Evolution of nuclear structure in and around Z = 50 closed shell: Generalized seniority in Cd, Sn and Te isotopes

We study the quadrupole moments and the B(E2; $2^{+}\to 0^{+}$) values for the $11/2^{-}$ states and the first $2^{+}$ states, respectively, by using a multi-j generalized seniority approach in the Cd ($Z=48$), Sn ($Z=50$) and Te ($Z=52$) isotopic chains. The g-factor trends have also been discussed. Although, Cd and Te isotopes represent two-proton hole and two-proton particle systems, thus involving both kind of particles (protons and neutrons) in contrast to Sn ($Z=50$) where only neutrons play a role, we find that a similar model based on neutron valence space alone is able to explain nearly all the gross features and trends. This paper represents the first attempt to test the validity of the generalized seniority scheme away from the semi-magic region and appears to be surprisingly successful. The linearly varying quadrupole moments in Cd, Sn and Te isotopes, are described by using a consistent multi-j configuration. The asymmetric double-hump behavior of B(E2) values in Cd and Te isotopes are understood in a manner identical to that of Sn isotopes by using the generalized seniority scheme for the first time. No shell quenching is supported in the calculations; hence, the neutron magic numbers, $N=50$ and $N=82$, remain robust in these isotopic chains.