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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 Ω. This relationship is of a 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 5 He and 5 Li. II. J -MATRIX DIRECT AND INVERSE SCATTERING FORMALISMThe J-matrix formalism [2] utilizes either the oscillator basis or the so-called Laguerre basis of a Sturmian type. The oscillator basis is of a particular interest for nuclear applications. Here we present a sketch of the oscillatorbasis J-matrix formalism (more details can be found in Refs. [2,7,9]) and some details of the inverse scattering J-matrix approach of Ref. [4]. The extension of J-matrix inverse scattering formalism to the case of charged particles is suggested in subsection II B while subsection II C describes how to relate the J-matrix inverse scattering results to those of the shell model. A. Scattering of uncharged particlesScattering in the partial wave with orbital angular momentum l is governed by a radial Schrödinger equation H l u l (E, r) = E u l (E, r).(1)

The SS-HORSE approach to analysis of resonant states is generalized to the case of charged particle scattering utilizing analytical properties of partial scattering amplitudes and applied to the study of resonant states in the 5 Li nucleus and non-resonant s-wave proton-α scattering within the no-core shell model using the JISP16 and Daejeon16 N N interactions. We present also the results of calculations of neutron-α scattering and resonances in the 5 He nucleus with Daejeon16 and compare with results published previously using JISP16.

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