Depth profile study of 210Pb in the surface of an NaI(Tl) crystal

The surface $^{210}$Pb is one of the main background sources for dark-matter-search experiments using NaI(Tl) crystals, and its spectral features associated with beta-decay events energies less than 60 keV depends on depth distribution in an crystal. Therefore, we must understand profile to precisely model measurement low-energy region low-background experiment crystals. We estimate contamination by modeling measured spectrum alpha emission from decay $^{210}$Po at sequence that obtained $^{222}$Rn-contaminated In order describe energy spectra perform a log-likelihood fit data sum Geant4 Mote Carlo simulations, weighted exponential curve as function depth. low- high-energy beta are also modeled improve shallow depths. simulate decays exponentially distributed following two functions where mean-depth coefficients free parameters fitting; observed good agreement data.