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We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion., Comment: 34 pages, 15 figures, 11 tables

Background: The exotic $^{9}\mathrm{He}$ nucleus, which presents one of the most extreme neutron-to-proton ratios, belongs to the $N=7$ isotonic chain famous for the phenomenon of ground-state parity inversion with decreasing number of protons. Consequently, it would be expected to have an unnatural (positive) parity ground state similar to $^{11}\mathrm{Be}$ and $^{10}\mathrm{Li}$. Despite many experimental and theoretical investigations, its structure remains uncertain. Apart from the fact that it is unbound, other properties including the spin and parity of its ground state, and the very existence of additional low-lying resonances are still a matter of debate.Purpose: In this work, we study the properties of $^{9}\mathrm{He}$ by analyzing the $n+^{8}\mathrm{He}$ continuum in the context of the ab initio no-core shell model with continuum (NCSMC) formalism with chiral nucleon-nucleon interactions as the only input.Methods: The NCSMC is a state-of-the-art approach for the ab initio description of light nuclei. With its capability to predict properties of bound states, resonances, and scattering states in a unified framework, the method is particularly well suited for the study of unbound nuclei such as $^{9}\mathrm{He}$.Results: Our analysis produces an unbound $^{9}\mathrm{He}$ nucleus. Two resonant states are found at the energies of $\ensuremath{\sim}1$ and $\ensuremath{\sim}3.5$ MeV, respectively, above the $n+^{8}\mathrm{He}$ breakup threshold. The first state has a spin-parity assignment of ${J}^{\ensuremath{\pi}}={1/2}^{\ensuremath{-}}$ and can be associated with the ground state of $^{9}\mathrm{He}$, while the second, broader state has a spin parity of ${3/2}^{\ensuremath{-}}$. No resonance is found in the ${1/2}^{+}$ channel, only a very weak attraction.Conclusions: We find that the $^{9}\mathrm{He}$ ground-state resonance has a negative parity and thus breaks the parity-inversion mechanism found in the $^{11}\mathrm{Be}$ and $^{10}\mathrm{Li}$ nuclei of the same $N=7$ isotonic chain.

How does nature hold together protons and neutrons to form the wide variety of complex nuclei in the Universe? Describing many-nucleon systems from the fundamental theory of quantum chromodynamics has been the greatest challenge in answering this question. The chiral effective field theory description of the nuclear force now makes this possible but requires certain parameters that are not uniquely determined. Defining the nuclear force needs identification of observables sensitive to the different parametrizations. From a measurement of proton elastic scattering on ^{10}C at TRIUMF and ab initio nuclear reaction calculations, we show that the shape and magnitude of the measured differential cross section is strongly sensitive to the nuclear force prescription.

The description of structural and dynamical properties of nuclei starting from the fundamental interaction between nucleons has been a long-standing goal in nuclear physics. The ab initio No-Core Shell Model combined with the Resonating-Group Method (NCSM/RGM) is capable of addressing both structural and reaction properties of light-nuclei. While promising results have already been achieved starting from a two-body Hamiltonian, a truly realistic prediction of nuclear observables requires the treatment of the three-nucleon interaction. Using similarity-renormalization-group evolved two- and three-nucleon interactions, we will present recent applications to n-4He scattering process when accounting for the chiral two- plus three-nucleon interaction versus the chiral two-nucleon interaction. We compare our results to phase shifts obtained from R-matrix analysis of data up to 16 MeV neutron energy, below the d-3H threshold., 4 pages, 2 figures, Proceedings of the 22nd European Conference on Few-Body Problems in Physics, Krakow, Poland, 9-13 September 2013

The weakly bound exotic ^{11}Be nucleus, famous for its ground-state parity inversion and distinct n+^{10}Be halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ^{11}Be spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the 3/2_{1}^{-} resonance energy. Finally, we predict low-lying 3/2^{+} and 9/2^{+} resonances that are not or not sufficiently measured in experiments.

We discuss the approximate inclusion of three-nucleon interactions into ab initio nuclear structure calculations using a multi-reference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens a path to open-shell nuclei and excited states. Based on different multi-determinantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that this multi-reference normal-ordered two-body approximation is able to capture the effects of the 3N interaction with sufficient accuracy, both, for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies., 6 pages, 4 figures, v2: update to published version

Starting from a set of different two- and three-nucleon interactions from chiral effective field theory, we use the importance-truncated no-core shell model for ab initio calculations of excitation energies as well as electric quadrupole (E2) and magnetic dipole (M1) moments and transition strengths for selected p-shell nuclei. We explore the sensitivity of the excitation energies to the chiral interactions as a first step towards and systematic uncertainty propagation from chiral inputs to nuclear structure observables. The uncertainty band spanned by the different chiral interactions is typically in agreement with experimental excitation energies, but we also identify observables with notable discrepancies beyond the theoretical uncertainty that reveal insufficiencies in the chiral interactions. For electromagnetic observables we identify correlations among pairs of E2 or M1 observables based on the ab initio calculations for the different interactions. We find extremely robust correlations for E2 observables and illustrate how these correlations can be used to predict one observable based on an experimental datum for the second observable. In this way we circumvent convergence issues and arrive at far more accurate results than any direct ab initio calculation. A prime example for this approach is the quadrupole moment of the first 2^+ state in C-12, which is predicted with an drastically improved accuracy., 11 pages, 8 figures

The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches - built upon the No-Core Shell Model - that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the $^6$He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of $^9$Be. Further, we discuss applications to the $^7$Be$(p,\gamma)^8$B radiative capture. Finally, we highlight our efforts to describe transfer reactions including the $^3$H$(d,n)^4$He fusion., Comment: Contribution to the Special Physica Scripta Edition - 40 year anniversary - Nobel Prize '75, 71 pages, 29 figures

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture 3N forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1\% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper $p$ and $sd$ shells. Finally, we address the $1^+$/$3^+$ ground-state inversion problem in $^{22}\text{Na}$ and $^{46}\text{V}$. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei., Comment: 6 pages, 5 figures

We present recent results for 4 He and 6 Li obtained with improved NN interactions derived from chiral effective field theory up to N4 LO. The many-body calculations are performed order-by-order in the chiral expansion. At N3 LO and N4 LO additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of 6 Li.

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of $p$- and lower-$sd$-shell nuclei. As a first application we concentrate on energy levels of the $^{9}\mathrm{Be}$ system for which all excited states lie above the n-$^{8}\mathrm{Be}$ threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the ${\frac{1}{2}}^{+}$ resonance energy, which is of astrophysical interest, in good agreement with experiment.

We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3H, 4He, and 6Li. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon force contributions agree well with expectations based on Weinberg's power counting. We identify the energy range in elastic Nd scattering best suited to study three-nucleon force effects and estimate the achievable accuracy of theoretical predictions for various observables., 5 pages, 5 figures

An {\em ab initio} (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable to further our understanding of the fundamental interactions among nucleons, and provide accurate predictions of crucial reaction rates for nuclear astrophysics, fusion-energy research, and other applications. In this contribution we review {\em ab initio} calculations for nucleon and deuterium scattering on light nuclei starting from chiral two- and three-body Hamiltonians, obtained within the framework of the {\em ab initio} no-core shell model with continuum. This is a unified approach to nuclear bound and scattering states, in which square-integrable energy eigenstates of the $A$-nucleon system are coupled to $(A-a)+a$ target-plus-projectile wave functions in the spirit of the resonating group method to obtain an efficient description of the many-body nuclear dynamics both at short and medium distances and at long ranges., Comment: 9 pages, 5 figures, proceedings of the 21st International Conference on Few-Body Problems in Physics

We solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on Ay puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported., 22 pages, 7 figures

We present the first ab initio construction of valence-space Hamiltonians for medium-mass nuclei based on chiral two- and three-nucleon interactions using the in-medium similarity renormalization group. When applied to the oxygen isotopes, we find experimental ground-state energies are well reproduced, including the flat trend beyond the drip line at 24O. Similarly, natural-parity spectra in 21,22,23,24O are in agreement with experiment, and we present predictions for excited states in 25,26O. The results exhibit a weak dependence on the harmonic-oscillator basis parameter and reproduce spectroscopy within the standard sd valence space., Comment: 6 pages, 5 figures, published version

We report ab initio calculations for neutron drops in a 10 MeV external harmonic-oscillator trap using chiral nucleon-nucleon plus three-nucleon interactions. We present total binding energies, internal energies, radii and odd-even energy differences for neutron numbers N = 2 - 18 using the no-core shell model with and without importance truncation. Furthermore, we present total binding energies for N = 8, 16, 20, 28, 40, 50 obtained in a coupled-cluster approach. Comparisons with Green's Function Monte Carlo results, where available, using Argonne v8' with three-nucleon interactions reveal important dependences on the chosen Hamiltonian., 7 pages, 5 figures

We generalize the coupled-cluster (CC) approach with singles, doubles, and the non-iterative treatment of triples termed $\Lambda$CCSD(T) to Hamiltonians containing three-body interactions. The resulting method and the underlying CC approach with singles and doubles only (CCSD) are applied to the medium-mass closed-shell nuclei O16, O24, and Ca40. By comparing the results of CCSD and $\Lambda$CCSD(T) calculations with explicit treatment of three-nucleon interactions to those obtained using an approximate treatment in which they are included effectively via the zero-, one-, and two-body components of the Hamiltonian in normal-ordered form, we quantify the contributions of the residual three-body interactions neglected in the approximate treatment. We find these residual normal-ordered three-body contributions negligible for the $\Lambda$CCSD(T) method, although they can become significant in the lower-level CCSD approach, particularly when the nucleon-nucleon interactions are soft., Comment: 21 pages, 3 figures

We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for open-shell nuclei using a multi-reference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the Importance-Truncated No-Core Shell Model and the Coupled Cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures., Comment: 5 pages, 4 figures, v2 corresponding to published version

We present the first ab initio coupled-cluster calculations of medium-mass nuclei with explicit chiral three-nucleon (3N) interactions. Using a spherical formulation of coupled cluster with singles and doubles excitations including explicit 3N contributions, we study ground states of 16,24-O, 40,48-Ca and 56-Ni. We employ chiral NN plus 3N interactions softened through a similarity renormalization group (SRG) transformation at the three-body level. We investigate the impact of all truncations and quantify the resulting uncertainties---this includes the contributions from triples excitations, the truncation of the set of three-body matrix elements, and the omission of SRG-induced four-body interactions. Furthermore, we assess the quality of a normal-ordering approximation of the 3N interaction beyond light nuclei. Our study points towards the predictive power of chiral Hamiltonians in the medium-mass regime., 6 pages, 3 figures, 2 tables

We study the use of truncated normal-ordered three-nucleon interactions in nuclear structure calculations starting from chiral two- plus three-nucleon Hamiltonians evolved consistently with the similarity renormalization group. We present three key developments: (i) a rigorous benchmark of the normal-ordering approximation in the importance-truncated no-core shell model for (4)He, (16)O, and (40)Ca; (ii) a direct comparison of the importance-truncated no-core shell model results with coupled-cluster calculations at the singles and doubles level for (16)O; and (iii) first applications of similarity renormalization group-evolved chiral NN+3N Hamiltonians in coupled-cluster calculations for medium-mass nuclei (16,24)O and (40,48)Ca. We show that the normal-ordered two-body approximation works very well beyond the lightest isotopes and opens a path for studies of medium-mass and heavy nuclei with chiral two- plus three-nucleon interactions. At the same time we highlight the predictive power of chiral Hamiltonians.

We use the recently proposed In-Medium Similarity Renormalization Group (IM-SRG) to carry out a systematic study of closed-shell nuclei up to $\nuc{Ni}{56}$, based on chiral two- plus three-nucleon interactions. We analyze the capabilities of the IM-SRG by comparing our results for the ground-state energy to Coupled Cluster calculations, as well as to quasi-exact results from the Importance-Truncated No-Core Shell Model. Using chiral two- plus three-nucleon Hamiltonians whose resolution scales are lowered by free-space SRG evolution, we obtain good agreement with experimental binding energies in $\nuc{He}{4}$ and the closed-shell oxygen isotopes, while the calcium and nickel isotopes are somewhat overbound., Comment: 11 pages, 7 figures, submitted to Phys. Rev. C