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Symmetries are known to play an important role in the low lying levelstructure of Sn isotopes, mostly in terms of the seniority and generalizedseniority schemes. In this paper, we revisit the multi-j generalized seniorityapproach for the first excited $2^+$ and $3^-$ states in the Cd ($Z=48$), Sn($Z=50$) and Te ($Z=52$) isotopes, where the Cd and Te isotopes representtwo-proton hole and two-proton particle nuclei, thus involving both kind ofparticles (protons and neutrons) in contrast to Sn isotopes. Interestingly, theapproach based on neutron valence space alone is able to explain the B(E2) andB(E3) trends respectively for the $2^+$ and $3^-$ states in all the three Cd,Sn and Te isotopes. The new results on the inverted parabolic behavior of B(E3)values in Cd and Te isotopes are understood in a manner identical to that of Snisotopes by using the generalized seniority scheme. No shell quenching issupported by these calculations; hence, the neutron magic numbers, $N=50$ and$N=82$, remain robust in these isotopic chains. It is quite surprising that thegeneralized seniority continues to be reasonably successful away from thesemi-magic region, thus providing a unifying view of the $2^+$ and $3^-$states.

A unified view of the first-excited $2^+$ and $3^-$ states of Cd, Sn and Te isotopes