J-matrix approach to loosely-bound three-body nuclear systems

We review our papers devoted to the studies of three-body loosely-bound nuclear systems within the J-matrix approach. In particular, we discuss the extension of the oscillator-basis J-matrix formalism on the case of true few-body scattering. The formalism is applied to loosely-bound ¹¹Li and ⁶He nuclei treated as three-body systems ¹¹Li= ⁹ Li+n+n and ⁶He=α+n+n. The J-matrix formalism is used not only for the calculation of the continuum spectrum wave functions of ¹¹Li and ⁶He nuclei excited in nuclear reactions and decaying via three-body channels ¹¹ Li→⁹Li+n+n and ⁶He→α+n+n, but also for the calculation of the S-matrix poles associated with the ¹¹Li and ⁶He ground states to improve the description of the binding energies and ground state properties. The J-matrix formalism is also used to derive a phase equivalent transformation of two-body interactions. The effect of the phase equivalent transformation on the properties of the ⁶He nucleus is examined.