Abstract
The aim of the present letter is to show that there exist two different longitudinal coordinations of the collective vibrational levels built on several quadrupoles phonons ($d$ bosons). The first one reproduces that given earlier by Saka\ifmmode \check{i}\else \v{i}\fi{}. The second one explains and generalizes the $X$, $Y$, $Z$, ${X}^{\ensuremath{'}}$, ${Z}^{\ensuremath{'}}$, $\ensuremath{\beta}$, and $\ensuremath{\Delta}$ bands recently introduced by Iachello and Arima.NUCLEAR STRUCTURE Classification of excited states in even-even nuclei.
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