvierten chiralen Wech- selwirkungen, welche eine sehr gute Vielteilchenkonvergenz bis zur vierten Ordnung aufweisen. Wir untersuchen dann neue chirale Wechselwirkungen bis zur N3LO, wobei simultane Fits an das Triton und an Saturierungseigenschaften mit natürlichen 3N-Niederenergiekopplungen erzielt werden können. Wir führen eine umfassende Weinberg-Eigenwert-Analyse mit einer repräsentativen Menge von moder- nen lokalen, semilokalen und nichtlokalen chiralen NN-Wechselwirkungen durch. Unsere detaillierten Vergleiche anhand von Weinberg-Eigenwerten gewähren verschiedenste Einblicke in die Eigenheiten von chiralen Potentialen für verschiedene Ordnungen und Partialwellen. Wie zeigen, dass ein direkter Vergleich von numerischen Cutoff-Werten für verschiedene Wechselwirkungen, aufgrund der unterschied- lichen analytischen Form von Regulatoren, täuschen kann. Das zeigt, Weinberg-Eigenwerte können auch als nützliche Hilfsmittel beim Erstellen von neuen Wechselwirkungen dienen. 1 3 3 Wir präsentieren
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