Anomalous thresholds in anNDapproach to nuclear reactions

The applicability of a recently developed coupled channel $\frac{N}{D}$ approach to nuclear reaction is extended to those cases where one of the channels contains a loosely bound particle giving rise to an anomalous threshold. The $\frac{N}{D}$ equations for the anomalous case are obtained by continuing the amplitudes in some external variable. We show that it is necessary to include part of the second order Born term in order to avoid certain singularities of the amplitudes in this external variable. The $\frac{N}{D}$ equations which are derived for the anomalous case are very similar to those in the normal case and quite amenable to numerical calculations. We also analyze the singularity structure of the second order Born terms in the energy plane. The occurrence of other types of singularities of the amplitudes in the external variable is investigated and their physical relevance is discussed.