Inverse scattering J-matrix approach to nucleon-nucleus scattering and the shell model

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 ℏΩ. 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 nα and pα scattering. The results are compared with the no-core shell-model calculations of ⁵He and ⁵Li.