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Excited states in neutron-rich nuclei located south-east of $^{132}$Sn areinvestigated by shell-model calculations. A new shell-model Hamiltonian isconstructed for the present study. The proton-proton and neutron-neutroninteractions of the Hamiltonian are obtained through the existing CD-Bonn $G$matrix results, while the proton-neutron interaction across two major shells isderived from the monopole based universal interaction plus the M3Y spin-orbitforce. The present Hamiltonian can reproduce well the experimental dataavailable in this region, including one-neutron separation energies, levelenergies and the experimental $B(E2)$ values of isomers in $^{134,136,138}$Sn,$^{130}$Cd, and $^{128}$Pd. New isomers are predicted in this region, $e.g.$ in$^{135}$Sn, $^{131}$Cd, $^{129}$Pd, $^{132,134}$In and $^{130}$Ag, in whichalmost no excited states are known experimentally yet. In the odd-odd$^{132,134}$In and $^{130}$Ag, the predicted very long $E2$ life-times of thelow-lying $5^{-}$ states are discussed, demanding more information on therelated proton-neutron interaction. The low-lying states of $^{132}$In arediscussed in connection with the recently observed $\gamma$ rays. The predicted$19/2^{-}$ isomer in $^{129}$Pd could decay by both electromagnetic transitionsand neutron emission with comparable partial life-times, making it a goodcandidate for neutron radioactivity, a decay mode which is yet to bediscovered.

Isomerism in the "south-east" of $^{132}$Sn and a predicted neutron-decaying isomer in $^{129}$Pd