In this work, we have presented a microscopic shell-model description of the structure and collective behavior of intermediate-mass nuclei around doubly magic Sn-100 and Sn-132 nuclei. The Sn-isotopes lie between the two doubly magic nuclei and cover a range from exotic proton-rich N=Z nuclei to exotic neutron-rich nuclei with N/Z > 1.6. The results obtained using BIGSTICK code for the low-level excitation states and transition probabilities for the studied Sn and Ba isotopic chains have been discussed in the radiance of available experimental data. We have used Sn-100 as a core for all the studied isotopes with the same valence space (i.e. 1d(5/2), 2s(1/2), 1d(3/2), 0g(7/2), 0h(11/2) or 'sdgh') for both protons (Z) and neutrons (N) between 50 and 82. These calculations are performed by means of globally optimized monopole effective interaction for the sdgh-shell.