Loosely bound three-body nuclear systems in the J-matrix approach

We discuss the extension of the oscillator-basis $J$-matrix formalism on the case of true $A$-body scattering. The formalism is applied to loosely-bound $^{11}$Li and $^6$He nuclei within three-body cluster models ${\rm {^9Li}}+n+n$ and $\alpha+n+n$. The $J$-matrix formalism is used not only for the calculation of the three-body continuum spectrum wave functions but also for the calculation of the $S$-matrix poles associated with the $^{11}$Li and $^6$He ground states to improve the description of the binding energies and ground state properties. The effect of the phase equivalent transformation of the $n{-}\alpha$ interaction on the properties of the $^6$He nucleus is examined.