Systematics of the first2+excitation in spherical nuclei with the Skryme quasiparticle random-phase approximation

Abstract

We use the quasiparticle random-phase approximation (QRPA) and the Skyrme interactions $\mathrm{SLy}4$ and ${\mathrm{SkM}}^{*}$ to systematically calculate energies and transition strengths for the lowest ${2}^{+}$ state in spherical even-even nuclei. The ${\mathrm{SkM}}^{*}$ 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 $\ensuremath{-}35%$ to $+55%$. The predictions of ${\mathrm{SkM}}^{*}$ and $\mathrm{SLy}4$ have significant differences, in part because of differences in the calculated ground state deformations; ${\mathrm{SkM}}^{*}$ 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.