Neutrinoless double-beta decay experiments can potentially determine the Majorana or Dirac nature of the neutrino, and aid in understanding the neutrino absolute mass scale and hierarchy. Future 76Ge-based searches target a half-life sensitivity of >10^27 y to explore the inverted neutrino mass hierarchy. Reaching this sensitivity will require a background rate of <1 count tonne^-1 y^-1 in a 4-keV-wide spectral region of interest surrounding the Q value of the decay. We investigate the overburden required to reach this background goal in a tonne-scale experiment with a compact (copper and lead) shield based on Monte Carlo calculations of cosmic-ray background rates. We find that, in light of the presently large uncertainties in these types of calculations, a site with an underground depth >~5200 mwe is required for a tonne-scale experiment with a compact shield similar to the planned 40-kg MAJORANA DEMONSTRATOR. The required overburden is highly dependent on the chosen shielding configuration and could be relaxed significantly if, for example, a liquid cryogen and water shield, or an active neutron shield were employed. Operation of the MAJORANA DEMONSTRATOR and GERDA detectors will serve to reduce the uncertainties on cosmic-ray background rates and will impact the choice of shielding style and location for a future tonne-scale experiment. 4/2013: The peer review process revealed that one of the veto rejection factors (the factor-of-4 described on p12) needs to be better established. Our reevaluation of this parameter to date has not yielded strong support for the value stated in the manuscript, and we require further study to develop a solid estimate. This further study will supersede the work described in this manuscript, and may or may not lead to the same conclusion regarding the ~>5200 mwe requirement for future tonne-scale 76Ge neutrinoless double beta decay experiments.
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