Matthias Heinz

Located at the neutron shell closure N = 8 , the long-lived radioactive isotope C 14 plays a critical role in geochronology and nuclear structure studies. Despite its widespread use, the nuclear charge radius of C 14 has remained less precisely known than that of its stable counterpart C 12 . Here, we report a high-precision determination of the C 14 charge radius using collinear laser spectroscopy at the COALA setup at TU Darmstadt, improving upon the precision of previous muonic measurements by a factor of 5 and revealing a 1.9 σ discrepancy of combined uncertainty, indicating a likely underestimated uncertainty in the muonic determination. This measurement challenges state-of-the-art nuclear theory calculations, including auxiliary field diffusion Monte Carlo, the valence-space in-medium similarity renormalization group, and the no-core shell model, augmented by neural-network techniques. With C 12 and C 14 now forming one of the most precisely characterized even-even isotope pairs, these results also enable improved QED tests.

Low-resolution nuclear Hamiltonians, obtained from chiral effective field theory (EFT) and softened using renormalization group techniques, have been very successful in nuclear structure theory. The associated EFT truncation uncertainty for these potentials is difficult to quantify. We use singular value decompositions of low-resolution nuclear forces to obtain an operator basis to study Hamiltonian uncertainties for these potentials. We perform Bayesian inference for the singular values and three-body low-energy constants, the free parameters of nuclear Hamiltonians in our framework, using likelihoods based on nucleon-nucleon phase shifts and triton observables to account for the EFT truncation uncertainties in these quantities. Validating our inference, we find good reproduction of input uncertainties for low-energy phase shifts and three-nucleon observables. On the other hand, uncertainties for higher-energy phase shifts are systematically underestimated, which we attribute to limitations of the singular value decomposition and neglected correlations between phase shifts at different energies. We propagate the resulting distribution of Hamiltonians forward to predictions for ground-state properties of 24 , 28 O and Ca 48 , comparing against other state-of-the-art nuclear structure predictions. Our approach makes it possible to account for EFT uncertainties when using low-resolution potentials, which is important for many ongoing studies in exotic nuclei.

Low-resolution nuclear Hamiltonians, obtained from chiral effective field theory (EFT) and softened using renormalization group techniques, have been very successful in nuclear structure theory. The associated EFT truncation uncertainty for these potentials is difficult to quantify. We use singular values decompositions of low-resolution nuclear forces to obtain an operator basis to study Hamiltonian uncertainties for these potentials. We perform Bayesian inference for the singular values and three-body low-energy constants, the free parameters of nuclear Hamiltonians in our framework, using likelihoods based on nucleon-nucleon phase shifts and triton observables to account for the EFT truncation uncertainties in these quantities. We propagate the resulting distribution of Hamiltonians forward to predictions for ground-state properties of $^{24,28}$O and $^{48}$Ca, comparing against other state-of-the-art nuclear structure predictions. Our approach makes it possible to account for EFT uncertainties when using low-resolution potentials, which is important for many ongoing studies in exotic nuclei.

The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For global nuclear calculations, density functional theories (DFTs) have been developed to reduce the complexity and computational cost required in describing nuclear systems. However, DFT often makes approximations and assumptions about terms included in the functional, which may introduce systematic uncertainties compared to microscopic calculations using EFTs. In this work, we investigate possible avenues of improving nuclear DFT using nonlinear relativistic mean-field (RMF) theory. We explore the impact of RMF model extensions by fitting the nonlinear RMF model to predictions of nuclear matter and selected closed-shell nuclei using four successful chiral EFT Hamiltonians. We find that these model extensions are impactful and important in capturing the physics present within chiral Hamiltonians, particularly for charge radii and neutron skins of closed-shell nuclei. However, there are additional effects that are not captured within the RMF model, particularly within the isoscalar sector of RMF theory. Additional model extensions and the reliability of the nonlinear RMF model are discussed.