  What effect do particle-emitting resonances have on the scattering cross
section? What physical considerations are necessary when modelling these
resonances? These questions are important when theoretically describing
scattering experiments with radioactive ion beams which investigate the
frontiers of the table of nuclides, far from stability. Herein, a novel method
is developed that describes resonant nuclear scattering from which centroids
and widths in the compound nucleus are obtained when one of the interacting
bodies has particle unstable resonances. The method gives cross sections
without unphysical behavior that is found if simple Lorentzian forms are used
to describe resonant target states. The resultant cross sections differ
significantly from those obtained when the states in the coupled channel
calculations are taken to have zero width, and compound-system resonances are
better matched to observed values.
