Search of the neutrino-less double beta decay of $$^{82}$$ 82 Se into the excited states of $$^{82}$$ 82 Kr with CUPID-0

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 $$_{2_1^+}$$ ) $$\,{