Universal description of the $0_2^{+}$ state in collective even-$A$ nuclei

A generalized description of the $0_2^{+}$ state in collective even-$A$ nuclei is obtained in the $Q$-excitation scheme. It is shown that for the whole symmetry triangle the two-$Q$ and three-$Q$ configurations are exhausted in a sum more than 90% of the norm of the $0_2^{+}$ state. For the parameter range important for the description of nuclear data it is about 95% of the norm. The results obtained are applied to the description of the $E2\mathrm{}$-decay branching ratio of the $0_2^{+}$ state in nondeformed nuclei.