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Global correlations between electromagnetic and spectroscopic properties of collective $2^+_1$ and $2^+_2$ states

By using the general triaxial rotor model (TRM) and the phonon-configuration mixing scheme within an anharmonic-vibrator(AHV) framework, a series of global correlations between electromagnetic properties of nuclear $2^+_1$ and $2^+_2$ states are analytically established. The correlations from both models can roughly describe the experimental data involving quadrupole collectivity with few exceptions. Furthermore, there seems to be a robust orthogonal transformation between the AHV and TRM bases for realistic nuclear systems, suggesting that the two models may in fact be describing the collective features of nuclear low-lying states in similar model spaces.