Systematics of the first 2⁺ excitation in spherical nuclei with the Skryme quasiparticle random-phase approximation

We use the quasiparticle random-phase approximation (QRPA) and the Skyrme interactions SLy4 and SkM^* to systematically calculate energies and transition strengths for the lowest 2⁺ state in spherical even-even nuclei. The SkM^* functional, applied to 178 spherical nuclei between Z=10 and 90, produces excitation energies that are on average 11% higher than experimental values, with residuals that fluctuate about the average by -35% to +55%. The predictions of SkM^* and SLy4 have significant differences, in part because of differences in the calculated ground state deformations; SkM^* performs better in both the average and dispersion of energies. Comparing the QRPA results with those of generator-coordinate-method (GCM) calculations, we find that the QRPA reproduces trends near closed shells better than the GCM, and that it overpredicts the energies less severely in general.