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A large effort has been carried out to characterize the background of sodiumiodide crystals within the ANAIS (Annual modulation with NaI Scintillators)project. In this paper, the background models developed for three 12.5-kgNaI(Tl) scintillators produced by Alpha Spectra Inc. and operated at theCanfranc Underground Laboratory are presented together with an evaluation ofthe background prospects for the full experiment. Measured spectra fromthreshold to high energy in different conditions are well described by themodels based on quantified activities. At the region of interest, crystal bulkcontamination is the dominant background source. Contributions from 210Pb, 40K,22Na and 3H are the most relevant. Those from 40K and 22Na could be efficientlysuppressed thanks to anticoincidence operation in a crystals matrix or inside aLiquid Scintillator Veto (LSV), while that from 210Pb has been reduced byimproving crystal production methods and 3H production could be reduced byshielding against cosmic rays during production. Assuming the activities of thelast characterized detector, for nine crystals with a total mass of 112.5 kgthe expected background rate is 2.5 counts/(keV kg d) in the region from 1 to 4keV, which could be reduced at 1.4 counts/(keV kg d) by using a LSV.

Assessment of backgrounds of the ANAIS experiment for dark matter direct detection