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In the present work recently available experimental data [A. Astier et al,Phys. Rev. C 85, 064316 (2012)] for high-spin states of five N=82 isotones,$^{136}_{54}$Xe, $^{137}_{55}$Cs, $^{138}_{56}$Ba, $^{139}_{57}$La, and$^{140}_{58}$Ce have been interpreted with state-of-the-art shell modelcalculations. The calculations have been performed in the 50-82 valence shellcomposed of $1g_{7/2}$, $2d_{5/2}$, $1h_{11/2}$, $3s_{1/2}$, and $2d_{3/2}$orbitals. We have compared our results with the available experimental data forexcitation energies including high-spin states, occupancy numbers andtransition probabilities. As expected the structure of these isotones are dueto proton excitations across Z=50 shell. The structure of the positive-paritystates are mainly from $(\pi g_{7/2}\pi d_{5/2})^n$ and $(\pi g_{7/2}\pid_{5/2})^{n-2}(\pi h_{11/2})^2$ configurations, while the negative-paritystates have $(\pi g_{7/2}\pi d_{5/2})^{n}(\pi h_{11/2})^1$ configuration.Additionally, for the $^{136}_{54}$Xe, $^{137}_{55}$Cs and $^{138}_{56}$Baisotones the excitation of the neutrons across N=82 gap is important.

High-spin structures of $^{136}_{54}$Xe, $^{137}_{55}$Cs, $^{138}_{56}$Ba, $^{139}_{57}$La, and $^{140}_{58}$Ce : A shell model description