The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the $J$-matrix is that it provides eigenstates directly related to the ones obtained in the shell model in a given model space and with a given value of the oscillator spacing $\hslash \Omega$. This relationship is of particular interest in the cases when a many-body system does not have a resonant state or the resonance is broad and its energy can differ significantly from the shell-model eigenstate. We discuss the $J$-matrix inverse scattering technique, extend it for the case of charged colliding particles, and apply it to the analysis of $n\alpha$ and $p\alpha$ scattering. The results are compared with the no-core shell-model calculations of ${}^5\mathrm{He}$ and ${}^5\mathrm{Li}$.

• Received 26 June 2008

DOI:https://doi.org/10.1103/PhysRevC.79.014610