Alpha backgrounds in the AMoRE-Pilot experiment

Searches for neutrinoless double beta decay generally require ultimate low backgrounds. Surface $\alpha$ decays on the crystals themselves or nearby materials can deposit a continuum of energies that can be as high as the $Q$-value of the decay and may cover in the region of interest (ROI). The AMoRE-Pilot experiment is an initial phase of the AMoRE search for neutrinoless double beta decay of $^{100}$Mo, with the purpose of investigating the level and sources of backgrounds. To understand those background events, we have studied backgrounds from radioactive contaminations internal to and on the surface of the crystals or nearby materials with Geant4-based Monte Carlo simulations. In this paper, we report the measured $\alpha$ energy spectra fitted with the simulated $\alpha$ energy spectra for the six crystal detectors, where sources of background contributions can be identified at high energy by $\alpha$ peaks for both surface and internal contaminations. We determine the low-energy contributions from internal and surface $\alpha$ contaminations by extrapolating from the $\alpha$ background fitting model.