Resonances and time-delay in three-body scattering

Time delay and resonant phenomena are examined in the context of a model three-body problem. The time-delay formalism is reviewed and summarized, as it applies to a three-body system. Calculations are carried out for a three-body model containing elastic, inelastic, and rearrangement channels. The two-body interactions in the model permit two-body resonances to be embedded in the three-body structure. Eigenvalues of the time-delay matrix are shown to provide a clear, unambiguous signature of resonant behavior in the multichannel system. A resonance always shows up as a positive peak in one eigenvalue of the time-delay matrix. This result is contrasted with the more usual means of identifying resonant behavior by studying the phases of the S-matrix elements, or the eigenphases of the S matrix.