Search of the neutrino-less double beta decay of

The CUPID-0 experiment searches for double beta decay using cryogenic calorimeters with double (heat and light) read-out. The detector, consisting of 24 ZnSe crystals 95$$\%$$ enriched in $$^{82}$$Se and two natural ZnSe crystals, started data-taking in 2017 at Laboratori Nazionali del Gran Sasso. We present the search for the neutrino-less double beta decay of $$^{82}$$Se into the 0$$_1^+$$, 2$$_1^+$$ and 2$$_2^+$$ excited states of $$^{82}$$Kr with an exposure of 5.74 kg$$\cdot $$yr (2.24$$\times $$10$$^{25}$$ emitters$$\cdot $$yr). We found no evidence of the decays and set the most stringent limits on the widths of these processes: $$\varGamma $$($$^{82}$$Se $$\rightarrow ^{82}$$Kr$$_{0_1^+}$$)8.55$$\times $$10$$^{-24}$$ yr$$^{-1}$$, $$\varGamma $$ ($$^{82}$$ Se $$\rightarrow ^{82}$$ Kr $$_{2_1^+}$$)$$\,{<}\,6.25 \,{\times }\,10^{-24}$$ yr$$^{-1}$$, $$\varGamma $$($$^{82}$$Se $$\rightarrow ^{82}$$Kr$$_{2_2^+}$$)8.25$$\times $$10$$^{-24}$$ yr$$^{-1}$$ (90$$\%$$ credible interval)