title: Ab initio calculations of neutron-rich nuclei with many-body operators
Creators: name: Heinz, Matthias
Publisher: name: UNSPECIFIED
Year: 2024

description: The structure of atomic nuclei has far reaching consequences, including implications for fundamental interactions, the astrophysical synthesis of heavy elements, and the properties of matter in neutron stars. First-principles, or ab initio, nuclear structure theory aims to describe the structure of atomic nuclei based on inter-nucleonic interactions, connecting our understanding of nuclear structure to our understanding of the strong interaction. This approach has two key ingredients: nuclear forces describing the interactions between the protons and neutrons, collectively nucleons, making up nuclei; and many-body calculations computing the properties of many-nucleon systems starting from these nuclear forces. In this thesis, we tackle key challenges in ab initio many-body calculations to reach higher accuracy and to describe heavier systems.

Ab initio many-body methods capable of describing more than just the lightest elements rely on controlled, systematically improvable approximations in their solution of the many-body problem. The in-medium similarity renormalization group (IMSRG) is one such method. Its standard truncation at the normal-ordered two-body level, the IMSRG(2), has been used very successfully over the past decade to develop a comprehensive ab initio description of medium-mass nuclei. In this thesis, we develop the IMSRG(3), the next truncation order including normal-ordered three-body operators in the many-body solution. The extension of the IMSRG to the IMSRG(3) level brings greater precision to theoretical predictions of energies and charge radii. Furthermore, it gives substantial corrections to other quantities of interest where IMSRG(2) predictions are insufficient, such as the prediction of shell structure at doubly-magic nuclei. With the IMSRG(2) and the IMSRG(3) together, many-body uncertainties due to the approximate solution of the many-body problem can be robustly quantified. In addition to developing the IMSRG(3), we improve the treatment of three-body forces in IMSRG calculations, extending the reach of ab initio calculations to heavy nuclei and providing converged predictions of ground-state properties of lead-208. We also introduce multiple ways to accelerate IMSRG calculations, through basis optimization via the perturbatively improved natural orbitals and through importance truncation techniques applied to many-body operators in the IMSRG.

Using the improvements of the IMSRG we developed, we investigate carbon, calcium, and ytterbium isotopes in close collaboration with current experimental efforts. The IMSRG(3) improves the description of the structure of calcium-48, resolving a long-standing overprediction of the closed-shell structure by the IMSRG(2). We also investigate the unresolved discrepancies between theory and experiment in calcium charge radii. In ytterbium isotopes, we provide nuclear structure input for a search for a possible new boson in isotope shifts of atomic transitions. Based on our input, we identify the leading signal in ytterbium isotope shifts to be due to the structure of ytterbium isotopes, not the possible new boson. From this, we extract information on δ⟨r⁴⟩, giving access to a new nuclear structure observable related to deformation. This highlights the importance of nuclear theory to understand nuclear structure effects in searches for new physics.

These developments break new ground for ab initio nuclear theory, paving the way to a more comprehensive and precise description of atomic nuclei with many promising and interesting applications.