We report the measurement of muons and muon-induced phosphorescence in DM-Ice17, a NaI(Tl) direct detection dark matter experiment at the South Pole. Muon interactions in the crystal are identified by their observed pulse shape and large energy depositions. The measured muon rate in DM-Ice17 is 2.93 +/- 0.04 muons/crystal/day with a modulation amplitude of 12.3 +/- 1.7%, consistent with expectation. Following muon interactions, we observe long-lived phosphorescence in the NaI(Tl) crystals with a decay time of 5.5 +/- 0.5 s. The prompt energy deposited by a muon is correlated to the amount of delayed phosphorescence, the brightest of which consist of tens of millions of photons. These photons are distributed over tens of seconds with a rate and arrival timing that do not mimic a scintillation signal above 2 keVee. While the properties of phosphorescence vary among individual crystals, the annually-modulating signal observed by DAMA cannot be accounted for by phosphorescence with the characteristics observed in DM-Ice17.
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