Project N2 aims at providing *ab initio* calculations of nuclear structure and reactions with quantified uncertainties using state-of-the-art few- and many-body methods. This is key to interpreting existing data, providing guidance for future experiments and helping searches of new physics in atomic and particle physics experiments at the interface with nuclear physics, which demand nuclear structure input with solid error estimates. The main highlights of this project are:

**Nuclear structure corrections in muonic atoms**

The discovery of the proton-radius puzzle and the subsequent deuteron-radius puzzle catalyzed an on-going discussion about explanations for the difference in the observed radii obtained from muonic atoms and electron-nucleus systems. Atomic nuclei have an intricate internal structure that must be taken into account when analyzing experimental results.*Ab**initio*nuclear theory provided the thus far most precise estimates of important nuclear correction to the Lamb shift in muonic atoms. It is proposed to not only improve the precision of such calculations, but also to extend the theory to compute nuclear structure corrections in the hyperfine splitting of muonic atoms with the aim to support the experimental program.**Photonuclear reactions in nuclei**Photonuclear reactions have traditionally been a golden tool for studying nuclear dynamics. They lead, for instance, to the discovery of giant dipole resonances and their interpretation in terms of collective modes. While a complete body of data has been collected over the years for stable nuclei, only recently have we begun to elucidate them in terms of first principle calculations. This was achieved thanks to the introduction of new

*ab initio*computational tools. Project N2 proposes to improve such tools and to push their limits of applicability to a larger mass number. The final goal is to provide theoretical support to the experimental efforts at MAMI/MESA to study the neutron-skin thickness in heavy nuclei.**Lepton-nucleus scattering**

Major national and international resources are being allocated to study properties of fundamental particles. The long-baseline neutrino program is one of the most prominent such examples, where nuclear physics plays an important role. Neutrino detectors involve complex nuclei and nuclear effects lead to systematic uncertainties in the extraction of oscillation parameters. A theoretical description of neutrino-nucleus reactions with a thorough assessment of error bars is called for. Project N2 aims at tackling neutrino-nucleus collisions using recently developed*ab initio*many-body tools. We will start from electron scattering reactions, providing at the same time not only a crucial test of theory, but also further support and motivation for the electron scattering experimental program in Mainz.