Background model for a NaI (Tl) detector devoted to dark matter searches

NaI (Tl) is a well known high light yield scintillator. Very large crystals can be grown to be used in a wide range of applications. In particular, such large crystals are very good-performing detectors in the search for dark matter, where they have been used for a long time and reported first evidence of the presence of an annual modulation in the detection rate, compatible with that expected for a dark matter signal. In the frame of the ANAIS (Annual modulation with NaI Scintillators) dark matter search project, a large and long effort has been carried out in order to characterize the background of sodium iodide crystals. In this paper we present in detail our background model for a 9.6 kg NaI (Tl) detector taking data at the Canfranc Underground Laboratory (LSC): most of the contaminations contributing to the background have been precisely identified and quantified by different complementary techniques such as HPGe spectrometry, discrimination of alpha particles vs. beta/gamma background by Pulse Shape Analysis (PSA) and coincidence techniques; then, Monte Carlo (MC) simulations using Geant4 package have been carried out for the different contributions. Only a few assumptions are required in order to explain most of the measured background at high energy, supporting the goodness of the proposed model for the present ANAIS prototype whose background is dominated by 40K bulk contamination. At low energy, some non-explained background components are still present and additional work is required to improve background understanding, but some plausible background sources contributing in this range have been studied in this work. Prospects of achievable backgrounds, at low and high energy, for the ANAIS-upgraded detectors, relying on the proposed background model conveniently scaled, are also presented.