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We consider the evolution of the neutron-nucleus scattering length for thelightest nuclei. We show that, when increasing the number of neutrons in thetarget nucleus, the strong Pauli repulsion is weakened and the balance with theattractive nucleon-nucleon interaction results into a resonant virtual state in$^{18}$B.  We describe $^{19}$B in terms of a $^{17}$B-$n$-$n$ three-body system wherethe two-body subsystems $^{17}$B-$n$ and $n$-$n$ are unbound (virtual) statesclose to the unitary limit. The energy of $^{19}$B ground state is wellreproduced and two low-lying resonances are predicted. Their eventual link withthe Efimov physics is discussed. This model can be extended to describe therecently discovered resonant states in $^{20,21}$B.

Low-energy neutron scattering on light nuclei and $^{19}$B as a $^{17}$B-$n$-$n$ three-body system in the unitary limit