New Limits on Double Electron Capture of ${}^{40}$Ca and ${}^{180}$W

We analyzed low-background data from the CRESST-II experiment with a total net exposure of 730 kg days to extract limits on double electron capture processes. We established new limits for ${}^{40}$Ca with $T_{1\mathrm{/}2}^{2v2K}>9.9\times {10}^{21}$ y and $T_{1\mathrm{/}2}^{0v2EC}>1.4\times {10}^{22}$ y and for ${}^{180}$W with T${}_{1\mathrm{/}2}^{2v2K}>3.1\times {10}^{19}$ y and $T_{1\mathrm{/}2}^{0v2EC}>9.4\times {10}^{18}$ y at 90% CL. Depending on the process, these values improve the currently best limits by a factor of $\sim$1.4-30.