Beta-delayed neutron spectroscopy of $^{133}$In

The decay properties of $^{133}$In were studied in detail at the ISOLDE Decay Station (IDS). The implementation of the Resonance Ionization Laser Ion Source (RILIS) allowed separate measurements of its $9/2^+$ ground state ($^{133g}$In) and $1/2^-$ isomer ($^{133m}$In). With the use of $\beta$-delayed neutron and $\gamma$ spectroscopy, the decay strengths above the neutron separation energy were quantified in this neutron-rich nucleus for the first time. The allowed Gamow-Teller transition $9/2^+\rightarrow7/2^+$ was located at 5.92 MeV in the $^{133g}$In decay with a logft = 4.7(1). In addition, several neutron-unbound states were populated at lower excitation energies by the First-Forbidden decays of $^{133g,m}$In. We assigned spins and parities to those neutron-unbound states based on the $\beta$-decay selection rules, the logft values, and systematics.

The decay properties of 133 In were studied in detail at the ISOLDE Decay Station (IDS).The implementation of the Resonance Ionization Laser Ion Source (RILIS) allowed separate measurements of its 9/2 + ground state ( 133g In) and 1/2 − isomer ( 133m In).With the use of β-delayed neutron and γ spectroscopy, the decay strengths above the neutron separation energy were quantified in this neutron-rich nucleus for the first time.The allowed Gamow-Teller transition 9/2 + → 7/2 + was located at 5.92 MeV in the 133g In decay with a logf t = 4.7 (1).In addition, several neutron-unbound states were populated at lower excitation energies by the First-Forbidden decays of 133g,m In.We assigned spins and parities to those neutron-unbound states based on the β-decay selection rules, the logf t values, and systematics.

I. INTRODUCTION
Doubly magic nuclei far from the stability line, such as 24 O, 78 Ni, 100 Sn, and 132 Sn, have attracted tremendous interest in the last decades.Their simple structures and imbalanced neutron-proton ratios provide a testing ground to study the nuclear shell evolution as a function of isospin both experimentally and theoretically, see, for example, Refs.[1][2][3][4][5] and references therein.It has been suggested that the residual N N interactions are responsible for the drift of single-particle orbitals and the modification of nuclear shell structure at extreme neutronproton ratios [6].Since these phenomena impact the decay properties of nuclei, nuclear β decay is a viable probe to study the shell evolution.Specifically, nuclear β decay is extremely sensitive to the occupation of proton and neutron orbitals.In the neutron-rich nuclei, the predominant allowed Gamow-Teller (GT) transitions require ∆L = 0 (L refers to the orbital angular momentum of proton and neutron) between neutron and proton spinorbital partners in the same shell.The First-Forbidden (FF) transitions, on the other hand, connect neutron and proton orbitals with ∆L = 1 from neighboring shells.Due to their different selection rules, the GT and FF operators transform the initial state of the parent nucleus into diverse groups of final states in the daughter.Thus, arXiv:2303.12173v1[nucl-ex] 21 Mar 2023 measuring the decay strengths as a function of excitation energy provides nuclear-structure information in the parent and daughter nuclei.In addition, β decays play an important role in various nucleosynthesis processes.In the r-process, for example, they compete with the rapid neutron-capture reaction and affect the final elemental distribution [7,8].Owing to these reasons, it is of particular interest to measure the β-decay properties in the vicinity of 132 Sn.Its proton and neutron shell closures at Z = 50 and N = 82 define one of the strongest doubly magic cores on the neutron-rich side of the nuclear chart [4,9,10], providing a reference point to study nuclear structure with extreme neutron excess.Furthermore, the proximity of the r-process path to 132 Sn gives those decay properties key impacts on the r-process abundance pattern near the mass number A = 130 region [11].
In this work, we studied the β decay of 133 In, a nucleus southeast of 132 Sn.Because of its substantial Q β window (∼ 13 MeV), a large number of states with different microscopic configurations can be populated in the daughter 133 Sn.The states below the neutron separation energy were attributed to a single neutron outside the 132 Sn core [4,12,13].The decay channels feeding those states can be understood by transforming a neutron above N = 82 into a proton below Z = 50 (e.g., νf 7/2 → πg 9/2 ).The subsequent γ decays had been surveyed thoroughly by Piersa et al. and Benito et al. [14,15].The current study focused on the measurement of decay strength above the neutron separation energy, which was less known experimentally.The investigated states were highly excited because they were dominated by the neutron or proton particle-hole (p-h) excitations with respect to the 132 Sn core.Promptly after the β decays, neutrons were emitted from those states, leaving the residual 132 Sn in either the ground state or excited states.Some of the experimental findings and their consequences were highlighted in Ref. [16].This article explains in full detail the experimental setup (Section II), the procedure to reconstruct the excitation energies of the neutron-unbound states and their β-decay feeding probabilities (Section III), and the spinparity assignments of these states (Section IV).

II. EXPERIMENT
The neutron-rich indium isotopes were produced at the Isotope Separator On-Line (ISOLDE) facility at CERN [17].A 1.4-GeV proton beam was delivered by the Proton Synchrotron Booster (PSB) and impinged on a tungsten solid neutron converter [18] with an average current of 2 µA.Radioactive isotopes, including 133 In, were produced in a uranium carbide (UC x ) target next to the neutron converter through neutron-induced fission.The indium atoms were ionized using the Resonance Ionization Laser Ion Source (RILIS) at ISOLDE [19].By using the narrow-band titanium-sapphire (Ti:Sa) laser at RILIS [20], selective ionization of 133 In of either the ground state or isomer can be achieved [14].Following the General Purpose Separator (GPS) [17] separating the isotopes of interest based on the mass-to-charge ratio, electrostatic quadrupoles transported the ion beam to IDS.The beam was implanted into a movable tape at the center of a decay chamber.After each proton pulse, the beam gate at ISOLDE was switched on for 300 ms for continuous implantation.Then, the implantation was stopped for 300 ms before the tape was rolled down to a shielded box to remove long-lived activities originating from the daughter and granddaughter β decays.The implantation and tape move cycle provided a 600-ms time window to measure decay products from the implanted 133 In.   [21,22].The detection setup consisted of 26 EJ-200 plastic scintillator modules.Each module was 3 × 6 × 120 cm 3 and had one photomultiplier tube (PMT) coupled to each end.The modules were mounted in a custom-built support frame describing an arch for a radius of 100 cm from the decay chamber.The intrinsic neutron efficiency of each module was 35% at 1 MeV [21].The total solid angle covered by 26 modules was about 15% of 4π.However, only 22 out of 26 modules were used in the analysis due to the shadow from the supporting frame of the decay chamber.The resulting solid angle was 12.6% of 4π.Two plastic scintillators surrounding the implantation tape defined the start signal of TOF.It provided average efficiency of up to ∼80% for β particles.The neutron data were taken in the so-called triple coincidence mode, requiring both PMTs of an INDiE module and one of the β triggers to record an event.This way, the neutron detection threshold was pushed down to 100 keV (or 5-keV ee energy loss in the detectors).The traces of β and INDiE signals were sampled by the 12-bit 250-MHz digitizers.The sub-nanosecond time resolution was achieved using the algorithm introduced in Ref. [23].The FWHM of the γ-flash peak in the obtained TOF spectrum was 1.5 ns.The actual neutron TOF distance between the implantation point and INDiE modules was determined as 104.2(3) cm using the online β decay of 17 N, which emits three fully resolved and well-studied neutron lines [24].
Figures 2 (a-g) present the neutron data taken in coincidence with the β decay of 133 In.The figures on the left (a, b, c, and d) are taken with the 133g In decay and those on the right (e, f, and g) with an admixture of 133g In (40%) and 133m In decays (60%).When RILIS was set on the 1/2 − isomer, there are still 133g In implanted into the decay station at the same time, giving rise to the contamination peaks in the isomer's neutron spectra.
Figures 2 (a, e) show the collected neutron spectra in two-dimensional (2D) histograms plotting the neutron TOF versus their energy loss in INDiE.The neutron events are seen following the banana-shaped distribution in the histograms.The neutron TOF spectra in Figs. 2  (b, f) were made by projecting the 2D histograms along the x-axis with energy loss greater than 5 keV ee .Due to the simple structure of 133 Sn and the β-decay selection rules, only a few prominent neutron peaks were visible in the spectra.Furthermore, no major peaks were observed in coincidence with γ decays in 132 Sn, including the strongest 2 + 1 → 0 + g.s.transition, see Fig. 2 (c).This implied those 133 Sn unbound states had a direct feeding to the 132 Sn ground state via neutron emissions.This lack of neutron-γ cascades was due to the first excited state (2 + ) in 132 Sn being above 4 MeV, making it energetically impossible for most of the neutron unbound states observed in the 133 In decay.Nevertheless, there was a small number of neutron emissions populating the 132 Sn excited states.Their numbers were estimated from the TOF spectra gated by the 4041-, 4352-, and 4416-keV γ rays observed by the clover detectors.These γ rays correspond to the 2 + 1 → 0 + g.s., 3 − 1 → 0 + g.s., and 4 + 1 → 0 + g.s.transitions in 132 Sn, respectively.According to Ref. [15], they carry mostly the entire γ-decay strength, via γ-γ cascade, from an excited state to the ground state, with a 5131-keV state being the sole exception.However, Ref. [15] reported an extremely weak ground-state feeding branching ratio from this state.Thus, the error introduced by not considering this weak neutron-γ cascade was much smaller than the statistical uncertainties in the analy-sis.The result showed about 7.0(5)% of total neutron emissions going to the 132 Sn excited states.Their contribution was subtracted from the total neutron activity to ensure the neutron intensities feeding the ground state were extracted properly.
The neutron TOF spectra in Figs. 2 (b, f) were fitted by a template neutron response function.The procedure to determine the response function of individual peaks is explained as follows.First, the TOF spectrum was simulated for monoenergetic neutrons with GEANT4 [25], which took into account all the neutron-scattering material at IDS and the time resolution of INDiE modules.Second, the simulated profile was convolved with a Breit-Wigner style distribution [26] if a state had a sizeable width in energy (broad resonance) greater than our resolution.The obtained response function was verified using the β decays of 49 K and 17 N, reproducing their neutron spectra with only known peaks from the literature [24,27].Fitting the spectra of the 133 In decays only involved "zero-width" peaks in the response function.This indicated the observed resonances in 133 Sn were narrower than our energy resolution, which was about 80 and 250 keV for 1-and 3-MeV neutrons, respectively, at the minimum energy threshold (5 keV ee ).Since the contribution from neutron-γ cascades had been subtracted from the fit, the peak intensity in the response function gave access to the neutron intensities directly feeding the 132 Sn ground state.The experimental background, which was drawn as the dashed lines in Fig. 2, consisted of a doubleexponential decaying tail from fast β-decay electrons and a constant plateau from random γ rays.
The results from a χ 2 -fitting analysis in Fig. 2 (b, f) are summarized in Table I and Fig. 3.The numbers of peaks in the response function to fit the ground-state and isomeric decays were 18 and 13, respectively.All the ground-state peaks were included in the analysis of isomeric decay due to contamination.Their contributions, as illustrated by the blue peaks in Fig. 2 (f) (and Fig. 2 (g)), were determined by fixing their relative intensities to the strongest peak at 41 ns with the ratios obtained from the ground-state decay.The neutron peaks associated with the isomeric decay were drawn in red in Fig. 2 (f) (and Fig. 2 (g)) to be differentiated from the groundstate peaks.The excitation energies E ex were derived by summing the neutron kinetic energy, corrected by recoil energy, with the neutron separation energy S n = 2.399(3) MeV in 133 Sn [28].The experimental error combined the uncertainty in neutron TOF centroid, flight distance, and neutron separation energy.In this analysis, the number of detected β decays N β was estimated from the number of detected neutrons divided by the β-delayed neutron emission probability (P n ), which is 90(2)% and 93(2)% for 133g In and 133m In respectively [15].Then, the decay probability I β of the state was calculated by normalizing the neutron intensity to N β .In cases where there were γ decays competing with neutron emissions, which will be discussed in more detail later, I β included the contribution from γ decays.It is noted that all the I β in Table I were calculated from the neutron emissions directly feeding the 132 Sn ground state.It is strictly correct  (d, g) focus on the TOF of high-energy neutrons with En > 3 MeV.They were made by projecting Figs.(a, e), respectively, along TOF with energy loss greater than 1 MeVee.All the neutron TOF spectra were fitted by the neutron response functions (magenta), with the neutron peaks attributed to the ground-state and isomeric decays drawn in blue and red, respectively.The dashed line is the β and γ-ray background in the neutron TOF spectra.
for the states below 6.44 MeV in 133 Sn.For the states above 6.44 MeV, where the neutron-γ cascade is energetically possible, these I β should be regarded as the lower limits.The ground-state (isomeric) decay logf t values were extracted using the I β in Table I, the β-decay halflife of 133g In ( 133m In) from Ref. [14], and the Q β = 13.2MeV (13.8 MeV) from the atomic mass difference between 133g In ( 133m In) [29] and 133 Sn [28].
A high-energy part of the neutron spectra in Figs. 2 (b, f), i.e., E n > 4 MeV and TOF< 40 ns, is more likely due to a continuum of strength distribution rather than due to isolated resonances.There, a peak in the response function should be regarded as a neutron quasi resonance [22].The distribution of transitions in the continuum was inferred by increasing the energy threshold of INDiE, resulting in better resolving power in the TOF spectrum than the previously quoted values.For instance, Figs. 2  (d, g) present the spectra with 1-MeV ee energy threshold for the 133g,m In decays, respectively, showing better resolution for the high-energy neutron peaks than Fig. 2  (b, f).The centroids of the high-energy neutron peaks were determined in Fig. 2 (d, g) before they were fixed in the fit of Fig. 2 (b, f) to extract intensities together with lower-energy neutron peaks.
The observations of γ decay from neutron-unbound states were reported previously in 133 Sn [14,15,30].Therefore, both γ and neutron intensities were measured in this work to ensure no strength was missing in I β .In (1/2 − ) between Sn = 2.399 MeV [28] and Eex = 6.0 MeV, where isolated resonances were observed in 133 Sn.Decays associated with the ground state and isomer are differentiated in blue and red, respectively.The states below the neutron separation energy are included for completeness [13,14].Half-lives and neutron-emission probabilities (Pn) in 133 In are taken from Refs.[14,15].The excitation energy of the 1/2 − isomer is from Ref. [29].The states with a solid spin-parity assignment are highlighted by " * " on their excitation energies.In the 133g In decay, five γ peaks at 3564, 3928, 4110, 6018, and 6088 keV were found to have half-lives and energies consistent with the corresponding neutron peaks in Table I.These observed γ rays agree with the previous β-decay study of 133 In using pure γ-ray spectroscopy [14,15].Figure 4 shows portions of γ-ray spectra in the relevant energy ranges.Statistically, none of these γ transitions were in coincidence with any other γ rays nor neutron emissions, suggesting they were single-γ transitions from a neutron unbound state to the ground state.
For the transitions at 3564, 3928, and 4110 keV, their γ intensities were added to the I β of 3561-, 3919-, and 4092-keV states in Table I, respectively.Regarding the two γ transitions around 6 MeV, their separation is only 70 keV, too close to be resolved by our neutron detectors.Instead, a neutron peak was observed at E n = 3642 keV (E ex = 6068 keV) with TOF∼39.5 ns, see Fig. 2(d).Thus, it was presumed that the neutron peak consists of an unresolved doublet at 6018 and 6088 keV, respectively.The I β of the 6068-keV state corresponds to the sum of the doublet.In contrast, no neutron-γ competition was identified following the 133m In decay.Below 6-MeV excitation energy, where β feedings are strong, the 1/2 − isomer is expected to populate low-spin positiveparity states in 133 Sn via FF transitions.From those states, the electromagnetic (EM) E2/M 1 transitions to the 7/2 − ground state in 133 Sn are forbidden, and higherorder EM transitions (M 2/E3) are too slow to compete with neutron emissions.From a low-spin negative-parity state fed by GT transitions at higher energy, the neutronγ competition is in principle possible, similar to 133g In as discussed above.However, no such candidates were found due to the combined effect of smaller β feeding and a limited number of implanted samples.
Figure 5 presents the extracted β-strength distribution, in the form of S β = 1/f t [31], of the 133g,m In decays with an energy interval of 200 keV.The distributions include the states listed in Table I and the decay strengths associated with the neutron emissions feeding the 132 Sn excited states, which is around 7% of total neutron emissions as discussed above.For these minor strengths, the neutron-γ coincidence analysis was needed TABLE I: A list of neutron-unbound states identified in 133 Sn.Those were derived from the neutron emissions directly feeding the 132 Sn ground state.The excitation energies Eex were calculated from neutron TOF and the Sn = 2.399(3) MeV [28].The I β is the β-decay feeding probability given in % per β decay.A value with * means the state decayed via competing neutron and γ channels, whereas that with † is likely a doublet at 6018 and 6088 keV respectively.See text for details.The logf t values were calculated using the half-lives from Ref. [14], β-decay Q β from the atomic mass difference between 133 In [29] and 133 Sn [28], and Eex, I β from this work.Spins and parities I π were assigned tentatively based on the β-decay selection rules, logf t, and systematics.
Parent Eex (keV)   to correct the excitation energies of the neutron-unbound states in 133 Sn.This can be easily applied to the neutron emissions that feed the 2 + , 3 − , or 4 + states in 132 Sn due to their relatively strong neutron-γ cascades.Additionally, Piersa et al. and Benito et al. observed weak neutron emissions feeding the states higher than the 4 + state in 132 Sn [14,15].Their observations were confirmed in our measurement, but the associated γ decays were generally too weak to perform credible neutron-γ coincidence analysis for the energy correction.To simplify the analysis and include their contribution in Fig. 5, two extreme cases were considered.First, the strength distribution was calculated assuming those weak neutron emissions only fed the lowest 2 + , 3 − , or 4 + states around 4 MeV in 132 Sn.Second, the calculation was repeated with the 132 Sn state shifted to 6.5 MeV, the highest observed state in the β-delayed neutron emissions of 133g,m In [15].The final results shown in Fig. 5 are the average between the two calculations, with the error bars covering their upper and lower limits.

IV. SPIN AND PARITY ASSIGNMENTS
Before this work, the only state known to have a neutron-hole configuration in 133 Sn was the 11/2 − state at 3564 keV [12,14,30].Its wavefunction is dominated by a neutron 2p-1h configuration, in which a neutron hole at h 11/2 couples to two neutron particles above N = 82.In the 133g In decay, the same state was observed at E ex = 3561 (18) keV, in good agreement with the literature value.It is the lowest neutron unbound state seen in the experiment (see Fig. 3).In an intuitive picture, the decay is associated with a FF transition νh 11/2 → πg 9/2 , during which the two neutron particles outside N = 82 persist as a spin J = 0 pair in the initial and final states.Fogelberg et al. observed the analogous transition without the neutron pair in 131 In→ 131 Sn with a logf t > 5.6 [32].According to the odd-mass tin isotopes with N < 82, there are two extra neutron orbitals d 3/2 and s 1/2 close to h 11/2 , giving rise to three neutron 2p-1h states at similar excitation energy in 133 Sn.Indeed, two states were observed in the isomeric decay at excitation energies of 3.62 and 3.79 MeV.Following the systematics, the lower state (logf t = 5.4) was assigned I π = 3/2 + , and the upper state (logf t = 5.8)I π = 1/2 + .Their underlying transitions are νd 3/2 → πp 1/2 and νs 1/2 → πp 1/2 , respectively, both of which are FF transitions.The most important neutron-hole orbital involved in the 133 In decay is the deeply bound νg 7/2 because it determines the GT strength of 133g In.In Fig. 5, one can see a remarkable strength at E ex = 5.92 MeV exclusive to the 133g In decay.Its I β gives a logf t = 4.7, which is significantly stronger than any other feeding in the decay.Thus, the state was assigned I π = 7/2 + originating from νg −1 7/2 .The newly determined GT strength of νg 7/2 → πg 9/2 in 133g In has a similar logf t as in the 131g In decay (=4.4 [32]).It is noted that this assignment is different from that in Ref. [14] suggesting the 6088-keV state to be populated via the dominant GT decay.[32,33].In 133 Sn, the spins, parities, and excitation energies of the ν1p-0h states are taken from Refs.[13,14], while those of ν2p-1h are from this work.The dashed lines connect groups of states with the same odd-even combination of neutron p-h configuration.
The result enables a complete comparison between 131 Sn and 133 Sn, see Fig. 6.Before this work, the neutron 1p-2h states in 131 Sn and the neutron 1p-0h states in 133 Sn had revealed remarkable similarity in neutron transfer reactions [4,33].Similarly, if one moved down the neutron 2p-1h states in 133 Sn and aligned the lowest 11/2 − state to the ground state in 131 Sn, the level scheme constructed in this work is analogous to that of the 0p-1h states in 131 Sn [32], supporting our spin-parity assignment discussed previously.
Besides, one notices strong β feedings at E ex ∼ 5 MeV in Fig. 5 in both ground-state and isomeric decays.At this excitation energy, it is possible to break the proton Z = 50 core and populate the proton 1p-1h excited states in 133 Sn.From the low-lying states in odd-mass antimony isotopes (Z = 51) around N = 82, πg 7/2 and πd 5/2 are expected to be the lowest two proton orbitals outside Z = 50.Thus, the lowest proton core excited states observed in the 133 In decay should be dominated by either π(g −1 9/2 g 7/2 ) × νf 7/2 or π(p −1 1/2 g 7/2 ) × νf 7/2 , depending on where the proton hole is in the initial state, i.e., whether the ground-state or isomeric decay.Both scenarios are carried by the FF transition νf 7/2 → πg 7/2 .At slightly higher excitation energy, states with the π(g −1 9/2 d 5/2 ) × νf 7/2 or π(p −1 1/2 d 5/2 ) × νf 7/2 configuration should also be accessible via νf 7/2 → πd 5/2 .Benito et al. observed analogous transitions in the decay from 132 In to 132 Sn at similar excitation energy [15].The I π of those states were assigned based on the β-decay selection rules of non-unique FF transitions: ∆I = 0 or 1 and ∆π = −1.The unique FF transitions with ∆I = 2 were not considered in the present spin assignment due to their significantly larger logf t and smaller intensities [34].For example, the neutron d −1 5/2 state in 131 Sn is populated in the isomeric decay of 131 In (νd 5/2 → πp 1/2 ) with a logf t = 9.5 [32], of which the feeding probability is far below our sensitivity.Above the 7/2 + state at 5.92 MeV, no isolated resonances were seen with strong feeding strength in either of the 133g,m In decay.The spectra follow a continuous distribution, which was attributed to the high level density and limited resolving power.In this energy region, β decay can populate both positive-and negative-parity states via GT or FF transitions.The GT transitions are favored because of their more significant matrix elements.Following the selection rule, the states with E ex > 6 MeV were assigned the spin I = (7/2, 9/2, 11/2) in the ground-state decay and (1/2, 3/2) in the isomeric decay.

V. SUMMARY AND CONCLUSIONS
In this work, the β-decay properties of 133g,m In were studied at IDS.With the use of β-delayed γ and neutron spectroscopy, their major components in the decaystrength distribution were located above the neutron separation energy in the daughter 133 Sn.The strong GT transformation νg 7/2 → πg 9/2 was observed in the 133g In decay, feeding a 7/2 + state at 5.92 MeV in 133 Sn.Besides, many neutron-unbound states originating from neutron or proton p-h excitations were found at lower energies following the FF decays of 133g,m In.The spins and parities of those states were assigned tentatively based on the β-decay selection rules, the extracted logf t values, and systematics along the isotopic chain.
The experimental findings greatly extend our knowledge of the 133 In decay from previous works [12,14,15], providing the β-strength distribution southeast of 132 Sn.The results are crucial to benchmark β-decay theories and will serve as a bridge to understand the decay properties of more neutron-rich nuclei, e.g., those r-process waiting-point nuclei near the N = 82 shell closure.

FIG. 1 :
FIG. 1: Schematic drawing of the experimental setup at IDS.The radioactive beam from ISOLDE was implanted on the tape at the center of the setup.The β-delayed γ rays from 133 In were detected by four HPGe clover detectors at backward angles relative to the beam direction.The INDiE array was placed on the other side to measure neutron spectroscopy following the 133 In decay.

Figure 1
Figure 1 draws the detector configuration at IDS.Four high-purity germanium (HPGe) clover detectors were placed closely outside the decay chamber to measure βdelayed γ radiation.The photopeak efficiency was 10% and 3% for 100-keV and 1-MeV γ rays, respectively, including combining energy deposition from Compton scattering inside all four crystals in each clover (addback).The neutron energies E n were deduced from their timeof-flight (TOF) measured by the IDS Neutron Detector (INDiE), an array similar to the Versatile Array of Neutron Detectors at Low Energy (VANDLE)[21,22].The detection setup consisted of 26 EJ-200 plastic scintillator modules.Each module was 3 × 6 × 120 cm 3 and had one photomultiplier tube (PMT) coupled to each end.The modules were mounted in a custom-built support frame describing an arch for a radius of 100 cm from the decay chamber.The intrinsic neutron efficiency of each module was 35% at 1 MeV[21].The total solid angle covered by 26 modules was about 15% of 4π.However, only 22 out of 26 modules were used in the analysis due to the shadow from the supporting frame of the decay chamber.The resulting solid angle was 12.6% of 4π.Two plastic

FIG. 2 :
FIG. 2:The neutron data taken in coincidence with the133 In β decay, with figures on the left corresponding to the pure ground-state decay and those on the right to an admixture of ground-state (40%) and isomeric decays (60%).Figures (a,e) plot the neutron TOF against their energy loss in INDiE, with the projections along TOF in Figs.(b, f), respectively.Figure (c) shows the ground-state neutron spectrum in coincidence with the 4041-keV γ decay in 132 Sn.Figures(d, g) focus on the TOF of high-energy neutrons with En > 3 MeV.They were made by projecting Figs.(a, e), respectively, along TOF with energy loss greater than 1 MeVee.All the neutron TOF spectra were fitted by the neutron response functions (magenta), with the neutron peaks attributed to the ground-state and isomeric decays drawn in blue and red, respectively.The dashed line is the β and γ-ray background in the neutron TOF spectra.

FIG. 4 :
FIG.4: Portion of γ-ray spectra measured in coincidence with the ground-state decay of133 In.The candidate γ deexcitations from the 133 Sn neutron-unbound states are marked by "•", to be distinguished from the γ decays in 132 Sn.SE stands for single-escape peak.See text for details.

FIG. 6 :
FIG.6: Reduced level schemes of 131 Sn and 133 Sn.Each group of states is labeled by the dominant neutron p-h configuration in the wave functions.Information in 131 Sn is taken from Refs.[32,33].In 133 Sn, the spins, parities, and excitation energies of the ν1p-0h states are taken from Refs.[13,14], while those of ν2p-1h are from this work.The dashed lines connect groups of states with the same odd-even combination of neutron p-h configuration.