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A search for double-beta decay of osmium has been realized for the first timewith the help of an ultra-low background HPGe gamma detector at the undergroundGran Sasso National Laboratories of the INFN (Italy). After 2741 h of datataking with a 173 g ultra-pure osmium sample limits on double-beta processes in184Os have been established at the level of T_{1/2} about 10^{14}-10^{17} yr.Possible resonant double-electron captures in 184Os were searched for with asensitivity T_{1/2} about 10^{16} yr. A half-life limit T_{1/2} > 5.3 10^{19}yr was set for the double-beta decay of 192Os to the first excited level of192Pt. The radiopurity of the osmium sample has been investigated andradionuclides 137Cs, 185Os and 207Bi were detected in the sample, whileactivities of 40K, 60Co, 226Ra and 232Th were limited at the mBq/kg level.

First search for double-beta decay of 184Os and 192Os