Characterisation of low background CaWO$_4$ crystals for CRESST-III

The CRESST-III experiment aims at the direct detection of dark matter particles via their elastic scattering off nuclei in a scintillating CaWO4 target crystal. For many years CaWO4 crystals have successfully been produced in-house at Technische Universität München with a focus on high radiopurity. To further improve the CaWO4 crystals, an extensive chemical purification of the raw materials has been performed and the crystal TUM93 was produced from this powder. We present results from an α-decay rate analysis performed on 344 days of data collected in the ongoing CRESST-III data-taking campaign. The α-decay rate could significantly be reduced.