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Nuclear structure corrections in muonic atoms with statistical uncertainty quantification Hernandez, Oscar Javier


The discovery of the proton and deuteron radius puzzles from Lamb shift measurements of muonic atoms has initiated experimental efforts to probe heavier muonic systems and casts doubt on earlier analysis based on ordinary atoms. For muonic atoms, the large muon mass results in a Bohr radius about 200 times smaller with respect to their electronic counterparts, making them sensitive to nuclear structure effects. These effects dominate the uncertainty budget of the experimental analysis and diminish the attainable accuracy of charge radii determinations from Lamb shift spectroscopy. This dissertation investigates the precision of nuclear structure corrections relevant to the Lamb and hyperfine splitting in muonic deuterium to support ongoing experiments and shed light on the puzzles. Using state-of-the-art nuclear models, multivariate regression analysis and Bayesian techniques, we estimate the contribution of all relevant uncertainties for nuclear structure corrections in muonic deuterium and demonstrate that nuclear theory errors are well constrained and do not account for the deuteron radius puzzle. This uncertainty analysis was carried out using the “η-expansion” method that has also been applied to A ≥ 2 nuclei. This method relies on the expansion of a dimensionless parameter η, with η < 1, up to second order. To estimate the truncation uncertainty of this method and to improve future calculations of nuclear structure effects in other nuclei, we introduce an improved formalism based on a multipole expansion of the longitudinal and transverse response functions that contains higher-order terms in η, and generalize the method to account for the cancellation of elastic terms such as the Friar moment (or third Zemach moment). This method is then adapted to address the nuclear structure corrections to the hyperfine splitting. The hyperfine splitting is dominated by magnetic dipole transitions that are sensitive to the effects of two-body currents. Therefore, we develop the formalism of the next-to-leading-order two-body magnetic moment contributions to the magnetic dipole. These operators are applied to A = 2,3 and A = 6 systems in anticipation of the upcoming experiments in µ⁶,⁷Li²⁺ ions. We find that two-body contributions are important to reach agreement with experiment.

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