Five N=82 isotones have been produced in two fusion-fission reactions and their gamma-rays studied with the Euroball array. The high-spin states of 139La have been identified for the first time, while the high-spin yrast and near-to-yrast structures of the four others have been greatly extended. From angular correlation analysis,spin values have been assigned to some states of 136Xe and 137Cs. Several cascades involving gamma-rays of 139La have been found to be delayed, they deexcite an isomeric state with T1/2= 315(35) ns located at 1800-keV excitation energy. The excited states of these five N=82 isotones are expected to be due to various proton excitations involving the three high-j subshells located above the Z=50 shell closure. This is confirmed by the results of shell-model calculations performed in this work. In addition, high-spin states corresponding to the excitation of the neutron core have been unambiguously identified in 136Xe, 137Cs, and 138Ba.
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