The study of neutron-rich nuclei near 132Sn is interesting and important for both nuclear structure and nuclear astrophysics. For a considerably large model space allowing cross-shell excitations, a new effective Hamiltonian is determined by employing the extended pairing-plus-quadrupole model with monopole corrections. Calculations for two mass regions, for the north-east quadrant of 132Sn with Z >50 and N >82 and for the south-west quadrant with Z <50 and N <82, have been performed recently. The structure of these nuclei is analyzed in detail, and the role of the monopole corrections can be clearly seen.
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