Ab initio approaches to nuclear structure, scattering and tests of fundamental symmetries




Gennari, Michael

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In recent decades, the accessibility of nuclear physics has been greatly improved due to the advent of modern supercomputers, as well as theoretical developments in effective field theory and ab initio (first--principles) nuclear approaches. As a result, in modern nuclear theory it is possible to perform realistic quantum many--body calculations of nuclear systems, beginning solely from underlying Standard Model symmetries. A fundamental object of interest in nuclear structure are the nuclear densities, which may be abundantly used in calculation of other nuclear observables. Utilizing the ab initio no--core shell model, a rigorous theoretical approach for calculations involving light--nuclei, we study the coordinate space densities of various nuclear systems and discuss the importance of nonlocality and translation invariance in the densities. In particular, this property is investigated at length in the context of scattering theory, in which optical potentials are constructed from the ab initio no--core shell model densities. We explore the impacts of nonlocality and translation invariance in proton and antiproton scattering, and in the latter we review the first fully microscopic optical potential for antiproton--nucleus scattering. In addition, while the full problem is intractable at present, we assess the potential impact of many--nucleon dynamics on scattering observables. We additionally present an analytic computation of the nuclear kinetic density distribution, derived from the nonlocal nuclear densities. While the nuclear problem has become increasingly tractable, the computational barrier is still ever present, with nuclear calculations pushing the frontier of modern supercomputing. Many approaches have been developed to quell the computational demand, e.g. the similarity renormalization group approach. We introduce and discuss another approach, namely the natural orbitals unitary transformation, which has been shown increase the convergence rate of quantum many--body calculations. Lastly, in the past three years there has revitalized interest in reevaluation of particular Standard Model symmetries. Notably, the Cabibbo--Kobayashi--Maskawa quark mixing matrix has been established as a high--precision test of the Standard Model, capable of pointing to novel physics. Recent theoretical advances in corrections needed to evaluate unitarity of the Cabibbo--Kobayashi--Maskawa matrix have indicated a statistical discrepancy with the Standard Model expectation. In light of this development, using the ab initio no--core shell model with continuum, we pursue a high--precision calculation of the isospin symmetry breaking correction, $\delta_C$. This correction is one of two nuclear structure dependent corrections needed to shed light on this discrepancy, and potentially identify physics beyond the Standard Model.



Nuclear structure, Fundamental symmetries, Ab initio, Scattering