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Aspects of the Many-Body Problem in Nuclear Physics

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Aspects of the Many-Body Problem in Nuclear Physics Aspects of the Many-Body Problem in Nuclear Physics DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Alexander Signatur Dyhdalo, MSc, BSc Graduate Program in Physics The Ohio State University 2018 Dissertation Committee: Prof. Richard Furnstahl, Advisor Prof. Robert Perry Prof. Michael Lisa Prof. Junko Shigemitsu c Copyright by Alexander Signatur Dyhdalo 2018 Abstract Low-energy nuclear physics has seen a renaissance of activity recently with the advent of the nuclear effective field theory (EFT) approach, the power of renormalization group techniques, and advances in the computational cost-effectiveness and sophistication of quan- tum many-body methods. Nevertheless challenges remain in part from ambiguities of the nuclear Hamiltonian via regulator artifacts and the scaling of the many-body methods to heavier systems. Regulator artifacts arise due to a renormalization inconsistency in the nuclear EFT as currently formulated in Weinberg power counting, though their ultimate impact on nuclear observables is unknown at present. This results in a residual cutoff dependence in the EFT to all orders. We undertake an examination of these regulator artifacts using perturba- tive energy calculations of uniform matter as a testbed. Our methodology has found that the choice of regulator determines the shape of the energy phase space and that different regulators weight distinct phase space regions differently. Concerning many-body calculations, at present only phenomenological energy density functionals are able to solve for the full table of nuclides. However these functionals are currently unconnected to QCD and have no existing method for systematic improvement. A technique, the density matrix expansion (DME), is one way to add microscopic chiral physics into these energy functionals. We develop a new formulation of the DME using local coordinate space regulators and allow for explicit Delta isobars in the chiral potentials. The resulting functionals show systematic improvement order-by-order in the chiral expansion and have non-trivial improvements in nuclear binding energy residuals over the previous Skyrme state of the art. ii Furthermore, renormalization group methods have also proved quite successful at tam- ing certain nonperturbative aspects of nuclear potentials. However at present a robust many-body power counting scheme for these softened interactions is lacking. We take ten- tative first steps in this direction by creating quantitative estimates for perturbative energy diagrams in nuclear matter for the particle-particle and hole-hole channel. Our estimates are validated to, in some cases, the few percent level and confirm that nuclear potentials are perturbative in these channels given a certain amount of renormalization group evolution. We also examine the widely used normal-ordered two-body approximation and set rigorous bounds for its validity in the case of a pure three-nucleon contact. Finally, we also implement a new many-body method for calculating nuclear systems. The method, termed reduced density matrix mechanics, originates from quantum chemistry where it has undergone a rebirth in the past few decades. The method parameterizes the many-body system via so-called reduced density matrices and solves the system with an algorithm termed semidefinite programming. We explore this method's formalism and implementation in a testbed system of neutron drops. We rigorously validate the method for the case of a one-body interaction and achieve accurate results for a two-body Minnesota potential. iii The self shines in space through knowing. iv Acknowledgments I would like to thank a few of my friends who made graduate school so much more enjoyable: Michael \Big Mike" Chilcote, Dave \Double D" Dawson, Evan Jasper, Tim McCormick, Greg Smith, and Kevin Wong. Whether chatting over colloquium donuts, playing Dungeons and Dragons, or procrastinating while doing homework late at night, our interactions and conversations have always been thought-provoking and enjoyable. I'd also like to thank my peers on the PRB mezzanine floor, Dennis Bazow and Russell \Rooster" Colburn. Both of you provided great companionship and intellectual stimulation throughout our classes and trials in the first few years of graduate school. Our late nights spent doing quantum field theory and particle physics homework in particular stand out in my mind (we'll get that 1-loop calculation down yet!). The mezzanine was also home to my research group and the associated colorful characters who have passed through it: Ryan Caulfield, Jordan Melendez, Sushant More, Sarah Wesolowski, Matthias Heinz, Heiko Hergert, Sebastian Koenig, along with my officemate Chris Plumberg. If anything is worthy of a divine reward, it would be your collective patience in enduring my ceaseless questions, tangents, and presentations. The collective antics and great times we've had together are too lengthy to recount here but a few highlights are: celebrating Heiko's birthday in Santa Fe and going hiking the next day, leaving Columbus at 5 AM to catch an early flight to a DNP conference, and exploring the various cities we've been so lucky to visit (Santa Fe, Vancouver, Pittsburgh, and Chicago). I'd also particularly like to acknowledge the housemates I've had for the past 4 years: Thuc Mai, Steve \The Asian Sensation" Tjung, Matt Sheffield, Tim Gorman, and honorary housemate Stephen \Beard" Hageman. I cherish all the times we've spent together exploring v Columbus, brewing beer, relaxing on the deck, traveling places (New York, Mammoth Cave, DC), and going camping. All you guys are so special to me and a person couldn't ask for a greater group of friends. Graduate school would have been far poorer without all of you coming along for the ride. I'd also like to single out for special mention some of the teachers who were a critical part of molding me into my present self. In particular I'd like to mention Joanne Roschmann, my English & Humanities teacher from middle school, and Preston Hayes, my chemistry teacher from high school. Both of them impressed on me the virtue of critical thinking and pursuing a life of the mind. Without their formative guidance, I would not be who I am today. My advisor Dick Furnstahl also deserves special mention. I've been continually aston- ished at his wealth of knowledge (both within physics and outside it), sharp mind, patience with students, intellectual stamina, positive attitude, and passion for science. He is an exemplary scientist who has earned every superlative uttered of him. I would be remiss if I also didn't mention the support given to me by my girlfriend Richelle Romanchik. Her encouragement, understanding, and belief in me carried me through on some difficult days. She has enriched my life immeasurably and we've both grown so much in the last two years. I look forward to our next adventure together wher- ever that may be! Also, I would not be where I am today without the foundational support and motiva- tion given to me by my parents, Nestor Dyhdalo and Diane Signatur. They have always emphasized the transformative power of education though they were likely surprised when I said I wanted to go back to graduate school to pursue my PhD in physics. However they always encouraged me to follow my passion and were incredibly supportive. Their sacrifices and diligence allowed me to become the person I am today, something for which I will be forever grateful. Finally, I'd like to mention my sister who I love so much. I made it Kate! vi Vita September 17, 1987 . Born|Evanston, IL May, 2010 . BSc, University of Illinois Urbana- Champaign December, 2014 . MSc, The Ohio State University Publications R. Navarro Prez, N. Schunck, A. Dyhdalo, R. J. Furnstahl, S. K. Bogner , (2018) [in press] A. Dyhdalo, S. K. Bogner, and R. J. Furnstahl , Phys. Rev. C 96, 054005 (2017) A. Dyhdalo, S. K. Bogner, and R. J. Furnstahl , Phys. Rev. C 95, 054314 (2017) A. Dyhdalo, R. J. Furnstahl, K. Hebeler, and I. Tews , Phys. Rev. C 94, 034001 (2016) Fields of Study Major Field: Physics vii Table of Contents Page Abstract........................................... ii Dedication......................................... iv Acknowledgments.....................................v Vita............................................. vii List of Figures ...................................... xii List of Tables ....................................... xxi 1 Introduction ..................................... 1 1.1 Overview and Brief History........................... 1 1.2 QCD........................................ 4 1.2.1 Chiral Symmetry............................. 7 1.2.2 Chiral Symmetry Breaking ....................... 8 1.3 Effective Theories of QCD............................ 10 1.3.1 Chiral Perturbation Theory....................... 11 1.3.2 Chiral Effective Field Theory...................... 14 1.3.3 The NN Potential............................ 18 1.3.4 Similarity Renormalization Group ................... 21 1.4 Many-Body Problem............................... 25 1.4.1 Liquid Drop Model and Nuclear Matter................ 30 1.4.2 Hartree-Fock ............................... 35 1.4.3 Density Functional Theory ....................... 37 1.4.4 Reference States ............................. 45 1.5 Thesis Overview ................................. 46 Chapters 2 Regulator Artifacts in Uniform Matter ................................... 53 2.1 Motivation and Overview ...........................
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