Background: Recent advances in nuclear structure theory have led to the availability of several complementary ab initio many-body techniques applicable to light and medium-mass nuclei as well as nuclear matter. After successful benchmarks of different approaches, the focus is moving to the development of improved models of nuclear Hamiltonians, currently representing the largest source of uncertainty in ab initio calculations of nuclear systems. In particular, none of the existing two- plus three-body interactions is capable of satisfactorily reproducing all the observables of interest in medium-mass nuclei.

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 , γ ) 8 B radiative capture. Finally, we highlight our efforts to describe transfer reactions including the ³ H ( d , n ) 4 He fusion.

We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{3\max }=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain the ground-state energy of ${}^{132}\mathrm{Sn}$ converged to within a few MeV with respect to the $E_{3\max }$ truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{\mathrm{rel}}>9/2$ to the ground-state energy is dominated by a basis-truncation artifact, which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of ${}^{132}\mathrm{Sn}$ agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.

We introduce a unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model (NCSM), a bound-state technique, with the no-core shell model/resonating group method (NCSM/RGM), a nuclear scattering technique. This new ab initio method, no-core shell model with continuum (NCSMC), leads to convergence properties superior to either NCSM or NCSM/RGM while providing a balanced approach to different classes of states. In the NCSMC, the ansatz for the many-nucleon wave function includes (i) a square-integrable $A$-nucleon component expanded in a complete harmonic oscillator basis and (ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly bound states, resonances, and scattering. The Schrödinger equation is transformed into a system of coupled-channel integral-differential equations that we solve using a modified microscopic $R$-matrix formalism within a Lagrange mesh basis. We demonstrate the usefulness of the approach by investigating the unbound ${}^7$He nucleus.

In recent years, the Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The substantial contribution of both induced and initial three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. We present the most recent progress on this work, extending the calculational capability to the $p$-shell nuclei and showing that the hierarchy of induced many-body forces is consistent with previous estimates. Calculations over a range of the flow parameter for ${}^6\mathrm{Li}$, including fully evolved $\mathit{NN}$ $+$ 3$N$ interactions, show moderate contributions due to induced four-body forces and display the same improved convergence properties as in lighter nuclei. A systematic analysis provides further evidence that the hierarchy of many-body forces is preserved.