The $S$ matrix for a wide class of complex and nonlocal potentials is studied, with special attention given to the motion of singularities in the complex $k$ plane as a function of the imaginary coupling strength. Modifications of Levinson's theorem are obtained and discussed. Analytic approximations to the $S$ matrix in the vicinity of narrow resonances are exhibited and compared to numerical results of resonating-group calculations. The problem of defining resonances in the case of complex interactions is discussed, making contact with the usual analysis of scattering in terms of Argand diagrams.

NUCLEAR REACTIONS Scattering theory, $S$ matrix for absorptive potentials.

• Received 30 March 1981

DOI:https://doi.org/10.1103/PhysRevC.26.22