High-spin structures of five N=82 isotopes: 54 136 Xe, 55 137 Cs, 56 138 Ba, 57 139 La, and 58 140 Ce

Five $N=82$ isotones have been produced in two fusion-fission reactions and their $\ensuremath{\gamma}$ rays studied with the Euroball array. The high-spin states of ${}^{139}$La have been identified, 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 ${}^{136}$Xe and ${}^{137}$Cs. Several cascades involving $\ensuremath{\gamma}$ rays of ${}^{139}$La have been found to be delayed; they deexcite an isomeric state with ${T}_{1/2}=315(35)$ 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 ${}^{136}$Xe, ${}^{137}$Cs, and ${}^{138}$Ba.