SummaryWhat is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus 48 Ca. We show that the neutron skin (difference between radii of neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities are currently targeted by precision measurements. Based on ab initio results for 48 Ca, we provide a constraint on the size of a neutron star.

The properties of exotic nuclei on the verge of existence play a fundamental part in our understanding of nuclear interactions. Exceedingly neutron-rich nuclei become sensitive to new aspects of nuclear forces. Calcium, with its doubly magic isotopes (40)Ca and (48)Ca, is an ideal test for nuclear shell evolution, from the valley of stability to the limits of existence. With a closed proton shell, the calcium isotopes mark the frontier for calculations with three-nucleon forces from chiral effective field theory. Whereas predictions for the masses of (51)Ca and (52)Ca have been validated by direct measurements, it is an open question as to how nuclear masses evolve for heavier calcium isotopes. Here we report the mass determination of the exotic calcium isotopes (53)Ca and (54)Ca, using the multi-reflection time-of-flight mass spectrometer of ISOLTRAP at CERN. The measured masses unambiguously establish a prominent shell closure at neutron number N = 32, in excellent agreement with our theoretical calculations. These results increase our understanding of neutron-rich matter and pin down the subtle components of nuclear forces that are at the forefront of theoretical developments constrained by quantum chromodynamics.

Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain ‘magic’ numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly magic features are known in ^40,48Ca, and recently suggested in two radioactive isotopes, ^52,54Ca. Although many properties of experimentally known calcium isotopes have been successfully described by nuclear theory, it is still a challenge to predict the evolution of their charge radii. Here we present the first measurements of the charge radii of ^49,51,52Ca, obtained from laser spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly magic nature of 52Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei

We link the structure of nuclei around ^{100}Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers (N=Z=50), to nucleon-nucleon (NN) and three-nucleon (NNN) forces constrained by data of few-nucleon systems. Our results indicate that ^{100}Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of ^{101}Sn based on three-particle-two-hole excitations of ^{100}Sn, and we find that one interaction accurately reproduces the small splitting between the lowest J^{π}=7/2^{+} and 5/2^{+} states.

We explore the impact of nuclear matter saturation on the properties and systematics of finite nuclei across the nuclear chart. Using the ab initio in-medium similarity renormalization group (IM-SRG), we study ground-state energies and charge radii of closed-shell nuclei from 4 He to 78 Ni, based on a set of low-resolution two-and three-nucleon interactions that predict realistic saturation properties. We first investigate in detail the convergence properties of these Hamiltonians with respect to model-space truncations for both two-and three-body interactions. We find one particular interaction that reproduces well the ground-state energies of all closed-shell nuclei studied. As expected from their saturation points relative to this interaction, the other Hamiltonians underbind nuclei, but lead to a remarkably similar systematics of ground-state energies. Extending our calculations to complete isotopic chains in the sd and pf shells with the valence-space IM-SRG, the same interaction reproduces not only experimental ground states but two-neutron-separation energies and first excited 2 + states. We also calculate radii with the valence-space IM-SRG for the first time. Since this particular interaction saturates at too high density, charge radii are still too small compared with experiment. Except for this underprediction, the radii systematics is, however, well reproduced. Our results highlight the importance of nuclear matter as a theoretical benchmark for the development of next-generation chiral interactions.

We study ground-and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8 N, Z 20, based on a set of low-resolution two-and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of ∼ 5 MeV. The first excited 2 + energies also show overall agreement, with a more narrow uncertainty range of ∼ 500 keV. In most cases, this range is dominated by the uncertainties in the Hamiltonian. Introduction. Recent advances in nuclear theory have established the importance of three-nucleon (3N) forces in understanding the structure of medium-mass nuclei, for the evolution to the neutron and proton driplines [1][2][3][4][5] and the formation of shell structure [6][7][8][9][10][11][12][13]. Threenucleon forces are also key for realistic saturation properties of nuclear matter [14][15][16][17][18], which in turn are obtained from global analyses of all nuclei. To date, ab initio studies of medium-mass nuclei have largely focused on closedshell nuclei or isotopic chains, generally in the vicinity of semi-magic nuclei, and no comprehensive study exists to explore nuclear forces over a full range of the nuclear chart, such as the sd shell.An additional challenge is the quantification of theoretical uncertainties [19]. Calculations in oxygen and calcium isotopes based on nuclear forces derived from chiral effective field theory (EFT) [20,21] suggest that the uncertainties from the many-body methods are well controlled [4,5,11,13,22]. Therefore, uncertainties in the input Hamiltonian, such as truncations in the chiral EFT expansion or uncertainties in the low-energy couplings, likely remain the dominant source of uncertainty. Note that recently, first studies of the statistical uncertainties from numerically optimized chiral forces [23,24] and to quantify correlations between chiral EFT couplings [25,26] have been performed.In this work we investigate all sd-shell nuclei based on chiral two-nucleon (NN) and 3N interactions with realistic saturation properties. We derive microscopic valence-space Hamiltonians, which we diagonalize to obtain ground-state energies, two-neutron and two-proton separation energies, and first excited 2

A precision mass investigation of the neutron-rich titanium isotopes 51−55 Ti was performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the N = 32 shell closure and the overall uncertainties of the 52−55 Ti mass values were significantly reduced. Our results conclusively establish the existence of weak shell effect at N = 32, narrowing down the abrupt onset of this shell closure. Our data were compared with state-of-the-art ab initio shell model calculations which, despite very successfully describing where the N = 32 shell gap is strong, overpredict its strength and extent in titanium and heavier isotones. These measurements also represent the first scientific results of TITAN using the newly commissioned Multiple-Reflection Time-of-Flight Mass Spectrometer (MR-TOF-MS), substantiated by independent measurements from TITAN's Penning trap mass spectrometer.Atomic nuclei are highly complex quantum objects made of protons and neutrons. Despite the arduous efforts needed to disentangle specific effects from their many-body nature, the fine understanding of their structures provides key information to our knowledge of fundamental nuclear forces. One notable quantum behavior of bound nuclear matter is the formation of shell-like structures for each fermion group [1], as electrons do in atoms. Unlike for atomic shells, however, nuclear shells are known to vanish or move altogether as the number of protons or neutrons in the system changes [2]. Particular attention has been given to the emergence of strong shell effects among nuclides with 32 neutrons, pictured in a shell model framework as a full valence ν2p 3/2 orbital. Across most of the known nuclear chart, this orbital is energetically close to ν1f 5/2 , which prevents the appearance of shell signatures in energy observables. However, the excitation energies of the lowest 2 + states show a relative, but systematic, local increase below proton number Z = 24 [3]. This effect, characteristic of shell closures, has been attributed in shell model calculations to the weakening of attractive proton-neutron interactions between the ν1f 5/2 and π1f 7/2 orbitals as the latter empties, making the neutrons in the former orbital less bound [4,5]. Ab initio calculations are also extending their reach over this sector of the nuclear chart, yet no systematic investigation of the N = 32 isotones has been produced so far.

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.