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 the 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.

Figure 1

$R=E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$ distribution of the 203 TRM-solvable nuclei in the ENSDF (see text). Peaks for $\gamma$ instability ($R\simeq 5/2$) and an axially symmetric rotor ($R\simeq 10/3$) are highlighted.

Figure 2

Experimental $E\left(2_2^{+}\right)$ versus $E\left(2_1^{+}\right)$ for the 177 nuclei with $R=2.05\sim 3.15$ in the ENSDF. The $E\left(2_2^{+}\right)=2E\left(2_1^{+}\right)$ line is highlighted.

Figure 3

Plot of the estimated $\left|Q\right(2_1^{+}\left)\right|$ values based solely on the use of experimental $B\left(E2\right)$ values according to Eqs. (12) and (13), against the experimental data, for the 78 nuclei with available data in the ENSDF. The diagonal line is a measure of the quality of the estimates.

Figure 4

Estimated $\left|Q\right(2_1^{+}\left)\right|$ values based on experimental excitation energies and $B\left(E2\right)\mathrm{s}$ (see text) against experimental values, for the 48 and 63 nuclei with available data in the ENSDF appropriate to the TRM and AHV, respectively. The diagonal line is a measure of the quality of the agreement. The TRM data points are shown in colors associated with the $R$ values (the map illustrated on the right). The red dashed ellipse, which highlights the TRM estimates that deviate most dramatically from the data. These deviations correspond to fairly typical vibrators with $R=2.1\sim 2.4$, including several Ru, Pd, and Cd isotopes.

Figure 5

$R$-normalized $P\left(\right|\theta \left|\right)$ distribution (square points) defined by Eq. (20). The error bar represents the statistical error. The peak fit (solid line) has its center at $\left|\theta \right|=34.9{\left(2\right)}^{\circ }$, as highlighted. This figure uses the same statistical ensemble as in Fig. 1.