Electromagnetic Moments of Radioactive ${}^{136}\mathrm{Te}$ and the Emergence of Collectivity $2\mathrm{p}\oplus 2\mathrm{n}$ Outside of Double-Magic ${}^{132}\mathrm{Sn}$

Radioactive ${}^{136}\mathrm{Te}$ has two valence protons and two valence neutrons outside of the ${}^{132}\mathrm{Sn}$ double shell closure, providing a simple laboratory for exploring the emergence of collectivity and nucleon-nucleon interactions. Coulomb excitation of ${}^{136}\mathrm{Te}$ on a titanium target was utilized to determine an extensive set of electromagnetic moments for the three lowest-lying states, including $B(E2;0_1^{+}\to 2_1^{+})$, $Q(2_1^{+})$, and $g(2_1^{+})$. The results indicate that the first-excited state, $2_1^{+}$, composed of the simple $2p\oplus 2n$ system, is prolate deformed, and its wave function is dominated by excited valence neutron configurations, but not to the extent previously suggested. It is demonstrated that extreme sensitivity of $g(2_1^{+})$ to the proton and neutron contributions to the wave function provides unique insight into the nature of emerging collectivity, and $g(2_1^{+})$ was used to differentiate among several state-of-the-art theoretical calculations. Our results are best described by the most recent shell model calculations.

Figure 1

The $\gamma$-ray spectra of (a) ${}^{136}\mathrm{Te}$, (b) ${}^{136}\mathrm{Te}$ with a reduced vertical scale, and (c) ${}^{46–50}\mathrm{Ti}$, using a different Doppler correction. The inset in panel (a) shows the $4_1^{+}\to 2_1^{+}$ $\gamma$-ray transition and the Compton background. The Compton edge component (red) was modeled from data on ${}^{126}\mathrm{Te}$.

Figure 2

Sensitivity of $⟨0_1^{+}||M(E2)||2_1^{+}⟩$ to $⟨2_1^{+}||M(E2)||2_1^{+}⟩$ per BareBall ring and the total ${\chi }^2$.

Figure 3

(a) Total ${\chi }^2$ vs $g^2\tau$ and (b) $G_k$ vs $g^2\tau$ calibration curves for BareBall ring 3. The best fit $g^2\tau$ value for ${}^{136}\mathrm{Te}$, and its uncertainty, is projected onto the curves (red filled). Also shown are calibration data from stable Te isotopes that define the $G_k$ curves [22]. Results for ${}^{125}\mathrm{Te}$ are blue filled. Note that there is no $G_4$ term for $I=3/2$ states and that the differences in $G_k$ values for $I=3/2,2,5/2$ are small compared to the experimental uncertainty.

Figure 4

The $g(2_1^{+})$ versus $B(E2;0_1^{+}\to 2_1^{+})$ experimental value (red), compared to the present SM1 and SM2 and previous MCSM [8] and QRPA [9] calculations.

Figure 5

The (a) $E(2_1^{+})$, (b) $B(E2;0_1^{+}\to 2_1^{+})$, and (c) $g(2_1^{+})$ systematics for ${}^{132,134,136}\mathrm{Te}$ from the present (red) and previous studies [3, 4, 6, 7], compared to the present SM1 (solid gray line) and SM2 (solid black line) and previous MCSM (dashed gray line) [8] and QRPA (dashed black line) [9] calculations.