With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, twonucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLOsat, yield accurate binding energies and radii of nuclei up to 40 Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low-lying collective J π = 3 − states in 16 O and 40 Ca are described accurately, while spectra for selected p-and sd-shell nuclei are in reasonable agreement with experiment. Introduction -Interactions from chiral effective field theory (EFT) [1][2][3][4] and modern applications of renormalization group techniques [5][6][7][8] have opened the door for a description of atomic nuclei consistent with the underlying symmetries of quantum chromodynamics, the theory of the strong interaction. Chiral nuclear forces can be constructed systematically from long-range pion physics augmented by contact interactions. Over the past decade, the renaissance of nuclear theory based on realistic nuclear forces and powerful computational methods has pushed the frontier of ab initio calculations from fewbody systems and light nuclei [6, 9, 10] to medium-mass nuclei [11][12][13][14][15][16][17][18][19].

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.

Chiral effective field theory (χEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, χEFT is able to provide well-founded estimates of statistical and systematic uncertainties -although this unique advantage has not yet been fully exploited. We fill this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous fit to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of χEFT. Finally, we study the effect on other observables by demonstrating forwarderror-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain efficient and machine-precise first-and second-order derivatives of the objective function with respect to the LECs. This is also vital for the regression analysis. We use power-counting arguments to estimate the systematic uncertainty that is inherent to χEFT, and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling, showing that statistical errors are, in general, small compared to systematic ones. In conclusion, we find that a simultaneous fit to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in χEFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector, in particular when varying the cutoff in the chiral potentials. The methodology and results presented in this paper open a new frontier for uncertainty quantification in ab initio nuclear theory.

We optimize chiral interactions at next-to-next-to leading order to observables in two-and threenucleon systems, and compute Gamow-Teller transitions in 14 C and 22,24 O using consistent twobody currents. We compute spectra of the daughter nuclei 14 N and 22,24 F via an isospin-breaking coupled-cluster technique, with several predictions. The two-body currents reduce the Ikeda sum rule, corresponding to a quenching factor q 2 ≈ 0.84 − 0.92 of the axial-vector coupling. The half life of 14 C depends on the energy of the first excited 1 + state, the three-nucleon force, and the two-body current.

We compute the S-factor of the proton-proton (pp) fusion reaction using chiral effective field theory (χEFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the pp cross section in momentum space, (ii) the statistical uncertainties in the lowenergy coupling constants of χEFT, (iii) the systematic uncertainty due to the χEFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon-nucleon interaction. We also examine the robustness of the polynomial extrapolation procedure, which is commonly used to extract the threshold S-factor and its energy-derivatives. By performing a statistical analysis of the polynomial fit of the energy-dependent S-factor at several different energy intervals, we eliminate a systematic uncertainty that can arise from the choice of the fit interval in our calculations. In addition, we explore the statistical correlations between the S-factor and few-nucleon observables such as the binding energies and point-proton radii of 2,3 H and 3 He as well as the D-state probability and quadrupole moment of 2 H, and the β-decay of 3 H. We find that, with the state-of-the-art optimization of the nuclear Hamiltonian, the statistical uncertainty in the threshold S-factor cannot be reduced beyond 0.7%.