Distribution of Low-Lying Quadrupole Phonon Strength in Nuclei

The distribution of quadrupole phonon strength to low-lying states in nuclei is examined. It is found that the $2_1^{+}$ and $4_1^{+}$ states of all nuclei from $Z=30\mathrm{} \mathrm{to} 100$ display almost perfect quadrupole phonon character even though they encompass widely ranging structures. The interacting boson approximation reproduces both the very small deviations from phonon purity and the distribution of those deviations as a function of mean field structure in a natural fashion. Simple physical mechanisms explain these results.