Lifetimes in ${}^{124}\mathrm{Te}$: Examining critical-point symmetry in the Te nuclei

The Doppler-shift attenuation method following inelastic neutron scattering was used to determine the lifetimes of nuclear levels to 3.3-MeV excitation in ${}^{124}\mathrm{Te}$. Level energies and spins, $\gamma$-ray energies and branching ratios, and multipole-mixing ratios were deduced from measured $\gamma$-ray angular distributions at incident neutron energies of 2.40 and 3.30 MeV, $\gamma$-ray excitation functions, and $\gamma \gamma$ coincidence measurements. The newly obtained reduced transition probabilities and level energies for ${}^{124}\mathrm{Te}$ were compared to critical-point symmetry model predictions. The $E\left(5\right)$ and ${\beta }^4$ potential critical-point symmetries were also investigated in ${}^{122}\mathrm{Te}$ and ${}^{126}\mathrm{Te}$.

Figure 1

Portions of the $\gamma \gamma$ coincidence spectrum from a gate set on the 646-keV $\gamma$ ray from the $4_1^{+}\to 2_1^{+}$ transition in ${}^{124}\mathrm{Te}$.

Figure 2

Angular distributions of emitted $\gamma$ rays from excited levels in ${}^{124}\mathrm{Te}$ are shown in Figs. 2, 2, and 2. The ${\chi }^2$ vs ${\tan }^{-1}\left(\delta \right)$ curve shown in Fig. 2(b) is for the 1580-keV $\gamma$ ray from the 2183-keV level. The 2183-keV level has previously been reported as having a spin of both $J=1$ [9] and $J=2$ [11]. The $J=1$ and $J=2$ possible spin solutions are shown by the solid and dashed lines, respectively, in Fig. 2.

Figure 3

Relative $\gamma$-ray production cross sections observed in ${}^{124}\mathrm{Te}$ compared to statistical model calculations are shown. Data and calculations shown in Figs. 3, 3, and 3 were used to clarify the spin of the 2083-keV level, verify a $2^{+}$ level at 2322 keV, and identify a new $0^{+}$ level at 2530, respectively. The legend for the model calculations for different spins is shown in Fig. 3.

Figure 4

Doppler shifts for several $\gamma$ rays in ${}^{124}\mathrm{Te}$ are shown in Figs. 4–4. The Doppler shifts and the experimental $F(\tau$) value for the 2747-keV $\gamma$ ray are shown in Fig. 4, while the theoretical $F(\tau$) curve generated using the Winterbon formalism is shown in Fig. 4, with the dashed line showing the extrapolated lifetime.

Figure 5

Experimental low-lying positive-parity levels and $B(\mathit{E}2$) values in ${}^{124}\mathrm{Te}$ compared to predicted values from ${\beta }^4$ potential [20] and $E\left(5\right)$ critical-point symmetry calculations [15, 18]. The dashed lines (red) are observed transitions for which $B(\mathit{E}2$) values are from Ref. [11]; the dot-dashed lines (blue) are observed transitions for which $B(\mathit{E}2$) values have not been determined; the dot-dot-dot-dashed lines (green) represent $B(\mathit{E}2$) values from Ref. [12]; and the solid and dashed (upper limits) black lines are from this work. The ordered pairs under the levels correspond to ($\xi ,\tau$) in ${\beta }^4$ and $E\left(5\right)$ symmetry calculations.

Figure 6

Experimental low-lying positive-parity levels and $B(\mathit{E}2$) values in ${}^{122}\mathrm{Te}$ compared to predicted values from ${\beta }^4$ potential [20] and $E\left(5\right)$ critical-point symmetry calculations [15, 18]. The dot-dashed lines (blue) are observed transitions for which $B(\mathit{E}2$) values have not been determined; the dashed lines (red) are observed transitions for which $B(\mathit{E}2$) values are from Ref. [46]; the dot-dot-dot-dashed lines (green) represent $B(\mathit{E}2$) values from Ref. [12]; and the solid and dashed (upper limits) black lines represent values from Ref. [21]. The ordered pairs under the levels correspond to ($\xi ,\tau$) in ${\beta }^4$ and $E\left(5\right)$ symmetry calculations.

Figure 7

Experimental low-lying positive-parity levels and $B(\mathit{E}2$) values in ${}^{126}\mathrm{Te}$ compared to predicted values from ${\beta }^4$ potential [20] and $E\left(5\right)$ critical-point symmetry calculations [15, 18]. The dashed lines (red) are observed transitions for which $B(\mathit{E}2$) values are from Ref. [47] and the black lines represent values from Ref. [22]. The ordered pairs under the levels correspond to ($\xi ,\tau$) in ${\beta }^4$ and $E\left(5\right)$ symmetry calculations.