Enhanced Quadrupole and Octupole Strength in Doubly Magic ${}^{132}\mathrm{Sn}$

The first $2^{+}$ and $3^{-}$ states of the doubly magic nucleus ${}^{132}\mathrm{Sn}$ are populated via safe Coulomb excitation employing the recently commissioned HIE-ISOLDE accelerator at CERN in conjunction with the highly efficient MINIBALL array. The ${}^{132}\mathrm{Sn}$ ions are accelerated to an energy of $5.49\mathrm{MeV}/\mathrm{nucleon}$ and impinged on a ${}^{206}\mathrm{Pb}$ target. Deexciting $\gamma$ rays from the low-lying excited states of the target and the projectile are recorded in coincidence with scattered particles. The reduced transition strengths are determined for the transitions $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+}$, $0_{\mathrm{g}.\mathrm{s}.}^{+}\to 3_1^{-}$, and $2_1^{+}\to 3_1^{-}$ in ${}^{132}\mathrm{Sn}$. The results on these states provide crucial information on cross-shell configurations which are determined within large-scale shell-model and Monte Carlo shell-model calculations as well as from random-phase approximation and relativistic random-phase approximation. The locally enhanced $B(E2;0_{\mathrm{g}.\mathrm{s}.}^{+}\to 2_1^{+})$ strength is consistent with the microscopic description of the structure of the respective states within all theoretical approaches. The presented results of experiment and theory can be considered to be the first direct verification of the sphericity and double magicity of ${}^{132}\mathrm{Sn}$.

Figure 1

(a) Low-energy part of the $\gamma$-ray spectrum detected in coincidence with scattered $A=132$, 166 nuclei after Doppler correction for nuclei with $A=132$ and background subtraction. Below 600 keV, several $\gamma$-ray transitions of the beam contaminants ${}^{132}\mathrm{Ba}$ and ${}^{166}\mathrm{Yb}$ are identified. The ground-state transition of ${}^{206}\mathrm{Pb}$ is Doppler broadened. (b) Partial spectrum, Doppler corrected for ${}^{206}\mathrm{Pb}$. (c) High-energy part of the $\gamma$-ray spectrum. The ${}^{132}\mathrm{Sn}$ $2_1^{+}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ and $3_1^{-}\to 0_{\mathrm{g}.\mathrm{s}.}^{+}$ transitions are identified. Accumulation of counts below 4 MeV is caused by the Compton edge superimposed by statistical fluctuations of $\gamma$ radiation following $\beta$ decay after background correction. (d) Same as in (c) with an additional restriction to scattering angles ensuring pure electromagnetic excitation. The peak integrals used for the analysis are shaded in blue. The red dashed line indicates the background fit.

Figure 2

The $1\sigma$ contour of the normalized total ${\chi }^2$ surface with respect to the $⟨0_{\mathrm{g}.\mathrm{s}.}^{+}|E2|2_1^{+}⟩$ and $⟨0_{\mathrm{g}.\mathrm{s}.}^{+}|E3|3_1^{-}⟩$ transitional matrix elements of ${}^{132}\mathrm{Sn}$ obtained with Gosia2. The inset illustrates the level scheme used for the calculations.

Figure 3

Comparison of the experimental excitation energies (a,c) and reduced transition probabilities (b,d) of ${}^{132}\mathrm{Sn}$ indicated with red lines, with latest LSSM, MCSM, and mean-field calculations utilizing RPA as well as RRPA (from Ref. [39]) for the $2_1^{+}$ (a,b) and for the $3_1^{-}$ (c,d) state. The gray bands display the $1\sigma$ deviations of the $B(E\lambda )$ values. Details are given in the text.

Figure 4

$T$-plots of the $0_{\mathrm{g}.\mathrm{s}.}^{+}$ (a,c,e) and $2_1^{+}$ states (b,d,f) of ${}^{130}\mathrm{Sn}$ (a,b), ${}^{132}\mathrm{Sn}$ (c,d), and ${}^{130}\mathrm{Sn}$ (e,f) show a pronounced potential-energy minimum for the spherical doubly magic configuration. Circles on the PES represent shape dynamics of MCSM basis vectors. See text for details and discussion.