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Search for rare alpha and double beta decays of Yb isotopes to excited levels of daughter nuclei

A search for alpha and double beta decays of ytterbium isotopes was performed with an ultra-low background high purity germanium detector at Gran Sasso Underground Laboratory (Italy). A 194.7 g Yb$_2$(C$_2$O$_4$)$_3$ powder sample was measured for 11.3~d with a total Yb exposure of 1.25 kg$\times$d. Half-life limits for $α$-decay modes of $^{168}$Yb, $^{170}$Yb, $^{171}$Yb, $^{172}$Yb, $^{173}$Yb, $^{174}$Yb and $^{176}$Yb into the first excited states have been obtained between $6\times10^{14}$ yr and $2\times10^{16}$ yr. These are the first experimental constraints of these decay modes. Double electron capture of $^{168}$Yb and double beta decay of $^{176}$Yb into the first excited 2$^+$ and 0$^+$ states could be excluded with limits between $1\times10^{14}$ yr to $8\times10^{16}$ yr. This improves the experimental information on some of the decay modes compared to previous constraints.