Scattering with absorptive interaction

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.