  Large basis untruncated shell model calculations have been done for the A=138
neutron -rich nuclei in the pi(gdsh) X nu(hfpi) valence space above the 132Sn
core. Two (1+2) -body nuclear Hamiltonians, viz., realistic CWG and empirical
SMPN in this model space have been used. Calculated ground state binding
energies, level spectra and other spectroscopic properties have been compared
with the available experimental data. Importance of untruncated shell model
calculations in this model space has been pointed out. Shell model results for
the very neutron rich Sn isotope (138Sn, N/Z=1.76) of astrophysical interest
for which no spectroscopic information except beta -decay half life is
available, have been presented. Shell structure and evolution of collectivity
in the even-even A=138 isobars have been studied as a function of valence
neutron and /or proton numbers. Calculations done for the first time, reproduce
remarkably well the collective vibrational states in 138Te and 138Xe.
Comparison of some of the important two-body matrix elements of the empirical
SMPN, CW5082 and the realistic CWG interactions has been done. These matrix
elements are important for ground state binding energies and low-lying spectra
of nuclei in this region. Consideration of the predictability of the two
interactions seems to suggest that, in order to incorporate the special
features of the N-N interaction in such exotic n-rich environment above the
132Sn core, the use of local spectroscopic information from the region might be
essential.
