Four categories of events have been identified in the EDELWEISS-I dark matter experiment using germanium cryogenic detectors measuring simultaneously charge and heat signals. These categories of events are interpreted as electron and nuclear interactions occurring in the volume of the detector, and electron and nuclear interactions occurring close to the surface of the detectors(10-20 mu-m of the surface). We discuss the hypothesis that low energy surface nuclear recoils,which seem to have been unnoticed by previous WIMP searches, may provide an interpretation of the anomalous events recorded by the UKDMC and Saclay NaI experiments. The present analysis points to the necessity of taking into account surface nuclear and electron recoil interactions for a reliable estimate of background rejection factors.
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