  I present ongoing developments on hybrid models which combine the potential
model, for the description of the background, with the R-matrix model, for the
description of discrete states. Physical parameters of discrete states are
converted into formal R-matrix parameters, taking into account the potential
background. The nuclear part of this potential is constructed by a new variant
of an inversion method based on supersymmetric quantum mechanics. The method is
illustrated on 12C + alpha S-wave elastic phase shifts.
