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

Abstract

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 ${}^9\mathrm{Li}+n+n$ 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.

41 pages, 16 figures

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• P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory
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