Skyrme energy functional and low lying2+states in Sn, Cd, and Te isotopes

We study the predictive power of Skyrme forces with respect to low lying quadrupole spectra along the chains of Sn, Cd, and Te isotopes. Excitation energies and $B\left(E2\right)$ values for the lowest quadrupole states are computed from a collective Schrödinger equation which is deduced through a collective path generated by constraint Skyrme-Hartree-Fock (SHF) plus self-consistent cranking for the dynamical response. We compare the results from four different Skyrme forces, all treated with two different pairing forces (volume versus density-dependent pairing). The region around the neutron shell closure $N=82$ is very sensitive to changes in the Skyrme while the midshell isotopes in the region $N<82$ depend mainly on the adjustment of pairing. The neutron rich isotopes are most sensitive and depend on both aspects.