Hybrid potential/R-matrix models for the 12C + α system

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 + α S-wave elastic phase shifts.