A search for double-beta decays of 136Xe to excited states of 136Ba has been performed with the first phase data set of the KamLAND-Zen experiment. The 01+, 21+ and 22+ transitions of 0νββ decay were evaluated in an exposure of 89.5 kg⋅yr of 136Xe, while the same transitions of 2νββ decay were evaluated in an exposure of 61.8 kg⋅yr. No excess over background was found for all decay modes. The lower half-life limits of the 21+ state transitions of 0νββ and 2νββ decay were improved to T1/20ν(0+→21+)>2.6×1025 yr and T1/22ν(0+→21+)>4.6×1023 yr (90% C.L.), respectively. We report on the first experimental lower half-life limits for the transitions to the 01+ state of 136Xe for 0νββ and 2νββ decay. They are T1/20ν(0+→01+)>2.4×1025 yr and T1/22ν(0+→01+)>8.3×1023 yr (90% C.L.). The transitions to the 22+ states are also evaluated for the first time to be T1/20ν(0+→22+)>2.6×1025 yr and T1/22ν(0+→22+)>9.0×1023 yr (90% C.L.). These results are compared to recent theoretical predictions.
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