Study of Grodzins relation of B(E2) with E(21+) in A=130, 100 and 80 regions

The nuclei in the A = 130, 100 and 80 regions, lying on both sides of the beta-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. [E(2(1)(+)) x B(E2, 0(1)(+) -> 2(1)(+)) = constant x Z(2) A(-2/3)], for the ground bands of even-Z even-N nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of B(E2) to [1/E(2(1)(+))], is illustrated for the Z = 30 Zn to Z = 48 Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of Z = 20, and 28 rather than Z = 40, for Mo to Cd isotopes for a microscopic calculation.