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The Borromean $^6$He nucleus is an exotic system characterized by two `halo neutrons orbiting around a compact $^4$He (or $alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of th
The $beta$-decay process of the $^6$He halo nucleus into the $alpha+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $alpha+n+n$ system in hyperspherical coordinates on a Lagrange-mesh. The shape and absol
It has been proposed that one can look for the QCD critical point (CP) by the Beam Energy Scan (BES) accurately monitoring event-by-event fluctuations. This experimental program is under way at the BNL RHIC collider. Separately, it has been studied h
A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the $alpha$+${}^6$He cluster system, so finding a model spectrum for ${}^{10}$Be to more than 10 MeV excitation. Three states o
A many-body calculation of $^{11}$Li is presented where the only input is the well-tested, finite-range {it D1S} effective interaction of {it Gogny}. Pairing correlations are included in a constrained Hartree-Fock-Bogolyubov calculation, while long-r