Detailed spectroscopy of doubly magic ${}^{132}\mathrm{Sn}$

The structure of the doubly magic ${}_{50}{}^{132}\mathrm{Sn}_{82}$ has been investigated at the ISOLDE facility at CERN, populated both by the ${\beta }^{-}\mathrm{decay}$ of ${}^{132}\mathrm{In}$ and ${\beta }^{-}$-delayed neutron emission of ${}^{133}\mathrm{In}$. The level scheme of ${}^{132}\mathrm{Sn}$ is greatly expanded with the addition of 68 $\gamma$ transitions and 17 levels observed for the first time in the $\beta$ decay. The information on the excited structure is completed by new $\gamma$ transitions and states populated in the $\beta \text{−}n$ decay of ${}^{133}\mathrm{In}$. Improved delayed neutron emission probabilities are obtained both for ${}^{132}\mathrm{In}$ and ${}^{133}\mathrm{In}$. Level lifetimes are measured via the advanced time-delayed $\beta \gamma \gamma$(t) fast-timing method. An interpretation of the level structure is given based on the experimental findings and the particle-hole configurations arising from core excitations both from the $N$ = 82 and $Z$ = 50 shells, leading to positive- and negative-parity particle-hole multiplets. The experimental information provides new data to challenge the theoretical description of ${}^{132}\mathrm{Sn}$.

Figure 1

Experimental single-particle and single-hole energies for neutrons ($\nu$) and protons ($\pi$) in the doubly magic nucleus ${}^{132}\mathrm{Sn}$. Following Ref. [9], the energy origin is set in the center of the shell gap (${\lambda }_F$) in order to remove Coulomb energy differences $\mathrm{\Delta }{E}_C$. Binding energies are taken from Ref. [10]. The absolute single-particle energies are given in MeV.

Figure 2

Singles $\gamma$-ray energy spectrum recorded by the HPGe detectors following the ${}^{132}\mathrm{In}$ decay. This histogram was built using the events measured during the 30- to 530-ms time interval after proton pulse. The strongest peaks observed in the spectra are labeled with their energies in keV. The SE and DE labels indicates single-escape and double-escape peaks. The inset is an enlargement of the 2400- to 4450-keV region.

Figure 3

Decay curves of the 375-, 4042-, 2268- and 4352-keV $\gamma$ rays recorded in singles in the HPGe detectors. The region considered for the fit goes from 700 ms, marked with a dark-blue dashed line, up to 2400 ms. This region has been adjusted in order to minimize dead-time effects.

Figure 4

Compton-subtracted $\gamma \text{−}\gamma$ energy spectrum gated on the $6^{+}\to 4^{+}299.3\text{−}\mathrm{keV}\gamma$ transition in ${}^{132}\mathrm{Sn}$. The previously known $\gamma$ rays are labeled with their energies in black. New transitions identified in this work are labeled in red with an asterisk. The negative peaks in the spectrum arise from background subtraction, due to Compton scattering between two HPGe clover detectors.

Figure 5

Level scheme of ${}^{132}\mathrm{Sn}$ observed following the $\beta$ decay of ${}^{132}\mathrm{In}$. Note that the energy gap from the g.s. to the $2_1^{+}$ state is not to scale. The positive-parity states are shown on the left-hand side and the negative-parity ones on the right-hand side. The high-lying $7^{-}$ and $6^{-}$ states feed states of both parities. Levels and transitions previously observed in this decay are colored in black, while those observed for the first time are highlighted in red. Levels previously known from ${}^{248}\mathrm{Cm}$ fission or from ${}^{133}\mathrm{In} \beta \text{−}n$ decay and observed here in the $\beta$ decay of ${}^{132}\mathrm{In}$ are colored in blue.

Figure 6

$\gamma \text{−}\gamma$ spectrum observed in the $\beta$ decay of ${}^{133}\mathrm{In}$, gated on the 4352-keV transition in ${}^{132}\mathrm{Sn}$. The contribution from Compton events beneath the 4352-keV peak has been subtracted. Newly observed $\gamma$ transitions are labeled in red with an asterisk.

Figure 7

Level scheme of ${}^{132}\mathrm{Sn}$ observed following the $\beta \text{−}n$ decay of the ${}^{133}\mathrm{In}$ ($9/2^{+}$) ground state and ($1/2^{-}$) isomer. Note that the energy gap from the g.s. to the $2_1^{+}$ state is not to scale. The positive-parity states are on the left-hand side and the negative-parity states are to the right. The isomer observed feeding to levels in ${}^{132}\mathrm{Sn}$ is provided separately for each decay. Note contributions coming from beam impurity cannot be excluded in the ($1/2^{-}$) decay. Levels and transitions observed for the first time in the $\beta$ decay of ${}^{133}\mathrm{In}$ are highlighted in red.

Figure 8

$\beta$-gated $\gamma$-ray spectra from the $\beta$ decay of ${}^{133}\mathrm{In}$ isomers highlighting the energy range above 5 MeV. Only the events recorded in the time window from 10 to 600 ms since the arrival of the proton pulse are used.

Figure 9

Time delay spectra between the $\beta$ and each of the two ${\mathrm{LaBr}}_3$(Ce) detectors for $\beta \gamma \gamma$(t) events. These distribution are built by selecting the events when the 526-keV transition in the HPGe detectors and the 375-keV transition in the ${\mathrm{LaBr}}_3$(Ce) detector. The lifetime is obtained by a ${\chi }^2$ fit of the whole time distribution to a exponential decay convoluted with a Gaussian function plus a constant background to account for the random background.

Figure 10

Time-delayed $\beta \gamma \gamma$(t) spectra used to measure the lifetime of the 4830-keV $4^{-}$ excited level. The blue spectra depicts the prompt time distribution used as reference, which is obtained by gating on the 479- and 2380-keV transitions in the HPGe and the ${\mathrm{LaBr}}_3$(Ce) detectors respectively. The red one corresponds to events obtained after reversing the gates, the 2380-keV one is applied to the HPGe, and the 479-keV one is for the ${\mathrm{LaBr}}_3$(Ce). The shift measured between the centroid position of each distribution $\mathrm{\Delta }\mathrm{C}$ is caused by the lifetime of the level, but also due the time walk $\mathrm{\Delta }\mathrm{FEP}$ between both energies. The lifetime $\tau$ is obtained by subtracting to the centroid shift the contribution due to the FEP time response.

Figure 11

Calculated energies for the different particle-hole multiplet states in ${}^{132}\mathrm{Sn}$, adopted from the work of J. Blomqvist [46, 47]. The energies and energy splitting within a given multiplet are estimated by scaling the analogous particle-hole states in ${}^{208}\mathrm{Pb}$ and taking into account single-particle energies from neighboring nuclei. Previously identified levels are plotted with continuous lines. The experimental energies from our work are shown for the newly identified states. The levels whose energies appear between brackets correspond to tentative assignments.