Characterization of resonances using an exact model S-matrix

The S-matrix, which is exact for a model potential that can be made to closely approximate a given physical potential, is found in closed form as a function of complex system energy. This allows a calculation of the density of resonance states for real scattering energies, from which real resonance position, total widths, and partial widths can easily be extracted. Alternatively, a direct search of the poles of the S-matrix in the complex energy plane locates the complex resonance energies while the residues of the S-matrix elements at each pole yield the resonance partial widths.