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It has been known that decays of daughter elements of $^{222}$Rn on thesurface of a detector cause significant background at energies below 10 keV. Inparticular $^{210}$Pb and $^{210}$Po decays on the crystal surface result insignificant background for dark matter search experiments with NaI(Tl)crystals. In this report, measurement of $^{210}$Pb and $^{210}$Po decays onsurfaces are obtained by using a $^{222}$Rn contaminated crystal. Alpha decayevents of $^{210}$Po on the surface are measured by coincidence requirements oftwo attached crystals. Due to recoiling of $^{206}$Pb, rapid nuclear recoilevents are observed. A mean time characterization demonstrates that $^{206}$Pbrecoil events can be statistically separated from those of sodium or iodinenuclear recoil events, as well as electron recoil events.

Measurement of low-energy background events due to $^{222}$Rn contamination on the surface of a NaI(Tl) crystal