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

The application of the hyperspherical adiabatic expansion to describe three-body scattering states suffers from the problem of very slow convergence. Contrary to what happens for bound states, a huge number of hyper-radial equations has to be solved, and even if done, the extraction of the scattering amplitude is problematic. In this Letter we show how to obtain accurate scattering phase shifts using the hyperspherical adiabatic expansion. To this aim two integral relations, derived from the Kohn variational principle, are used. The convergence of this procedure is as fast as for bound states. Introduction.-Few-body collisions involving either nuclei, atoms, or molecules are frequently investigated. To this aim different methods are at present available depending on the interaction under study. In nuclear physics, collisions involving three or four nucleons have been extensively studied within the Faddeev method or the hyperspherical harmonic (HH) method [1][2][3]. These two methods show sufficient flexibility to treat the complexities of the nucleon-nucleon interaction. A different problem arises when the interaction presents a hard core, as in the case of the atom-atom interaction, or in systems with A > 4. In the first case, the Faddeev equations have been extended to deal with a hard core repulsion [4] whereas the hyperspherical adiabatic (HA) expansion method proved to be a very efficient tool [5]. In nuclear systems with A > 4 tentatives to describe scattering states have recently appeared [6,7].Here we are interested in describing a 1 þ 2 collision using the HA expansion method. For bound states the convergence of the HA expansion has proved to be very fast. However, the convergence of the expansion slows down significantly in the case of low energy scattering states [8]. On the other hand, this method is extensively used to describe few-atom systems in the ultracold regime (see Refs. [9,10] and references therein) and, in particular, atom-dimer collisions. Therefore, a detailed study of its convergence properties is timely.In this Letter we show for the first time how the HA expansion method can be used to describe elastic scattering with a pattern of convergence similar to a bound state calculation. This is achieved in a simple but very general way in which a second order estimate of the phase shift is extracted from the wave function using two integral relations derived from the Kohn variational principle (KVP) [11]. The number of HA terms needed to obtain completely stable results depends very little on the structure of the potential, exactly as for bound state calculations. The integral relations are governed by the wave function in the

The low-lying continuum spectrum of the 6 He nucleus is investigated for the first time within an ab initio framework that encompasses the 4 He+n+n three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core-shell model combined with the resonating-group method, in which energy-independent non-local interactions among three nuclear fragments can be calculated microscopically starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hypersphericalharmonic method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known J π = 2 + resonance as well as a result consistent with a new low-lying second 2 + resonance recently observed at GANIL at 2.6 MeV above the 6 He ground state. We also find resonances in the 2 − , 1 + and 0 − channels, while no low-lying resonances are present in the 0 + and 1 − channels.

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