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

The structure of the doubly magic $^{132}_{50}$Sn$_{82}$ has been investigated at the ISOLDE facility at CERN, populated both by the $\beta^-$decay of $^{132}$In and $\beta^-$-delayed neutron emission of $^{133}$In. The level scheme of $^{132}$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 $\beta$-n decay of $^{133}$In. Improved delayed neutron emission probabilities are obtained both for $^{132}$In and $^{133}$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 \textit{N} = 82 and \textit{Z} = 50 shells, leading to positive and negative parity particle-hole multiplets. The experimental information provides new data to challenge the theoretical description of $^{132}$Sn.


I. INTRODUCTION
The 132 Sn nucleus is one of the bastions of our understanding of nuclear structure in the framework of the nuclear shell model. With 50 protons and 82 neutrons it is one of the most exotic doubly-magic nuclei within reach of current experimental facilities. One of the signatures of its doubly-magic nature is the high lying first-excited state at 4041.6 keV [1][2][3]. This value, once scaled by a factor of A 1/3 to account for the size of the nucleus, is large in comparison to other doubly magic nuclei such as 208 Pb and 16 O, which points to a strong double shell closure. The 132 Sn doubly magic structure is also manifested by the almost pure single-particle nature of the levels in 133 Sn. This nature was probed by a transfer reaction in inverse kinematics [4] yielding very large spectroscopic factors.
The region of the nuclear chart around 132 Sn plays an important role in the astrophysical rapid neutroncapture process (r-process), which impacts elemental abundances in the solar system. Recently, the identification of the nucleosynthesis site for neutron-rich nuclei around N = 82 has been reported [5,6] associated to a "kilonova" [7], observed by multimessenger astronomy. The robustness of the N = 82 neutron shell is one of the important parameters when modeling r-process nucleosynthesis and describing light curves arising from compact object mergers. The shell structure in this region is also necessary to understand the role of fission in the r-process [8].
From the point of view on nuclear structure the nuclei with a valence particle or hole around 132 Sn are relevant for investigating single-particle states and transition probabilities. They provide observables that are the main ingredients in state-of-the-art large scale shellmodel calculations to understand the nuclear structure in the region. The single-particle states in the region are represented in Figure 1 following the procedure described in [9], and employing binding energies from [10] and the excitation spectra from 131 Sn, 133 Sn, 133 Sb and 131 In. In particular, the neutron single-particle orbits above the N = 82 shell gap have been taken from lowlying states in 133 Sn: the νf 7/2 ground state and the νp 3/2 , νp 1/2 , νh 9/2 and νf 5/2 states at 854, 1367, 1561 and 2005 keV excitation energy [4,[11][12][13][14][15][16]. The νi 13/2 single-particle state has not been experimentally identified to date [17]. These single particle states are not only relevant for 132 Sn but also for neutron-rich nuclei in its vicinity.
Experimental data on 132 Sn is essential for the shell- * jabenito@ucm.es † lmfraile@ucm.es   FIG. 1. Experimental single-particle and single-hole energies for neutrons (ν) and protons (π) in the doubly-magic nucleus 132 Sn. Following [9] the energy origin is set in the center of the shell gap (λF ) in order to remove Coulomb energy differences ∆EC . Binding energies are taken from [10]. The absolute single-particle energies are given in MeV.
model description of the exotic nuclear region around N = 82 and to provide insight into particle-hole couplings for both protons and neutrons. Most of the excited levels in 132 Sn correspond to particle-hole (p-h) configurations where a proton or a neutron is promoted across the closed shell. The coupling of single particle and single hole configurations ( Figure 1) leads to multiplets of excited states with an expected low admixture of other configurations. The particle-hole residual interaction makes the level energies within a multiplet non-degenerate. The identification of these multiplets provides information on the nuclear two-body matrix elements to first order. Experimentally measured transition rates between states within a multiplet, and also between states of different multiplets, give important knowledge of the underlying single particle structure.
The investigation of the doubly-magic 132 Sn is thus essential for theoretical models aiming at the understanding neutron-rich nuclei in the region. The development of these models is furthermore needed for the description of r-process nuclei that are at present experimentally out of reach.
The most complete β-decay experiment was performed by Fogelberg et al. [18][19][20] at the OSIRIS facility in the 1990s, where the level scheme of 132 Sn was expanded to 21 excited levels, including negative and positive parity states up to the neutron separation energy. Proton particle-hole states were identified for the first time, and the 4352-keV J π = 3 − state was confirmed to have an octupole vibrational character. Lifetime measurements of the excited states down to the ps range were performed, and spin and parities assignments were made for the levels below 5 MeV.
Despite all the detailed studies on 132 Sn attained through the β-decay and fission experiments, many of the expected particle-hole multiplet states remain without experimental identification. Beta decay is the ideal tool to investigate the excited structure of 132 Sn, both directly from 132 In (7 − ) g.s. and via beta-delayed neutron emission from the 133 In (9/2 + ) g.s. and the (1/2 − ) 330-keV beta-decaying isomer. This is due to the large energy window available for the decay, of Q β ( 132 In) = 14140(60) keV and Q βn ( 133 In) = 11010(200) keV (from systematics) [10], respectively, and due to the high spin of the parent nuclei that makes it possible to feed many states in 132 Sn.
In this work we focus on the investigation of the excited structure of 132 Sn populated in β and β-n decay. Taking advantage of the enhanced yield and selectivity achieved at the ISOLDE facility at CERN some of the missing particle-hole multiplet states have been identified. In addition, lifetimes of excited states in 132 Sn have been measured using fast-timing techniques. The results from the β decay study of the 133 In isomers have been partially covered in [16]. Details on the experimental method used in the present work are provided in Section II. The experimental results are presented in Section III and discussed in Section IV. Conclusions are drawn in Section V.

II. EXPERIMENTAL DETAILS
The experiment was carried out at the ISOLDE facility at CERN. It was performed in two separate datataking campaigns in 2016 and 2018, where the excited structure in 132 Sn was populated in the β decay of 132 In and in the β-n decay of the 133 In (9/2 + ) and (1/2 − ) states. The 132 In and 133 In isotopes were produced by the bombardment of a UC x target equipped with a neutron converter by 1.4-GeV protons from the CERN PS-Booster (PSB). The indium ions thermally diffused out of the target and were ionized using the ISOLDE resonance ionization laser ion source (RILIS) [25]. The use of RILIS granted isomeric selectivity, by taking advantage of the difference in the hyperfine splitting of the isomer and ground state. More details on the isomer selection can be found in [26]. Following the ionization, indium ions were extracted and accelerated by a 40-kV potential difference, mass analyzed [27] and implanted on an aluminized mylar tape located at the center of our detector setup at the ISOLDE Decay Station (IDS) [28]. The ions reached the IDS following the time structure of the PSB supercycle whereby proton pulses were grouped into sets of 34 or 35 pulses, out of which around half of them are delivered to the ISOLDE target-unit separated in time by multiples of 1.2 s. The beam was collected on the tape for a fixed time varying from 200 to 400 ms after the impact of each proton pulse. Once every supercycle the tape was moved in order to reduce the activity of long-lived daughter nuclides. The average beam intensity at the experimental station was of the order of 4·10 4 and 2·10 3 ions per second for 132 In and 133 In, respectively. Data were collected for 20 hours for each mass.
The IDS setup consists of a set of detectors aimed at measuring the β and γ radiation emitted after the β-decay of the implanted isotopes. They are arranged in close geometry surrounding the implantation point. The setup can be divided in two branches. The first branch is composed of four clover-type HPGe detectors for γ-ray spectroscopy, with a combined full-energy peak efficiency of 4% at 1173 keV. The second branch is aimed at lifetime measurement of excited states using the Advanced Time-Delayed βγγ(t) (fast timing) technique [29][30][31]. It consists of two LaBr 3 (Ce) crystals with the shape of truncated cones [32] coupled to fast photomultiplier tubes (PMTs) [33], with 1% of total efficiency at 1 MeV each, and an ultrafast 3-mm thick NE111A plastic scintillator used as a β detector, with a ∼20% efficiency. The energy and fast-timing signals are taken from the PMT dynode and anode outputs, respectively. The timing signals are processed by analog constant fraction discriminators and introduced in pairs in timeto-amplitude converter (TAC) modules that provide the time difference between them. In this experiment, time differences between the β and the two LaBr 3 (Ce) detectors as well as between the two LaBr 3 (Ce) detectors were recorded. More details on the setup are provided in [31,34].
All the signals from both branches were read and digitized by the Nutaq digital data acquisition system [35]. Logic signals, such as the time of arrival of the proton pulse on target and the tape movement, were also digitized. Data were collected in a triggerless mode. Events were built during the offline analysis where they were sorted in coincidence windows, and correlated with the proton arrival time. At this stage, the energy calibration for each detector was applied, as well as add-back corrections for the clover detectors. Due to the large energy of the 132 Sn γ rays, a precise efficiency calibration is needed in a wide energy range. Therefore, 152 Eu, 138 Cs, 140 Ba and 133 Ba radioactive sources were used to build the energy calibration. The calibration was extended up to 7.6 MeV by including high-energy γ rays originating from the capture of thermal neutrons produced at the ISOLDE target station, mainly in iron (IDS frame) and germanium (HPGe detectors).
For the timing measurements, the calibration of the LaBr 3 (Ce) time response for full-energy peaks (FEP) as a function of energy, the FEP walk curve, is required. It was built for each LaBr 3 (Ce) detector using βγ(t) and γγ(t) coincidences with 140 Ba/ 140 La and 152 Eu γ-ray sources, 138 Cs and 88 Rb on-line sources and by including several transitions in 132 Sb as an internal calibration source. In this way, we obtained FEP time response curves for each LaBr 3 (Ce) detector in the energy range 100 keV to 2.6 MeV, with an average one-sigma error of 3 ps. A similar procedure was implemented to build the Compton walk curve in order to take care of the corrections due to Compton events.

III. EXPERIMENTAL RESULTS
The excited structure of 132 Sn was populated through the β decay of 132 In (7 − ), and from the β-n decay of the 133 In (9/2 + ) g.s. and the (1/2 − ) isomer. The large differences in the spin and parity of the parent nuclei result in distinct feeding patterns for each decay, which provides information on the spin and parity of the levels fed.
Owing to the large difference in the β-decay half-lives of 132 In and 132 Sn, of 200(2) ms and 39.7(8) s [3], respectively, the time distribution relative to the arrival of the proton on target makes it possible to identify whether a γ ray has been emitted during the β decay of 132 In or from the daughters. A similar situation occurs for the β decay of 133 In. Apart from the time distribution, the identification of the γ-rays belonging to 132 Sn is based on γ-γ coincidences with previously-known transitions.

A. Beta decay of 132 In
The Q β in 132 In is 14140(60) keV, while the neutron separation energy in 132 Sn is 7353(4) keV [10]. Hence, the feeding of excited states up to ≈ 7 MeV is possible in this decay and high energy γ-rays may be observed. The excited structure populated in the 132 In β decay is very complex. The high spin of the parent, (7 − ) [36], favors the population of high spin (6-8) excited states in the energy range from 4 to 7 MeV. Those levels can only de-excite to the ground state by means of γ-ray cascades of 3 or more transitions. As discussed before, due to the doubly magic nature of 132 Sn, the first excited state appears at a very high energy, 4041 keV.Therefore, it is not expected to find new levels in this decay that can de-excite directly to the g.s. with an energy below 4 MeV.
The energy spectra recorded by the HPGe clover detectors, setting a time window of 30-530 ms after proton impact are depicted in Figure 2. This condition was imposed in order to reduce the contribution of the different contaminants. The contribution of neutron-induced background coming from the target is suppressed by removing the first 30 ms of the time window. An upper limit of the time window at 530 ms was chosen to reduce the contribution of the long-lived daughters, while keeping most of the statistics. Singles γ-ray energy spectrum recorded by the HPGe detectors following the 132 In decay. This histogram was built using the events measured during the 30-530 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 zooms in the 2400-4450 keV region.

Half-life of 132 In ground state
The half-life of 132 In was measured by fitting the time distribution of the 10 strongest γ rays (labeled in Fig. 2 except for the 4416 keV). Since the activity at the experimental station is pulsed by the proton beam structure and the release from the target, the time distribution is fitted to an exponential decay function with a constant background after the end of the implantation. The background contribution was estimated by analyzing the time range from 2400 to 3600 ms after proton impact. Due to the high count rates, dead time effects are sizable, mainly during implantation, but also at the beginning of the decay. In each HPGe crystal an average count rate of 3·10 3 counts per seconds (cps) was observed, however, during the implantation time the count rate could rise up to 1.5·10 4 cps. To account for this effect the beginning of the fit range was shifted by a few half-lives towards higher times and a χ 2 fit test was performed to verify that the expected exponential decay behavior was recovered. The lifetime measurement was performed independently for each of the two data sets of 132 In decay measured in the two experimental campaigns. The analysis made use of single events recorded in the HPGe detectors. The contribution of the Compton background under full-energy peaks was subtracted. This investigation furnishes 20 independent values for the 132 In, 10 from each data set, which are all statistically compatible with each other. The final value of the 132 In half-life was adopted as the weighted average of these measurements yielding T 1/2 =202.2(2) ms. The statistical uncertainty of the weighted average is calculated and increased by multiplying by the χ 2 obtained. No systematic error is included. This half-lifes is in agreement with, but more precise than, the value reported in the latest evaluation, T 1/2 =200(2) ms [3]. In Figure 3 the decay curves for 4 of the γ rays under consideration, from the 2016 data set, are shown.

Identification of new γ-rays in 132 Sn
The analysis of γ-γ coincidences was done using the full statistics independently for the two data sets from each campaign. The assignments were cross-checked by requiring coincidences with the β detector and/or a time range since proton impact from 30 to 530 ms. Figure  4 shows the γ rays in coincidence with the 6 + → 4 + 299.3 keV transition in 132 Sn. The spectrum illustrates the amount of statistics and the quality of the γ-ray coincidence spectra.
The level scheme of 132 Sn has been greatly expanded with the addition of 57 new γ transitions and 11 new levels, observed following the direct 132 In β decay. The level scheme is shown in Figure 5. A list of the γ rays is provided in Table I. The states located at 5766 and 5446 keV were previously observed in the β-delayed neutron emission of 133 In [16]. The assignment is confirmed in this work with the uncovering of new cascades in the 132 In decay involving both levels.
A new level is found at 5754 keV defined by the 1457-1038 keV γ cascade. This sequence had already been observed by Fogelberg et al. [18], however the order of the γ rays they proposed was inverted, giving rise to an excited level at 6173 keV with suggested (6 + ) spinparity. This level has been ruled out in our analysis due to the finding of another γ-ray that de-excites the 5754-keV state, confirmed by γ-γ coincidences.
The 5280-keV level was already reported in 248 Cm fission studies [24], and tentatively identified as the (9 + ) state that arises from the particle-hole νf 7/2 h −1 11/2 configuration. That level is confirmed in this work by the observation of the de-exciting 431.8-keV transition in de-layed coincidence with the 132-keV γ-ray that de-excites the 8 + 4848-keV level.
The direct β feeding to states in 132 Sn was determined from the balance between feeding and de-exciting γ rays to each level. The intensities of the γ rays were obtained from the measured HPGe singles with neither coincidence nor condition on the time from the impact of protons on target. Theoretical internal conversion coefficients have been taken from [37] if required. The β feeding to the states should be understood as upper limits and the logf t values as lower limits due to possible missing transitions.

β-delayed neutron branches in 132 In
The β-delayed one neutron emission of 132 In has been confirmed by the observation of γ rays belonging to the excited structure of 131 Sn. Two transitions have been identified in this decay, specifically, the 2435.0(3) keV and 4273.6(5) keV with an absolute intensity of 0.11(1)% and 0.04(1)% respectively. The P n value has been obtained from the analysis of the γ-ray intensities of the β and β-n branches, following the β decay of the 132 Sn and 131 Sn daughters. For the 132 Sn → 132 Sb decay branch, the intensities of the 5 most intense γ rays were considered. The absolute intensities for those transitions were adopted from [38]. Previous measurements of the 131 Sn → 131 Sb decay [39] were not able to disentangle the decay of the 131 In isomers. Besides, in our analysis we observed that the intensity of the γ rays emitted in this decay mainly originate from the population of levels with high spin (11/2, 13/2, 15/2). This indicates that the 132 In isotopes that decay by β-n mostly feed the 11/2 − isomer in 131 Sn directly, which is strongly favored against the 3/2 + g.s. due to the angular momentum difference.
The total intensity from 131 Sn → 131 Sb decay was calculated from the analysis of the γ rays from 131 Sb observed in this data set. An absolute intensity of 69(7)% has been estimated for the most intense transition, of 1226 keV. This value was obtained by making two assumptions: firstly that 132 In β-n decay mainly populates the (11/2 − ) isomer, which is consistent with our observations, and secondly that no direct intensity was lost due to direct population of 131 Sn to the 131 Sb g.s. This is to be expected in order to be consistent with the first assumption due to the large spin difference (11/2 − → 7/2 + transition). The 7% uncertainty in the value takes into account these assumptions.
Finally, the number of decays calculated for each tin isotope was corrected to account for the movement of the tape at the end of each super-cycle, considering the different half-lives of each isotope and for dead time effects. From this analysis a P n =12(2)% value was found for the 132 In β-n decay, which is notably higher than the 6.8(14)% in [40] but in good agreement with the 10.7(33)% from [41].   The negative peaks in the spectrum arise from background subtraction, due to Compton scattering between two HPGe clover detectors.
TABLE I: List of γ rays observed in the β decay of 132 In to 132 Sn, including transition energies and intensities. The initial and final levels for each connecting transition are also given. (5) (13) 4715.9(4) 6 + 982.2(5) 0.08 (2) (4) 6008.2(4) (7 + ) 1202.4(6) 0.024 (7) 1.7(4) 6630.6(4) (6 + ) 580.8 (5)  Given the two-neutron separation energy in the 132 Sn S 2n ( 132 Sn)=12557.0(27) keV [10], there is a 1583 keV energy window, within Q β ( 132 In), that makes the decay via a β-delayed two neutron branch possible. We have searched for γ rays belonging to the A = 130 mass chain. Nevertheless, no evidence has been found that would point to the existence of a β-2n decay branch in 132 In. This is consistent with expectations, since the only levels in 130 Sn that could be populated are the 0 + g.s. and 2 + at 1221 keV [42]. Assuming a (7 − ) spinparity assignment for the 132 In g.s. [36], this decay will be highly suppressed. The large Q β =13.4(2) MeV value along with the low neutron separation energy in 133 Sn, S n =2.399(3) MeV [10], favor the 133 In decay via β-delayed neutron emission to 132 Sn. This gives rise to the large P n values for both 133 In β-decaying isomers [16]. The lower spin of the 133 In (9/2 + ) ground state and (1/2 − ) isomer, in comparison with 132 In (7 − ), is expected to favor the population of low spin p-h excited states that are not fed in the β decay of 132 In due to the large spin of the parent (7 − ). The population of 132 Sn excited levels in the β decay of 133 In was already reported in [16], where the β decay of 133 In was investigated focusing on the excited structure of 133 Sn. In the present work, we concentrate on results of the β-n decay of 133 In to 132 Sn, discuss excited states in 132 Sn and report new transitions following the β-n decay branch of 133 In.

Feeding of excited states in 132 Sn
Gamma rays emitted after the β decay of 133 In can be clearly distinguished from the background by their time distribution following the impact of protons on target. Nevertheless, the decay curve does not allow the separation of the transitions that belong to 132 Sn from those of 133 Sn, neither from the background induced by βdelayed neutrons from 133 In β-n decay.
The identification of new γ rays that belong to 132 Sn is based on γ-γ coincidences. Gamma rays with energies below 4 MeV are always a part of a cascade since they cannot directly feed the g.s. The analysis allows to identify several levels and γ rays in 132 Sn that are not observed in the 132 In decay, see Figure 6. Among them we confirm the states at 4965, 5131, 5431 and 5790 keV.  II: List of observed states in 132 Sn following the β-n decay of the 133 In (9/2 + ) g.s. (>95% pure), labeled 133g In, and the beam with enhanced content of the (1/2 − ) isomeric state, with a contamination of ∼30% of 133g In, labeled 133m In.  The low spin of the states to which they can de-excite suggests a small spin value (2-4) for these levels, which makes them good candidates for the remaining particlehole states with low spin expected in this energy range. In Figure 7 the level-scheme of 132 Sn in the β-n decay of 133 In is depicted. The direct feeding to each level (I β−n ) is measured by analyzing the γ-ray intensities calculated separately for each isomer. The indium beams for each isomer were separated taking advantage of the isomer selectivity provided by RILIS. However the separation was not complete, and the 133m In beam contained a contribution of ∼30% of 133g In [16]. The amount of 133m In in the 133g In beam is below 5%. The total feeding has been calculated using the intensities of the γ-rays emitted by the daughters. The observed states in 132 Sn following the β-n decay of the 133 In (9/2 + ) g.s. and (1/2 − ) isomeric state are listed in Table II.

High energy γ-rays
Another interesting feature observed in the β-decay of 133 In is the presence of several γ rays at very high energies, above 5 MeV, with a time behavior compatible with the decay of 133g,m In. The existence of those γ rays was already reported in [16], where the 6088-keV transition was assigned to 133 Sn. Some other γ-rays were discussed in [16] as being emitted in the decay of 133 In, however the lack of γ-γ coincidences does not allow to identify the daughter tin isotopes they belong to.
The high energy γ lines observed in the 133g,m In decays are shown in Figure 8. As it can be seen, the observed peaks differ notably depending on the selected β-decaying indium state. In the decay of the 133g In (9/2 + ) g.s. there are two predominant γ-rays, the one at 6088 keV mentioned above, and another one at 6019 keV. Although the 6019-keV peak has the same energy as a transition in 57 Fe produced by the neutron background as discussed in [16] its intensity is only a small fraction of the total γ-ray intensity from the excited 7647-keV level in 57 Fe, while the other, more intense transitions, are not observed. Therefore the 6019-keV transition is FIG. 7. Level scheme of 132 Sn observed following the β-n decay of the 133 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 on the left-hand side and the negative parity states to the right. The isomer observed feeding to levels in 132 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 β-decay of 133 In are highlighted in red. likely to be emitted following the β-decay of 133 In, and predominantly from the (9/2 + ) g.s. In the decay of the 133m In (1/2 − ), the 6088-and 6019-keV transitions are suppressed, but several other peaks, which are absent in the decay of the 133g In, can be identified. Those peaks appear at the energies of 5440, 5712, 5770, 5952, and 6067 keV. Two more tentative peaks, at the detection limit of the HPGe detectors, are seen at 6220 and 6463 keV. Some of these γ lines may be compatible with escape peaks from other γ rays (for instance single and double escape peaks from 6463 keV), but it is not possible to make a consistent identification for all of the energies. It is interesting to observe transitions having this energy from the decay of the (1/2 − ) isomer, as there are unidentified members of particlehole multiplets in 132 Sn, such as νp 3/2 d −1 3/2 , πg 7/2 g −1

9/2
and νp 3/2 s −1 1/2 , that can give rise to low spin levels. It is very unlikely to populate them in the decay of 132 In with (7 − ). However, the feeding of such levels would be strongly favored in the β-n decay of the (1/2 − ) state in 133m In. All of this points towards these transitions likely originating from the de-excitation of such p-h multiplet states.
It is worth mentioning that a 5131-keV peak can be seen in both the 133g In and 133m In decays. This γ ray has been firmly identified to belong to 132 Sn since its energy perfectly matches the de-excitation of the new 5131-keV level proposed in this work. In addition, the existence of a transition to the 0 + g.s. supports the tentative assignment of this level to the 2 − state of the νf 7/2 d −1 3/2 multiplet. For the sake of completeness, the γ-rays observed in the 133 In decay that have not been assigned to any decay branch are listed in Table III.   TABLE III. Gamma rays observed in the 133 In decay that could not been assigned to any specific decay branch. Intensities are given relative to the 4042-keV γ-ray intensity. The label 133g In refers to the 133 In (9/2 + ) g.s., with an estimated purity above 95%, while the label 133m In is used for the beam with enhanced content of the (1/2 − ) isomeric state, with a contamination of ∼30% of 133g In.
Eγ  (5). c Intensity obtained from β-gated spectrum. d Energy compatible with the escape peaks from the tentative 6463-keV γ-ray. e Energy compatible with the single escape peak from the tentative 6220-keV γ-ray.

β-delayed neutron emission from 133 In
We have used the same procedure described above for 132 In to determine the β-delayed neutron emission probabilities from the 133 In (9/2 + ) ground state and (1/2 − ) isomer. The most intense γ rays have been considered in the analysis. For 133 Sn → 133 Sb decay, the absolute intensity of 12(2)% for the 962-keV transition was adopted from [43], while for the 132 Sn → 132 Sb an absolute intensity of 48.8(12)% for the 340-keV transition was taken from [38]. The relative decay activity of the tin daughter nuclei was corrected for the tape movement. In particular, the supercycle structure of the proton beam has to be considered for the evaluation of the unobserved activity. Our analysis yields P n =90(3)% for the decay of the 133 In 9/2 + g.s., and P n =93(3)% for the decay of the (1/2 − ) isomer. The results differ from those previously reported by us in [16], which were obtained from the same dataset but where the supercycle structure was not fully taken into account. The re-evaluated results are in agreement with the P n =85(10)% value in [11].

C. Lifetime measurements
Lifetimes of excited levels in 132 Sn have been investigated by means of the Advanced Time-Delayed βγγ(t) fast-timing method [29][30][31]. The lifetimes were mainly obtained from the time differences between the fast β and LaBr 3 (Ce) detectors. A coincidence condition on the HPGe detectors is applied. The HPGe detectors do not participate in the timing information, but are essential in this complex level scheme due to their energy resolution to obtain the required γ-ray selectivity.
The use of two different LaBr 3 (Ce) detectors gives us the possibility to obtain two independent measurements for the same lifetime, one per β-LaBr 3 (Ce) combination. In addition, γγ(t) time differences between the two LaBr 3 (Ce) detectors are used when possible. To illustrate the analysis and the results here obtained, we discuss the half-life of the 4416-keV 4 + and 4831-keV 4 − levels, depicted in Figure 9 and Figure 10 respectively.
To measure the 4416-keV 4 + level half-life using βγγ(t) events a time distribution was generated by selecting the 526-and 375-keV transitions in the HPGe and LaBr 3 (Ce) detectors respectively. Corrections were included to account for the contribution of Compton background. The 4416-keV 4 + state lifetime is free from the influence of other long-lives states and shows up as an exponential tail which can be fitted to measure the half-life. The analysis was done separately for each of the two LaBr 3 (Ce) as well as for each of the two available data sets. In the case of γγ(t) events, the 299-keV and 375-keV transitions are selected. Here no extra gate in the HPGe energies is needed thanks to the large peak to background ratio. The lifetime is measured from time difference distributions with the direct and reversed energy selection on the LaBr 3 (Ce) detectors, giving two independent measurements for each of the two data sets. Using the two experimental data sets, our analysis yields 8 independent measurements for the half life, 4 from βγ(t) events and another 4 from γγ(t), all of them consistent with each other. The final value is obtained from the weighted average from these measurements, yielding a final value of 3.99(2) ns, which is in good agreement with the 3.95(13) ns reported by Fogelberg et al. [19].
Shorter lifetimes were measured using the centroid shift method. In Figure 10, the analysis to extract the lifetime of the 4830-keV 4 − level is is illustrated for βγγ(t) events for one of the LaBr 3 (Ce) detectors. In this case the mean life is derived from the centroid shift of the time distribution with respect to a prompt cascade, corrected by the FEP time response calibration.
The analysis has been repeated for both LaBr 3 (Ce) detectors and both data sets, and also using the γγ(t) method, yielding six independent values for the 4830-keV 4 − level mean-life.
The weighted average of T 1/2 =27(2) ps is adopted as the final result. The halflife is in very good agreement with the 26(5) ps reported by Fogelberg et al. [19]. It should be noted that the uncertainties in [18] are too small to be compatible with a fast-timing measurement; the values within brackets in [19] are actually the errors in ps [44], so the uncertainties from [19] are adopted.
The lifetime of the 4848-keV 8 + level is beyond the fast-timing time range, but it can be investigated using βγ(t) coincidences between the plastic scintillator Time delay spectra between the β and each of the two LaBr3(Ce) detectors for βγγ(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 LaBr3(Ce) detector. The lifetime is obtained by a χ 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. and the HPGe detectors. Three β-HPGe(t) time differences spectra were obtained by selecting the 132-, 299and 375-keV γ rays, respectively. The half-life was measured by fitting the delayed slope of the spectra in a long time range of ∼30 µs. The contribution of random coincidences to the time spectra in this range had to be carefully taken into account. Our analysis yields T 1/2 =2.108 (14) µs for the 4848-keV level in agreement with the value of 2.080 (17) µs reported in the latest eval-uation [3]. The analysis procedures were extended to the other observed levels, provided sufficient statistics were available. The data sets from the two experimental runs have been combined for the analysis. The lifetimes of 7 different states were measured. In addition, upper limits for additional 7 levels were obtained. The results obtained in this work for level lifetimes in 132 Sn are compiled in Tables IV and compared to the previous β-decay studies.
The overall agreement is quite good, with the exception of the 4919-keV 7 + level whose half-life is 104(4) ps, much higher than the value of 62(7) ps reported earlier [18], which was measured using BaF 2 scintillator detec-tors. Since this level can only be measured by analyzing the time distribution of the 203-keV γ-ray, where the contribution of Compton background is very important, the difference may stem from time corrections in this difficult energy range.
The reduced transition probabilities for de-exciting γ-transitions in 132 Sn have been determined using the measured lifetimes, branching ratios and energies, and using theoretical internal conversion coefficients [37]. The most likely spin-parity assignments are employed (see Section IV). The transition rates are calculated assuming a pure multipolarity character of the transitions. Half-lives and reduced transition probabilities of the transitions in 132 Sn. The B(Xλ) values have been derived from the lifetimes and branching ratios obtained from 132 In decay in this work I, as well as the theoretical internal conversion coefficients, calculated using Bricc [37]. Transition rates have been calculated assuming a pure multipolarity character of the transitions, using the assignments from [18]. For those levels where no previous assignment had been made, the B(Xλ) values corresponding to the most likely multipolarities are presented.

Ei(keV)
Configi   [19] since those in [18] contain several typographical errors [44]. b Calculated from the B(E3) rate measured in Coulomb excitation [45] c Assigned multipolarity in [18] IV. DISCUSSION All new levels in 132 Sn observed in this investigation are candidates for the remaining unidentified states within the particle-hole multiplets. In Figure 11 the energies for the 24 particle-hole multiplets in 132 Sn expected to appear below the neutron separation energy are represented. The energies and the splitting of the different levels for the same multiplet are estimated by taking into account the single particle energies from neighboring nuclei, and the analogous particle-hole states in 208 Pb, taken from [19,46,47], where a A −1/3 scale is introduced to take into account the nuclear potential depth. These empirical calculations provide guidance for the location of the p-h states, which allows to propose spin-parity assignments to the new levels found in this work.
The other piece of information is provided by the vast number of new transitions which connect the new states to known levels. By assuming that the transitions are predominantly of dipole character (mainly of M1 multipolarity) and using the electromagnetic selection rules it is possible to make tentative spin-parity assignments of the newly-identified levels. The transition rates obtained from the measured lifetimes and lifetime limits of the new levels also provide constraints. Together with the information from the systematics of p-h states tentative configurations for the new levels are proposed. In the level schemes presented above, the tentative spin and parity assignments are already shown.
A. Low energy neutron particle-hole states The unique identification of every observed state in 132 Sn with a specific state from a given p-h multiplet is a very complex task. In previous β-decay studies [2,18] the tentative assignment of several states was done by considering the analogies between the 132 In [(πg 9/2 ) −1 νf 7/2 ] decay and its two neighbors 131 In [πg −1 9/2 ] and 133 Sn [νf 7/2 ] decays. The 6 − and 7 − levels observed above 7 MeV, attributed to the νf 7/2 g −1 7/2 configuration, receive the main fraction of the total βfeeding intensity. This strong transition would be equivalent to the Gamow-Teller transition in the 131 In decay πg −1 9/2 → νg −1 7/2 [48]. Keeping up with the 131 In decay analogy, the second strongest decay branch corresponds to the first-forbidden transition πg −1 9/2 → νh −1 11/2 . In the 132 In decay the equivalent transition would populate the νf 7/2 h −1 11/2 multiplet. Consequently the positive parity states that appear below 5 MeV are suggested to be members of this configuration. On the other hand, the strong 2435-keV γ transition in 131 Sn that connects the single hole states νg −1 7/2 → νd −1 3/2 would be analogue to the 2380-keV and 2268-keV transitions in 132 Sn, which indicates that the 4 − and 5 − found below 5 MeV are indeed members of the νf 7/2 d −1 3/2 p-h multiplet. In this way there are two neutron p-h multiplets identified within this energy range. However, several of the expected levels from those configurations lack experimental identification. Specifically the 3 + and 8 + levels  FIG. 11. Calculated energies for the different particle-hole multiplet states in 132 Sn, adopted from J. Blomqvist [46,47]. The energies and energy splitting within a given multiplet are estimated by scaling the analogous particle-hole states in 208 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. from the νf 7/2 h −1 11/2 coupling, as well as the 2 − and 3 − levels from the νf 7/2 d −1 3/2 multiplet, which are expected to be found at excitation energies around 5 MeV, remain unseen. In a previous investigation from the 248 Cm spontaneous fission [24], a level at 5280 keV was suggested to be the missing νf 7/2 h −1 11/2 8 + level. On the contrary, in our work we observe the population of this level in the 132 In decay, which de-excites by a γ ray to the 4848-keV state. This level has a very large apparent logf t value, around 7.2, as it would be expected for a high spin such as 9 + , which suggests its identification as the missing 9 + level.
The remaining three levels found within that energy range are the 4949-, 4965-and 5131-keV states. They are directly populated in the β-n decay of 133g,m In, but not directly fed from the 132 In (7 − ) decay. The 4949-keV level is observed in the 132 In decay, but indirectly populated by a γ-transition from the 5387 keV (4 − ) level without any noticeable direct β feeding. The β-n feeding from the (1/2 − ) and (9/2 + ) 133 In states points towards a low spin value for these three levels. Specifically the 5131-keV state is populated more favorably in the β-n decay of the (1/2 − ) isomer, which, along with the γ tran-sition which connects that level with the g.s., suggests a lower spin for that level than for the other ones. This is an indication that the 5131-keV state is very likely the 2 − member of the νf 7/2 d −1 3/2 multiplet. The systematics of the transitions that de-excite the 4949-and 4965-keV levels suggests angular momenta J =3. Therefore one of them would correspond to the 3 + state from νf 7/2 h −1 11/2 and the other matches the 3 − from νf 7/2 (p 3/2 ) −1 . There is no direct information to determine their parity, since both of them are linked to positive and negative parity levels. However, there are analogies between the 4949 keV and the 5 − 4942-keV levels. Firstly, both are being populated from the 5387-keV state, interpreted as νf 7/2 s −1 1/2 (4 − ), with similar intensities. Secondly both levels have a transition to the 4352-keV 3 − collective state, and another one to the νf 7/2 d −1 3/2 4 − level whose intensity ratio is about 10:1 in both cases. Those similarities strongly suggest that 4949-keV level is indeed the 3 − member from the νf 7/2 d −1 3/2 multiplet, and therefore the 4965 keV can only be the 3 + member of the νf 7/2 h −1 11/2 p-h configuration.
The new assignments are shown in Figure 11.
B. Particle-hole states from 5 to 6 MeV In the investigation by Fogelberg et al. [18,19], the 5399-keV (6 + ), 5478-keV (8 + ) and 5629-keV (7 + ) levels were identified as members of the proton p-h πg 7/2 g −1 9/2 multiplet. This assignment was supported by the intense feeding of the 5629 keV (7 + ) state, which would be the equivalent to the strongest transition in the 133 Sn decay, νf 7/2 → πg 7/2 . Within this region we have found 7 new levels with expected angular momenta from 4 to 8. In addition to the proton πg 7/2 g −1 9/2 p-h levels, states from the neutron νp 3/2 h −1 11/2 and νf 7/2 s −1 1/2 configurations are also expected. All the levels found from 5.3 to 6 MeV could be related to p-h levels from those multiplets. There is not much information apart from γray intensities and the lifetimes and lifetime limits that point towards dominant M1 transitions. This, together with the possibility that the configurations are mixed, hinders a clearer assignment. Nevertheless several conclusions about them can be drawn.
For the 5431-keV level, observed only in the 133 In decay, a J = 3 spin assignment can be assumed based on the γ transitions systematics. Thus, this level can be either identified with the 3 + state of the πg 7/2 g −1 9/2 or with the 3 − of the νf 7/2 s −1 1/2 configuration. At similar excitation we expect two 4 + states belonging to the two positive parity multiplets mentioned above. In our analysis two levels have been found within this energy range with a tentative angular momenta J = 4. There is a level at 5446 keV (4 + ), populated indirectly by γ transitions in 132 In and directly in the β-n decay of 133g,m In. This level is a good candidate to be a member of the proton πg 7/2 g −1 9/2 multiplet, but it can also be interpreted as the 4 + level from the neutron νp 3/2 h −1 11/2 configuration. At 5790 keV another level was identified, this one can be only observed in the 133 In β-n decay, and its de-exciting transitions point towards a spin of (3,4). Therefore, this level can be identified either as the 4 + from the νp 3/2 h −1 11/2 particle-hole coupling expected in this region, or the 3 + from πg 7/2 g −1 9/2 . The (5 + ) levels at 5698 keV and 5766 keV, which are observed in this work in both the 132 In and 133 In decays, can be related to the 5 + states from the πg 7/2 g −1 9/2 and the νp 3/2 h −1 11/2 multiplets. The two remaining levels in this region are the 5754-keV (6 + ) and the 6008-keV (7 + ) ones, which we tentatively suggest as members of the νp 3/2 h −1 11/2 particle-hole configuration. These tentative assignments are reflected in Figure 11.

C. States from 6 to 7 MeV
Moving up to the next energy interval the identification becomes even more complicated, due to all the possible p-h multiplets that are expected in this region, and the likely admixture of configurations. Nevertheless, since most of these levels are populated only in the direct β-decay of 132 In, they are constrained by the selective nature of β decay that favors, in this case, states with a large spin (6)(7)(8). Because there are not so many p-h multiplets at this energy that could give rise to levels with such a large spin ( Figure 11) we can draw some conclusions about them.
Regarding the negative parity states, there are two high-lying levels with most likely (6 − ) assignments observed only in the 132 In decay, at 6598 and 6709 keV. Only two neutron multiplets, the νh 9/2 d −1 3/2 and νf 7/2 d −1 5/2 have a negative parity member with J = 6, and therefore these two levels can only be related to those. The remaining two negative parity levels appearing at 6297 and 6476 keV are present in both the 132 In and 133 In β decays. The systematics of the transitions that de-excite and populate them suggest a (5 − ) spinparity and therefore they are likely to be members of the νh 9/2 d −1 3/2 and νf 7/2 d −1 5/2 multiplets as well. On the positive parity side the situation is more involved due to the larger amount of multiplets predicted at these high energies. There are 8 different states with an assumed positive parity. These were only observed in the direct β decay of 132 In, out of which 5 have been identified in this work for the first time. Relying on the systematics of the transitions between these levels, along with the selectivity of the β-decay population from the (7 − ) g.s. in 132 In, they can have angular momenta from 5 to 8. Four different positive parity p-h multiplets are predicted in this energy range, three of them expected to arise from neutron configurations (νh 9/2 h −1 11/2 , νf 5/2 h −1 11/2 and νp 3/2 h −1 11/2 ), and another one coming from the proton πd 5/2 g −1 9/2 coupling. Almost all of them can be give rise to (5,6,8) + states, which hampers their identification. Moreover the states are probably mixed.
The only noticeable difference observed among the positive parity levels is the larger feeding measured for the 6631-keV state, around 1% with a logf t of the order of 6.4 ( Figure 5). This enhanced population can be interpreted on the grounds of the equivalence mentioned before between the 132 In and 133 Sn decays. In 133 Sn, the β decay is dominated by the first forbidden νf 7/2 → πg 7/2 transition populating the g.s. in 133 Sb with 86% of the total β intensity and logf t ≈ 5.5 [49], which is similar to the population of the πg 7/2 g −1 9/2 multiplet in the 132 In decay. Moreover, the second strongest transition found in 133 Sn decay corresponds to the νf 7/2 → πd 5/2 transition, receiving 11% of the total feeding with logf t ≈ 6.1 [49]. This transition would be equivalent to the population of the proton πd 5/2 g −1 9/2 configuration in the 132 In βdecay. Comparing the population of the 6631-keV level with the population of 5629-keV level, identified as the (7 + ) state of the πg 7/2 g −1 9/2 multiplet, we can see that they keep the 8:1 β intensity ratio, and similar logf t values for the level at 5629 keV. Such a large popula-tion might be an indication of a predominant πd 5/2 g −1 9/2 configuration for the 6631 keV (6 + ) state.

V. CONCLUSIONS
Experimental information about the 132 Sn structure plays a crucial role in the shell-model interpretation of nuclei around N = 82, because it provides direct knowledge about the particle-hole couplings for both protons and neutrons. In this work the properties of excited states in 132 Sn have been studied from the β decay of 132 In. By taking advantage of the isomer selectivity capabilities of the ISOLDE RILIS, independent investigations of the β-decay of the 133 In g (9/2 + ) g.s. and the 133m In (1/2 − ) isomer were performed as well. Thanks to both decay modes, the knowledge of the 132 Sn structure has been largely expanded in this work. A total of 17 new levels and 68 new γ-transitions have been added (including those already quoted in the previous publication [16] derived from the same experiment). A complete fast-timing investigation of the excited levels in 132 Sn has been performed as well, confirming and extending previous results.
An interpretation of the level structure is provided in terms of particle-hole configurations arising from core breaking states both from the N = 82 and Z = 50 shells across the gap. The interpretation is based on empirical calculations [19,46,47] leading to positive and negative parity particle-hole multiplets, where the energies are obtained from the single-particle energies from neighboring nuclei and from the analogous particle-hole states in 208 Pb. These empirical calculations, together with the experimental information on the β and β-n feeding, the level lifetimes and the γ decay branches provide guidance for the identification of the levels as proton-hole members of the multiplets, facilitating tentative spinparity assignments to the new levels.
The number of states is consistent with the one calculated from the angular momentum couplings. The identification of all remaining missing levels from the νf 7/2 h −1 11/2 and νf 7/2 d −1 3/2 neutron-hole configurations has been completed. A tentative interpretation has been provided for the rest of observed states, where we have been able to observe most of the expected p-h levels with angular momenta close to 7.
Most of the missing information is related to the anticipated low spin states, which are very unlikely to be populated in the 132 In (7 − ) β-decay. However, the identification of many γ-rays around 7 MeV from the 133g,m In β-decay strongly suggests feeding of those missing lowspin multiplet states. Enhanced statistics for this decay will be beneficial to provide more firm assignments.
In conclusion the knowledge about states in the doubly magic 132 Sn has been largely expanded by the investigation of the β-decay of 132 In and β-n decay of 133 In performed at the ISOLDE facility at CERN. The identification of particle-hole multiplets both for protons and neutrons and the transition rates connecting different ph configurations and states within multiplets may provide input on the two-body matrix elements and single particle states. The new data challenges the theoretical description of 132 Sn, which is relevant for the understanding of nuclear structure in the region.