  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.
