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We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost., 6 pages, 5 figures, 1 table

We present the first ab initio calculations of nuclear ground states up into the domain of heavy nuclei, spanning the range from 16-O to 132-Sn based on two- plus three-nucleon interactions derived within chiral effective field theory. We employ the similarity renormalization group for preparing the Hamiltonian and use coupled-cluster theory to solve the many-body problem for nuclei with closed sub-shells. Through an analysis of theoretical uncertainties resulting from various truncations in this framework, we identify and eliminate the technical hurdles that previously inhibited the step beyond medium-mass nuclei, allowing for reliable validations of nuclear Hamiltonians in the heavy regime. Following this path we show that chiral Hamiltonians qualitatively reproduce the systematics of nuclear ground-state energies up to the neutron-rich Sn isotopes., 5 pages, 5 figures

We summarize recent advances in ab initio nuclear structure theory, aiming to connect few- and many-body systems in a coherent theoretical framework. Starting from chiral effective field theory to construct the nuclear Hamiltonian and the similarity renormalization group to soften it, we address several many-body approaches that have seen major developments over the past few years. We show that the domain of ab initio nuclear structure theory has been pushed well beyond the p-shell and that quantitative predictions connected to QCD via chiral effective field theory are becoming possible all the way from the proton to the neutron drip line up into the medium-mass regime.

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

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.

The fundamental description of both structural properties and reactions of light nuclei in terms of constituent protons and neutrons interacting through nucleon-nucleon and three-nucleon forces is a long-sought goal of nuclear theory. I will briefly present a promising technique, built upon the {\em ab initio} no-core shell model, which emerged recently as a candidate to reach such a goal: the no-core shell model/resonating-group method. This approach, capable of describing simultaneously both bound and scattering states in light nuclei, complements a microscopic cluster technique with the use of two-nucleon realistic interactions, and a microscopic and consistent description of the nucleon clusters. I will discuss applications to light nuclei binary scattering processes and fusion reactions that power stars and Earth based fusion facilities, such as the deuterium-$^3$He fusion, and outline the progress toward the inclusion of the three-nucleon force into the formalism and the treatment of three-body clusters., 8 pages, 6 figures, Proceedings of the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japan

Low-energy nuclear theory has entered an era of ab initio nuclear structure and reaction calculations based on QCD. One of the most promising paths from QCD to nuclear observables employs Hamiltonians constructed within chiral effective field theory as starting point for precise ab initio studies. However, the full inclusion of chiral two- plus three-nucleon (NN+3N) interactions in exact and approximate many-body calculations poses a formidable challenge. We discuss recent breakthroughs that allow for ab initio calculations for ground states and spectra of nuclei throughout the p- and the lower sd-shell with full 3N interactions using consistent Similarity Renormalization Group (SRG) transformations and the Importance Truncated No-Core Shell Model (IT-NCSM). Moreover, we discuss extensions of these ab initio calculations to heavy nuclei within coupled cluster theory using a normal ordering approximation of the 3N interaction.

Author(s): Smalley, D; Iwasaki, H; Navratil, P; Roth, R; Langhammer, J; Bader, VM; Bazin, D; Berryman, JS; Campbell, CM; Dohet-Eraly, J; Fallon, P; Gade, A; Langer, C; Lemasson, A; Loelius, C; Macchiavelli, AO; Morse, C; Parker, J; Quaglioni, S; Recchia, F; Stroberg, SR; Weisshaar, D; Whitmore, K; Wimmer, K | Abstract: We studied transition rates for the lowest 1/2+ and 5/2+ excited states of C17 through lifetime measurements with the GRETINA array using the recoil-distance method. The present measurements provide a model-independent determination of transition strengths giving the values of B(M1;1/2+→3/2g.s.+)=1.04-0.12+0.03×10-2μN2 and B(M1;5/2+→3/2g.s.+)=7.12-0.96+1.27×10-2μN2. The quenched M1 transition strength for the 1/2+→3/2g.s.+ transition, with respect to the 5/2+→3/2g.s.+ transition, has been confirmed with greater precision. The current data are compared to importance-truncated no-core shell model calculations addressing effects due to continuum and three-body forces.

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

We present the first ab initio calculations for p-shell single-Lambda hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit $\Lambda$ and $\Sigma^+$, $\Sigma^0$, $\Sigma^-$ hyperons including $\Lambda$-$\Sigma$ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two- and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-shell hypernuclei and apply it to p-shell hypernuclei, in particular to $^7_\Lambda$Li, $^9_\Lambda$Be and $^{13}_\Lambda$C. We show that the chiral hyperon-nucleon interactions provide ground-state and excitation energies that agree with experiment within the cutoff dependence. At the same time we demonstrate that hypernuclear spectroscopy provides tight constraints on the hyperon-nucleon interactions and we discuss the impact of induced hyperon-nucleon-nucleon interactions., Comment: 6 pages, 4 figures

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 discuss the building blocks for a consistent inclusion of chiral three-nucleon ($3N$) interactions into ab initio nuclear structure calculations beyond the lower $p$ shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the $3N$ sector, a $JT$-coupled storage scheme for $3N$ matrix elements with efficient on-the-fly decoupling, and the importance-truncated no-core shell model with $3N$ interactions. Together, these developments make converged ab initio calculations with explicit $3N$ interactions possible also beyond the lower $p$ shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-$3N$ contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper $p$ shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.

We investigate selected static and transition properties of $^{12}\mathrm{C}$ using ab initio no-core shell model (NCSM) methods with chiral two- and three-nucleon interactions. We adopt the similarity renormalization group (SRG) to assist convergence including up to three-nucleon ($3N$) contributions. We examine the dependencies of the ${}^{12}$C observables on the SRG evolution scale and on the model-space parameters. We obtain nearly converged low-lying excitation spectra. We compare results of the full NCSM with the importance truncated NCSM in large model spaces for benchmarking purposes. We highlight the effects of the chiral $3N$ interaction on several spectroscopic observables. The agreement of some observables with experiment is improved significantly by the inclusion of $3N$ interactions, e.g., the $B(M1)$ from the first ${J}^{\ensuremath{\pi}}T={1}^{+}1$ state to the ground state. However, in some cases the agreement deteriorates, e.g., for the excitation energy of the first ${1}^{+}0$ state, leaving room for improved next-generation chiral Hamiltonians.

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 present a cross-section of recent advances in ab initio nuclear structure theory, which have changed the horizons of this field. Starting from chiral effective field theory to construct the nuclear Hamiltonian and the similarity renormalization group to further soften it, we address several many-body approaches that have seen major developments over the past few years. We show that the domain of ab initio nuclear structure theory has been pushed well beyond the p-shell and that quantitative QCD-based predictions are becoming possible all the way from the proton to the neutron drip line up into the medium-mass regime.

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

This paper describes initial steps to leverage accelerators, such as GPUs, in ab initio nuclear physics calculations. Specifically, parallel nuclear structure calculations performed by the MFDn package are considered with selected stages adapted for GPUs. This paper outlines the necessary steps to make MFDn utilize GPUs in its matrix construction stage. The experiments are presented to compare the multithreaded CPU-based version of this phase with the newly designed GPU-based version. Four-to ten-fold speedups were observed for the code executing on GPUs.

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 apply degenerate many-body perturbation theory at high orders for the ab-initio description of ground states and excitation spectra of open-shell nuclei using soft realistic nucleon-nucleon interactions. We derive a recursive formulation of standard degenerate many-body perturbation theory that enables us to evaluate order-by-order perturbative energy and state corrections up to the 30th order. We study 6,7-Li as test cases using a similarity renormalization group (SRG) evolved nucleon-nucleon interaction from chiral effective field theory. The simple perturbation series exhibits a strong, often oscillatory divergence, as was observed previously for ground states of closed-shell nuclei. Even for very soft interactions resulting from SRG evolutions up to large flow parameter, i.e. low momentum scales, the perturbation series still diverges. However, a resummation of the perturbation series via Pad\'e approximants yields very stable and converged ground and excited-state energies in very good agreement with exact no-core shell-model calculations for the same model space., Comment: 8 pages, 4 figures; minor changes to match published version

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

We present first ab initio no-core shell model (NCSM) calculations using similarity renormalization group (SRG) transformed chiral two-nucleon (NN) plus three-nucleon (3N) interactions for nuclei throughout the p-shell, particularly (12)C and (16)O. By introducing an adaptive importance truncation for the NCSM model space and an efficient JT-coupling scheme for the 3N matrix elements, we are able to surpass previous NCSM studies including 3N interactions. We present ground and excited states in (12)C and (16)O for model spaces up to N(max) = 12 including full 3N interactions. We analyze the contributions of induced and initial 3N interactions and probe induced 4N terms through the sensitivity of the energies on the SRG flow parameter. Unlike for light p-shell nuclei, SRG-induced 4N contributions originating from the long-range two-pion terms of the chiral 3N interaction are sizable in (12)C and (16)O.

We apply high-order many-body perturbation theory for the calculation of ground-state energies of closed-shell nuclei using realistic nuclear interactions. Using a simple recursive formulation, we compute the perturbative energy contributions up to 30th order and compare to exact no-core shell model calculations for the same model space and Hamiltonian. Generally, finite partial sums of this perturbation series do not show convergence with increasing order, but tend to diverge exponentially. Nevertheless, through a simple resummation via Pade approximants it is possible to extract rapidly converging and highly accurate results for the ground state energy., 6 pages, 2 figures, 1 table

The atomic nucleus is a self-bound system of strongly interacting nucleons. In No-Core Configuration Interaction calculations, the nuclear wavefunction is expanded in Slater determinants of single-nucleon wavefunctions (Configurations), and the many-body Schrodinger equation becomes a large sparse matrix problem. The challenge is to reach numerical convergence to within quantified numerical uncertainties for physical observables using finite truncations of the infinite-dimensional basis space. We discuss strategies for constructing and solving the resulting large sparse matrices for a set of low-lying eigenvalues and eigenvectors on current multicore computer architectures. Several of these strategies have been implemented in the code MFDn, a hybrid MPI/OpenMP Fortran code for ab initio nuclear structure calculations that scales well to over 200,000 cores. We discuss how the similarity renormalization group can be used to improve the numerical convergence. We present results for excitation energies and other selected observables for 8Be and 12C using realistic 2- and 3-body forces obtained from chiral perturbation theory. Finally, we demonstrate that collective phenomena such as rotational band structures can emerge from these microscopic calculations.