Spectra of Open-Shell Nuclei with Pad\'e-Resummed Degenerate Perturbation Theory

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 versio

Ab Initio Path to Heavy Nuclei

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.Comment: 5 pages, 5 figure

Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States

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.Comment: 6 pages, 5 figures, 1 tabl

Ab Initio Calculations of Medium-Mass Nuclei with Explicit Chiral 3N Interactions

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.Comment: 6 pages, 3 figures, 2 table

Ab initio many-body calculations of nucleon-4He scattering with three-nucleon forces

We extend the ab initio no-core shell model/resonating-group method to include three-nucleon (3N) interactions for the description of nucleon-nucleus collisions. We outline the formalism, give algebraic expressions for the 3N-force integration kernels, and discuss computational aspects of two alternative implementations. The extended theoretical framework is then applied to nucleon-4He scattering using similarity-renormalization-group (SRG) evolved nucleon-nucleon plus three-nucleon potentials derived from chiral effective field theory. We analyze the convergence properties of the calculated phase shifts and explore their dependence upon the SRG evolution parameter. We include up to six excited states of the 4He target and find significant effects from the inclusion of the chiral 3N force, e.g., it enhances the spin-orbit splitting between the 3/2- and 1/2- resonances and leads to an improved agreement with the phase shifts obtained from an accurate R-matrix analysis of the five-nucleon experimental data. We find remarkably good agreement with measured differential cross sections at various energies, while analyzing powers manifest larger deviations from experiment for certain energies and angles.Comment: 18 pages, 12 figure

Chiral Three-Nucleon Interactions in Ab-Initio Nuclear Structure and Reactions

The prediction of nuclear structure and reaction observables based on nuclear Hamil- tonians including two- and three-nucleon (NN+3N) interactions derived from chiral effective field theory constitutes a challenging task for ab-initio nuclear theory. In particular, the consistent inclusion of 3N interactions requires formal extensions of the many-body methods and, at the same time, causes a significant increase of the computational cost. This work presents the necessary steps for the inclusion and the subsequent application of 3N interactions in different ab-initio nuclear structure and reaction approaches. The first part is dedicated to the preparation of the chiral nuclear forces before they enter the many-body methods. It addresses the similarity renormalization group (SRG) as a tool to soften the initial chiral interactions and its generalization to consistently include 3N interactions. Moreover, the technically important 3N matrix-element management in a convenient basis for the subsequent many-body methods including an efficient storage scheme is discussed. In addition, a possibility to derive approximative schemes for 3N interactions using normal ordering is presented. In the second part the SRG-evolved chiral NN+3N Hamiltonians are applied in nuclear structure calculations using the importance truncated no-core shell model (IT-NCSM) as well as coupled-cluster theory. The impact of SRG-induced and chiral 3N interactions on ground-state energies and low-energy spectra of different p -shell nuclei is studied, includ- ing a sensitivity analysis concerning uncertainties of the chiral interactions in the 12C and 10B spectra. Furthermore, the first ab-initio study of even oxygen isotopes with explicit 3N interactions is presented, and by means of the normal-ordered two-body approximation the ground-state energy systematics of selected closed-shell nuclei throughout the calcium, nickel, and tin isotopic chains are obtained in qualitative agreement with experiment. The third part of this work focuses on 3N interactions in ab-initio nuclear scattering approaches. This includes a detailed discussion of the inclusion of 3N interactions in the no-core shell model combined with the resonating-group method (NCSM/RGM) with emphasis on the ability to treat targets beyond the lightest nuclei. The extended formalism is then applied to nucleon-4He scattering, where the 3N interaction overall improves scattering phase shifts, differential cross sections and analyzing powers. Finally, the no-core shell model with continuum approach, which constitutes a unified ab-initio approach to bound and scattering states resulting from the combination of the NCSM and the NCSM/RGM, is generalized to 3N interactions and applied to the neutron-8Be system to study the impact of the continuum on the 9Be energy levels. The results demonstrate the importance of the consistent treatment of continuum states

Extension of coupled-cluster theory with a non-iterative treatment of connected triply excited clusters to three-body Hamiltonians

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 figure