Low energy pulses with anomalously low time constant have been observed rec
ently in sodium iodide crystals. A model is presented based on partial ener
gy deposits from alpha particles passing out of the crystal from a thin con
taminated layer, which would generate events of similar characteristic. The
predicted 1/E-2 form of the spectrum is consistent with observation. The r
equired level of contamination is estimated both for U/Th impurities and fo
r radon decay products but is found to be higher than would be expected fro
m the crystal fabrication process and history. Possible experimental tests
of the model are suggested. (C) 2000 Published by Elsevier Science B.V.