We predict the limits of existence of atomic nuclei, the proton and neutron drip lines, from the light through medium-mass regions. Starting from a chiral two- and three-nucleon interaction with good saturation properties, we use the valence-space in-medium similarity renormalization group to calculate ground-state and separation energies from helium to iron, nearly 700 isotopes in total. We use the available experimental data to quantify the theoretical uncertainties for our ab initio calculations towards the drip lines. Where the drip lines are known experimentally, our predictions are consistent within the estimated uncertainty. For the neutron-rich sodium to chromium isotopes, we provide predictions to be tested at rare-isotope beam facilities.

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{3\max }=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of ${}^{132}\mathrm{Sn}$ converged to within a few MeV with respect to the $E_{3\max }$ truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{\mathrm{rel}}>9/2$ to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of ${}^{132}\mathrm{Sn}$ agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

In the shell-model framework, valence-space Hamiltonians connecting multiple major-oscillator shells are of key interest for investigating the physics of neutron-rich nuclei, which have been the subject of intense experimental activity for decades. Here we present an extension of the ab initio valence-space in-medium similarity renormalization group, which allows the derivation of such Hamiltonians nonperturbatively. Starting from initial two- and three-nucleon forces from chiral effective field theory, we then calculate properties of nuclei in the important island-of-inversion region above oxygen, so far unexplored with ab initio methods. Our results in the neon and magnesium isotopes indicate the importance of neutron excitation from the $sd$ to $pf$ shells and ground states dominated by intruder configurations around $N=20$, consistent with the conclusions from phenomenological studies. We also benchmark the excitation spectrum of ${}^{16}\mathrm{O}$ with coupled-cluster theory, finding generally good agreement, and discuss implications for ground-state energies and charge radii in oxygen and calcium isotopes. Finally we outline the proper procedure for treating the longstanding issue of center-of-mass contamination, and show that with a particular choice of valence space, these spurious states can be removed successfully.

We calculate basis-space converged neutrinoless $\beta \beta$-decay nuclear matrix elements for the lightest candidates: ${}^{48}\mathrm{Ca}$, ${}^{76}\mathrm{Ge}$, and ${}^{82}\mathrm{Se}$. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed $\beta \beta$-decay operators. We find that the tensor component is non-negligible in ${}^{76}\mathrm{Ge}$ and ${}^{82}\mathrm{Se}$, and the resulting nuclear matrix elements are overall 25%–45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless $\beta \beta$ decay in all nuclei relevant for ongoing large-scale searches.

${}^9\mathrm{Be}$-induced inelastic scattering of ${}^{62,64,66}\mathrm{Fe}$ and ${}^{60,62,64}\mathrm{Cr}$ was performed at intermediate beam energies. Excited states in ${}^{64}\mathrm{Cr}$ were measured for the first time. Energies and population patterns of excited states in these neutron-rich Fe and Cr nuclei are compared and interpreted in the framework of large-scale shell-model calculations in different model spaces. Evidence for increased collectivity and for distinct structural changes between the neighboring Fe and Cr isotopic chains near $N=40$ is presented.

The observation of neutrinoless double-beta ($0\nu \beta \beta$) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in $0\nu \beta \beta$ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the $0\nu \beta \beta$-decay NME, in the key nucleus ${}^{76}\mathrm{Ge}$. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of ${2.60}_{-1.36}^{+1.28}$, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of ${187}_{-62}^{+205}\mathrm{meV}$. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.