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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 of ${}^6$He are included and the resonance character of the two excited states taken into account in finding solutions. A model Hamiltonian has been found that gives very good agreement with the known bound states and with some low-lying resonances of ${}^{10}$Be. More resonance states are predicted than have as yet been observed. The method also yields $S$-matrices which we have used to evaluate low-energy ${}^6$He-$alpha$ scattering cross sections. Reasonable reproduction of low-energy differential cross sections and of energy variation of cross sections measured at fixed scattering angles is found.
Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is derived desc
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
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 extende
The bound state of uclide[6][LambdaLambda]{He} is studied as a three-body ($LambdaLambdaalpha$) system in a cluster effective field theory at leading order (LO). We find that the system exhibits the limit cycle which is associated with the formation
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