Nuclear Physics at Low Renormalization Group Resolution PDF Download

Author: Anthony J. Tropiano
Publisher:
ISBN:
Category : Nuclear forces (Physics)
Languages : en
Pages : 0

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Book Description
Low-energy nuclear physics encompasses the physics of many-body systems of protons and neutrons (nucleons) ranging from atomic nuclei to neutron stars. Experimental facilities, such as the Facility of Rare Isotope Beams (FRIB), seek to answer overarching questions central to our understanding of atomic nuclei, astrophysics, and fundamental symmetries, such as the origin of heavy elements. Theoretical approaches face the challenge of describing this wide range of physics starting from the force between nucleons. Traditionally, low-energy nuclear theory is split into structure and reaction theory, where the former deals with the static properties of nuclei and the latter with dynamic nuclear processes. Understanding the interplay of reaction and structure theory is critical for reliable predictions and analysis of FRIB experiments. The renormalization group (RG) allows for consistent treatments of reaction and structure. RG transformations continuously shift the resolution scale of structure and reaction components (i.e., wave functions and reaction operators) under a specified scheme, where the resolution scale corresponds to the largest momentum of low-energy wave functions, and the scheme reflects the details of the starting Hamiltonian and RG implementation. Observable quantities are invariant under RG transformations, though structure and reaction components individually depend on the RG resolution scale and scheme. We can take advantage of this latter RG dependence by shifting the resolution scale to make complicated problems feasible. RG transformations decouple low- and high-energy scales in nuclear interactions, facilitating large-scale nuclear structure approaches that rely on many-body basis expansions. The RG has widely been applied to nuclear structure, but not to nuclear reactions or the combination of the two. RG transformations can facilitate nuclear reaction approaches by simplifying initial and final states in transition matrix elements, where RG-transformed reaction operators gain induced many-body contributions. Process-independent quantities (e.g., momentum distributions) can be extracted from experiment via a factorization of nuclear structure components and the reaction operators (the probe), but as a result of factorization, are scale and scheme dependent. The RG provides a natural tool for handling this scale and scheme dependence, which is crucial for interpreting experiments and comparing extracted quantities to theory. This thesis demonstrates each of these points by using the similarity RG (SRG) to transform chiral effective field theory (EFT) or phenomenological interactions, and their associated operators, to low RG resolution. We explore aspects of operator evolution that have particular relevance in the context of scale and scheme dependence of nuclear processes. These aspects include SRG implementations based on the Magnus expansion, band- versus block-diagonal operator flow, universality for chiral EFT interactions and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. We show how the features of short-range correlation phenomenology are cleanly identified at low RG resolution using simple two-body operators and local-density approximations with uncorrelated wave functions, all of which can be systematically generalized. We verify that the experimental consequences to date follow directly at low RG resolution from well-established properties of nuclear interactions. We describe the quasi-deuteron model at low RG resolution and determine the Levinger constant, which is proportional to the ratio of nuclear photo-absorption to that for photo-disintegration of a deuteron. Implications for consistently extracting spectroscopic factors in electron-induced proton knock-out reactions are discussed. The results of this thesis contribute to a broader effort to model processes relevant to FRIB, such as knock-out or break-up reactions.