Systematics of 2+ states in semi-magic nuclei

Abstract

We propose a simple systematics of low lying 2 + 1 energy levels and electromagnetic transitions in semi-magic isotopic chains Z = 28, 50, 82 and isotonic chains N = 28, 50, 82, 126. To this purpose we use a two-level pairing plus quadrupole Hamiltonian, within the spherical Quasiparticle Random Phase Approximation (QRPA). We derive a simple relation connecting the 2 + 1 energy with the pairing gap and quadrupole-quadupole (QQ) interaction strength. It turns out that the systematics of energy levels and B(E2) values predicted by this simple model is fulfilled with a reasonable accuracy by all available experimental data. Both systematics suggest that not only active nucleons but also those filling closed shells play an important role.