Observation of a low energy nuclear recoil peak in the neutron calibration data of an Al$_{2}$O$_{3}$ crystal in CRESST-III

The current generation of cryogenic solid state detectors used in direct dark matter and CE\textnu NS searches typically reach energy thresholds of $\mathcal{O}$(10)$\,$eV for nuclear recoils. For a reliable calibration in this energy regime a method has been proposed, providing mono-energetic nuclear recoils at low energies $\sim\,$100$\,$eV$\,$-$\,$1$\,$keV. In this work we report on the observation of a peak at (1113.6$^{+6.5}_{-6.5}$)$\,$eV in the data of an Al$_{2}$O$_{3}$ crystal in CRESST-III, which was irradiated with neutrons from an AmBe calibration source. We attribute this mono-energetic peak to the radiative capture of thermal neutrons on $^{27}$Al and the subsequent de-excitation via single $γ$-emission. We compare the measured results with the outcome of Geant4 simulations and investigate the possibility to make use of this effect for the energy calibration of Al$_{2}$O$_{3}$ detectors at low energies. We further investigate the possibility of a shift in the expected energy scale of this effect caused by the creation of defects in the target crystal.