The angular dependence of a broad peripheral resonance state

We discuss the angular dependence of the shape-elastic resonance wave function for a state so broad decay occurs before the ions orbit the interaction region. In the shadow of the interaction region the non-stationary angular dependence is described by a Legendre function for complex angular momentum, P_α (cos θ{symbol}). In the lit region the same state has the angular dependence e^-iπαP_α(-cos θ{symbol}). After presenting theoretical arguments which show the necessity of using these different analytic continuations in the shadow and lit regions to states of complex angular momentum we show, by way of illustration of the theoretical argument, results for a strong absorption model introduced several years ago by Austern.