First ${\beta}$-decay spectroscopy of $^{135}$In and new ${\beta}$-decay branches of $^{134}$In

The $\beta$ decay of the neutron-rich $^{134}$In and $^{135}$In was investigated experimentally in order to provide new insights into the nuclear structure of the tin isotopes with magic proton number $Z=50$ above the $N=82$ shell. The $\beta$-delayed $\gamma$-ray spectroscopy measurement was performed at the ISOLDE facility at CERN, where indium isotopes were selectively laser-ionized and on-line mass separated. Three $\beta$-decay branches of $^{134}$In were established, two of which were observed for the first time. Population of neutron-unbound states decaying via $\gamma$ rays was identified in the two daughter nuclei of $^{134}$In, $^{134}$Sn and $^{133}$Sn, at excitation energies exceeding the neutron separation energy by 1 MeV. The $\beta$-delayed one- and two-neutron emission branching ratios of $^{134}$In were determined and compared with theoretical calculations. The $\beta$-delayed one-neutron decay was observed to be dominant $\beta$-decay branch of $^{134}$In even though the Gamow-Teller resonance is located substantially above the two-neutron separation energy of $^{134}$Sn. Transitions following the $\beta$ decay of $^{135}$In are reported for the first time, including $\gamma$ rays tentatively attributed to $^{135}$Sn. In total, six new levels were identified in $^{134}$Sn on the basis of the $\beta \gamma \gamma$ coincidences observed in the $^{134}$In and $^{135}$In $\beta$ decays. A transition that might be a candidate for deexciting the missing neutron single-particle $13/2^+$ state in $^{133}$Sn was observed in both $\beta$ decays and its assignment is discussed. Experimental level schemes of $^{134}$Sn and $^{135}$Sn are compared with shell-model predictions. Using the fast timing technique, half-lives of the $2^+$, $4^+$ and $6^+$ levels in $^{134}$Sn were determined.

substantially above the two-neutron separation energy of 134 Sn. Transitions following the β decay of 135 In are reported for the first time, including γ rays tentatively attributed to 135 Sn. In total, six new levels were identified in 134 Sn on the basis of the βγγ coincidences observed in the 134 In and 135 In β decays. A transition that might be a candidate for deexciting the missing neutron single-particle 13/2 + state in 133 Sn was observed in both β decays and its assignment is discussed. Experimental level schemes of 134 Sn and 135 Sn are compared with shell-model predictions. Using the fast timing technique, half-lives of the 2 + , 4 + and 6 + levels in 134 Sn were determined. From the lifetime of the 4 + state measured for the first time, an unexpectedly large B(E2; 4 + → 2 + ) transition strength was deduced, which is not reproduced by the shell-model calculations.

I. INTRODUCTION
The region around 132 Sn, the heaviest doubly-magic nucleus far from the valley of β-stability, is of great relevance for the development of the theoretical description of neutron-rich nuclei. New experimental data for nuclei in that region allow for a better understanding of phenomena that occur when the N/Z ratio becomes large, such as evolution of shell structure [1][2][3][4] and rare processes of β-delayed multiple-neutron emission [5][6][7][8].
Properties of nuclei around 132 Sn are also important for modeling the rapid neutron capture nucleosynthesis process (r -process), since the A ≈ 130 peak in the r -process abundance pattern is linked to the N = 82 shell closure [9][10][11][12].
Due to the robust nature of the 132 Sn core [13], tin isotopes above N = 82 offer a rare opportunity to investigate neutron-neutron components of effective nucleon-nucleon interactions for heavy-mass nuclei with large neutron excess [14]. At present, the 132 Sn region is a unique part of the chart of nuclides where spectroscopic information for neutron-rich nuclei with one and few neutrons beyond the double-shell closure was obtained [14][15][16]. The 133 Sn nucleus, with only one neutron outside the doubly magic 132 Sn, is the heaviest odd-A tin isotope for which excited states were reported so far [13,15,[17][18][19][20][21][22]. This nuclide has been extensively studied for over two decades to gain information about neutron (ν) single-particle (s. p.) states just outside the closed shell at N = 82. Still, the energy of the ν1i 13/2 s. p. state in 133 Sn remains unknown. Recently, states having dominant two-particle one-hole (2p1h) neutron configurations with respect to the 132 Sn core were identified in 133 Sn [20,22]. In the case of even-A tin isotopes above N = 82, information on excited states was obtained for 134 Sn, 136 Sn and 138 Sn [14,16,23,24]. All members of the two-neutron ν2f 7/2 (ν2f 2 7/2 ) multiplet were reported in these isotopes. An additional state belonging to the ν2f 7/2 1h 9/2 configuration is known in 134 Sn [23]. Despite extensive studies, information on tin isotopes beyond N = 82 still appears to be scarce.
In the present work, we report on the results of a βdecay study of 134 In and 135 In nuclei that provide new experimental insights into tin isotopes above N = 82.
In an r -process sensitivity study, 134 In and 135 In were indicated to be among those β-delayed neutron (βn) emitters that have the greatest impact on the abundance pattern in cold wind r -process simulations [25]. More-over, for neutron densities around 10 25 cm -3 , where the rmatter flow has already broken through the N = 82 shell, the 135 In nuclide acts as an important waiting-point [26].
The neutron-rich isotopes 134 In and 135 In represent rare cases of experimentally accessible nuclei for which the β-delayed three neutron (β3n) decay is energetically allowed [6,27]. Therefore, these isotopes are representative nuclei to investigate competition between βdelayed one-(β1n) and multiple-neutron (β2n, β3n, ...) emission as well as the γ-ray contribution to the decay of neutron-unbound states [28,29]. Recently, a significant γ-ray branch for levels above the neutron separation energy (S n ) was observed in 133 Sn [20,22]. As reported in Ref. [20], the main factor that makes the neutron emission from highly excited 2p1h states in 133 Sn hindered is the small overlap of the wave functions of the states involved in the βn decay. It is expected that similar nuclear structure effects play a role for other nuclei southeast of 132 Sn, including 134 In and 135 In [20].
So far, the β decay of 134 In was investigated via β-delayed γ-ray spectroscopy in only one measurement, which provided the first information about neutron s. p. states in 133 Sn [15,17]. The population of excited states in other tin isotopes was not observed. The βn emission probability (P n ) was estimated to be around 65% and a β-decay half-life of 138(8) ms was reported for 134 In [6,15]. Later, the measurement of β-delayed neutrons from 134 In yielded the more precise value of 141(5) ms [26]. Recently, a half-life of 126 (7) ms was obtained at RIKEN for 134 In [30]. In the case of the 135 In β decay, no information on the population of states in tin isotopes existed prior to this work. The βdecay half-life of 135 In was measured in two experiments, which yielded values of 92(10) ms [26] and 103(5) ms [30], respectively.
In this work, we observed for the first time the β-decay (βγ) and β2n-decay branches of 134 In. Transitions following the 135 In β decay, including those belonging to the βγ-, β1n-and β2n-decay branches, were also established for the first time.

II. EXPERIMENTAL DETAILS
The 134 In and 135 In nuclei were produced at the ISOLDE-CERN facility [31]. The 1.4-GeV proton beam from the Proton Synchrotron Booster (PSB) was directed onto a solid tungsten proton-to-neutron converter [32] producing spallation neutrons that induced fission in a thick uranium carbide target. The indium atoms diffused out of the target material and subsequently effused via a transfer line into the hot cavity ion source, where they were selectively ionized by the Resonance Ionization Laser Ion Source (RILIS) [33]. After extraction and acceleration by a 40 kV potential, the indium isotopes were separated according to the mass-to-charge ratio by the General Purpose Separator and then transmitted to the ISOLDE Decay Station (IDS) [34]. They were implanted on an aluminized mylar tape at the center of the detection setup. The time structure of ions reaching IDS varied depending on the composition of a repetitive sequence of proton pulses, called the supercycle, distributed by the PSB at intervals of 1.2 s. The supercycle structure varied during the experiment and its length ranged from 26 to 34 proton pulses, corresponding to 31.2 and 40.8 s, respectively. The extraction of the ion beam was started 5 ms after each proton pulse from PSB and lasted 500 ms for 134 In and 225 ms for 135 In.
Data were collected during the beam implantation and the subsequent decay of the isotopes of interest. To suppress the long-lived activity from the decay of daughter nuclei, the tape was moved after each supercycle. Additional measurements were performed with the 134 In beam in which the tape was moved after each proton pulse. Surface-ionized isobaric contaminants, 134 Cs and 135 Cs, were present in the A = 134 and A = 135 ion beams, respectively. In the case of the A = 135 measurements, the isomeric state of 135 Cs was a severe source of background. For identification of beam impurities, an additional measurement was performed at mass A = 135 with one of the RILIS lasers turned off. In such laseroff mode, only surface-ionized elements reached the IDS, while in the laser-on mode, RILIS-ionized indium was additionally present in the beam.
To detect β particles, a fast-response 3-mm-thick NE111A plastic scintillator was used. It was positioned directly behind the ion collection point and provided a detection efficiency of around 20%. For the γ-ray detection, four high-purity germanium (HPGe) Clover-type detectors and two truncated cone-shaped LaBr 3 (Ce) crystals [35] coupled to fast photomultiplier tubes (PMTs) were utilized. The PMT anode signals from fast-response detectors were processed by analog constant fraction discriminators and then sent to timeto-amplitude converters (TACs), which provided the time difference between coincident signals from plastic and LaBr 3 (Ce) detectors. With this configuration, it was possible to perform lifetime measurements for excited states using the advanced time-delayed βγγ(t) (fast timing) technique [36][37][38].
The Nutaq digital data acquisition system [39] was used to record and sample energy signals from all detectors along with outputs from TACs and reference signal from the PSB. Data were collected in a triggerless mode. Events were reconstructed in the offline analysis, in which they were correlated with the occurrence of the proton pulse.
Energy and efficiency calibrations of γ-ray detectors were performed using 152 Eu, 140 Ba-140 La and 133 Ba radioactive sources as well as 88 Rb and 138 Cs samples produced on-line. High-energy γ rays originating from the background induced by neutrons from the target area were used to extend the energy calibration of HPGe detectors up to 7.6 MeV. The γ-ray photopeak efficiency of the HPGe detectors reached 4% at 1173 keV after the add-back procedure. For each LaBr 3 (Ce) detector, an efficiency of around 1% at 1 MeV was obtained. Timeresponse calibrations of LaBr 3 (Ce) detectors for fullenergy peaks as a function of γ-ray energy as well as corrections due to Compton events were included in the fast-timing analysis. More details on the lifetime measurements using the same experimental setup are provided in Refs. [38,[40][41][42].

III. RESULTS
A. β decay of 134 In Transitions following the β decay of 134 In were identified by comparing β-gated γ-ray spectra sorted using various conditions on the time of the event with respect to the proton pulse. Lines that can be attributed to γ rays in daughter nuclei are enhanced when this time window is limited to a few hundred milliseconds. Figure 1 shows the β-gated γ-ray spectrum obtained at A = 134 during the first 400 ms following the proton pulse. Long-lived background, originating from decays of daughter nuclei and the surface-ionized 134m Cs contaminant, was subtracted from the data presented. Apart from γ rays that can be assigned to the 134 In β decay, neutron-induced background arising from inelastic scattering of fast neutrons [44][45][46][47][48], which were emitted from 134 In as β-delayed particles, is also prominent.
The three most intense lines in the spectrum shown in Fig. 1, at energies of 854, 1561 and 2004 keV, were observed in the previous β-decay study of 134 In [15,17]. They were assigned to the 133 Sn nucleus as transitions depopulating the 3/2 − , (9/2 − ) and 5/2 − states, respectively. These assignments were confirmed later in oneneutron transfer reactions [13,18,19]. The most intense transition at 1561 keV was used to determine the β-decay half-life of 134 In. From the time distribution relative to the proton pulse, shown in Fig. 2, the halflife was deduced to be 118 (6) ms. This value is consistent with the 134 In half-life measured recently at RIKEN, 126(7) ms [30] and slightly differs from the values previously reported in Ref. [15], 138(8) ms, and in Ref. [26], 141(5) ms.
In the present work, the β1n-decay branch of 134 In is expanded with three transitions, all of which depopulate states above S n in 133 Sn, 2398.7 (27) keV [27]. The peak visible in Fig. 1 Figure 1: The β-gated γ-ray spectrum obtained at A = 134 in the first 400 ms relative to the proton pulse from which long-lived background has been subtracted. Transitions assigned to the daughter nuclei of 134 In are labeled with filled symbols, while those attributed to activities of daughter or contaminant nuclei are marked with open symbols. Transitions that can be assigned to the 134 In β decay but not to a specific decay branch are indicated by energy only. Lines marked with an ampersand indicate possible weak transitions whose identification is uncertain. Energies of possible peaks, which might correspond to artifacts due to the background subtraction procedure, are given in parentheses. The presence of a negative peak at 962 keV is the consequence of subtracting the contribution from the daughter nucleus 133 Sn [43]. Triangular-shaped peaks arising from inelastic neutron scattering in the HPGe detectors [44][45][46][47][48] are indicated with asterisks. The peak at 197 keV is also considered as induced by neutrons [46]. The abbreviations SE and DE indicate single-escape and double-escape peaks, respectively. Broad peaks marked with a hash symbol remained unidentified.
A 3570(50)-keV γ ray was first identified in 133 Sn via oneneutron knockout from 134 Sn [20]. This was confirmed in a β-decay study of 133 In that provided improved precision of its energy, 3563.9(5) keV [22]. The peak visible in Fig. 1 at 4110 keV can be associated with the 4110.8(3)-keV γ ray, which was seen previously in the β decay of 133 In [40], but the absence of βγγ coincidence relations hindered its assignment to a particular daughter nucleus. An observation of this line in the β decays of both 133 In and 134 In provides support for its assignment to the 133 Sn nucleus.
In the energy range corresponding to the predicted excitation energy of the 13/2 + state in 133 Sn, 2511(80) keV [50] or between 2360 and 2600 keV [51], one relatively-intense transition was registered at 2434 keV (see Fig. 1). No βγγ and γγ coincidence relationships were observed for this line, making its assignment to either 134 Sn or 132 Sn unlikely and thus providing an argument for its assignment to 133 Sn. The 2792-keV transition, discussed in Ref. [19] as a possible candidate for γ ray depopulating the 13/2 + state in 133 Sn, was not observed in the β decay of 134 In.
Among the known low-lying levels in 133 Sn, only the 1/2 − state [13,19,22] was not seen in the 134 In β decay. The 354-keV transition that was identified in the previous β-decay study of 134 In but remained unassigned de-  spite being registered in coincidence with β-delayed neutrons [15,17], was observed in the present study. No βγγ and γγ coincidence relations were found for this transition, making its attribution to any of the daughter nuclei impossible. The 802-keV transition for which a coincidence with neutrons emitted from 134 In was also reported in Refs. [15,17] was not present in our spectra.
We now turn to the βγ-decay branch of 134 In, leading to the population of states in 134 Sn, which was observed for the first time in this work. Figure 1 shows clearly the presence of the 174-, 347-and 726-keV transitions that were assigned to the yrast 6 + → 4 + → 2 + → 0 + g.s.
Analysis of βγγ coincidences reveals three new transitions in 134 Sn. The 1666-, 3512-and 3763-keV lines are seen in spectra of γ rays in coincidence with previously known transitions in this nucleus. Figure 3a-c displays the γ-ray spectra in coincidence with new transitions assigned to the daughter nucleus produced in the βγdecay branch of 134 In. Two of them depopulate neutronunbound states at excitation energies exceeding the S 1n of 134 Sn, 3631(4) keV [27], by more than 1 MeV.
The β2n-decay branch of 134 In, leading to the population of states in 132 Sn, was observed for the first time. Transitions depopulating the 2 + , 3 − , 4 + and 6 + states in 132 Sn [52], with energies of 4041, 4351, 375 and 300 keV, respectively, were identified (see Fig. 1). Coincidence relationships observed for γ rays in the daughter nucleus produced in the β2n-decay branch of 134 In are shown in Figure 3d.
Transitions assigned to the βγ-, β1n-and β2n-decay branches of 134 In are summarized in Table I. Several additional transitions were observed with a time pattern consistent with the 134 In β-decay half-life. However, due to the lack of βγγ and γγ coincidence relationships, they could not be placed in the β-decay scheme of 134 In. These transitions are also listed in Table I. The β-decay scheme of 134 In established in the present work is shown in Fig. 4. The previously reported scheme [15] is now complemented by the βγ-and β2ndecay branches, with thirteen new transitions assigned to this β decay. Neutron-unbound states decaying via γ rays were identified in two daughter nuclei, 134 Sn and 133 Sn. It should be emphasized that presumably only a partial β-decay scheme is established in this work, since the β-decay energy of 134 In is large (Q β ≈ 14.5 MeV [27]) and, as we have presented, the contribution of γ ray deexcitation to the decay of neutron-unbound states in 134 Sn and 133 Sn is significant.
Relative intensities of transitions following the 134 In β decay were determined from the β-gated γ-ray spectrum. These intensities, normalized to the most intense 1561-keV γ ray, agree with those reported in the previ- Excited states in the daughter nuclei are labeled with energies (in keV) given relative to the ground state of each tin isotope. The spin-parity assignments for previously known states in tin isotopes are taken from Refs. [15,16,20,52]. The ground-state spin and parity of 134 In was proposed based on our experimental findings. Shell-model predictions and systematics discussed in Sec. IV A favor the 7 − assignment. The left vertical scale (in MeV) shows the excitation energy and (multi-) neutron separation energies with respect to the 134 Sn ground-state. The shaded regions represent energy windows for population of (multi-) neutron-unbound states. The Q β , Sn, S2n and S3n values are taken from Ref. [27].
ous β-decay study of 134 In [15,17]. For the γ rays involved in the 174-347-726 keV cascade decaying from the 6 + isomeric state in 134 Sn, a correction to the intensity extracted from the β-gated γ-ray spectrum due to an isomer half-life of 81.7 (12) ns (see Sec. III C) was included. The transition intensities determined from the β-gated γ-ray spectrum as peak areas corrected for efficiency and internal conversion were found to be equal for the 174-, 347-and 726-keV transitions, suggesting that the 2 + and 4 + states in 134 Sn are not fed directly in the β decay of 134 In within the intensity uncertainties. This is further confirmed by the analysis of the γ-ray spectrum in coincidence with the 347-keV transition, where the ratio of transition intensities for the 174-and 726-keV lines a Relative intensities were corrected for internal conversion assuming E2 character: αtot(174 keV)=0.227(4) and αtot(347 keV)=0.0221(4) [53]. b See the discussion section for more details on this assignment. c The identification is uncertain due to low statistics. d Upper limit, this intensity includes a contribution from SE peak.
was deduced to be 1.0(1). These observations points to the lack of direct β-decay feeding to the 2 + and 4 + states in 134 Sn and consequently provides an argument for the high spin value of the ground state of the parent nucleus, which can be 6 − or 7 − . The probabilities of β1n and β2n emission from 134 In were determined from the ratio of daughter nuclei produced in a given β-decay branch to the total number of daughter nuclei, using γ rays emitted in their decays.
The following transitions and their absolute intensities were used: 872 keV in 134 Sb from the 134 Sn β decay with 6(3)% [54], 341 keV in 132 Sb from the 132 Sn β decay with 48.8(12)% [55,56], and 962 keV in 133 Sb from the 133 Sn β decay with 12(2)% [43]. For the latter, both the β decay of 133 Sn and the βn decay of 134 Sn contribute to the intensity. For the βn-decay branch of 134 Sn we use the 1.4% feeding of the 962-keV state in 133 Sb reported in Ref. [54]. The γ-ray intensities obtained from the singles γ-ray spectrum were used to derive the probabilities. Corrections to the recorded activity of daughter nuclei due to tape movement were included based on the reconstructed average supercycle structure. In this way we obtained branching ratios for the β decay of 134 In: P 0n = 2.2(15)%, P 1n = 89(3)% and P 2n = 9(2)%. The P 1n value obtained in our estimate is larger than the βn-decay branching ratio evaluated from the previous β-decay study of 134 In, P n ≈ 65% [6,15,57].
B. β decay of 135 In Spectra acquired at A = 135 are dominated by the decay of the surface-ionized 135 Cs. Figure 5 shows a comparison of the β-gated γ-ray spectra measured in laser-on and laser-off modes. Despite strong isobaric contamination of the RILIS-ionized beam, we were able to identify for the first time transitions following the 135 In β decay. The two most intense lines seen only in the spectrum collected when RILIS was used to ionize indium, at 347 and 726 keV, correspond to known γ rays in 134 Sn. The β-decay half-life of 135 In was determined from the time distributions of the 347-and 726-keV transitions which yielded T 1/2 = 89(10) ms and 90(9) ms, respectively. The decay curve of the 347-keV γ ray is shown in Fig. 6. The weighted average of 89(7) ms is in agreement with the half-life previously determined at ISOLDE by measuring the β-delayed neutrons, 92(10) ms [26], and slightly lower than the half-life of 103(5) ms measured at RIKEN [30]. Based on the systematics of the lighter odd-A indium isotopes, a β-decaying isomer in 135 In is expected to exist, with a half-life similar to the ground state [58]. However, no evidence for its presence was found in this work.
Suppression of the background observed at A = 135 became crucial for the identification of other transitions following the 135 In β decay. Two approaches were used independently in our analysis to reduce contaminants. One strategy was to apply a gate on the first few hundred milliseconds after the proton pulse and subtract events recorded at delayed intervals, leading to a substantial decrease in contamination from 53(2)-min 135m Cs [59]. The second approach was to study γ rays observed in coincidence with the highest-energy deposit in the plastic detector, in order to preferentially select 135 In β decay. Figure 7 shows the γ-ray spectra built using two different β-gating conditions. By comparing these spectra, transitions following the 135 In β decay were established. Their energies and relative intensities, which were determined from the β-gated γ ray spectrum, are listed in Table II. Figure 8 shows the β-decay scheme of 135 In established in this work.
The most intense transitions observed in the 135 In β decay belong to 134 Sn. Three lines that can be attributed to the previously known γ rays in 133 Sn were also identified. The 2434-keV transition, which was seen in the 134 In β decay, was also observed in the 135 In β decay and is a plausible candidate for a new transition in 133 Sn. As for the possible β3n-decay branch of 135 In, a slight excess of counts over background appears in the γ-ray spectrum around 4041 keV, corresponding to the energy of the first-excited state in 132 Sn [40,52]. The low statistics does not allow it to be firmly established whether the β3n-decay branch has been observed in this work for 135 In.
Using βγγ coincidence data, new transitions were iden- tified in 134 Sn. Figure 9 displays the β-gated γ-ray spectra in coincidence with the 347-and 726-keV transitions that reveal three new γ rays in 134 Sn with energies of 857, 1094 and 1405 keV. These transitions were placed in the level scheme of 134 Sn as depopulating levels at excitation energies of 1930, 2167 and 2478 keV, respectively (see Fig. 8). Tentative assignment to 134 Sn was made for the 595-keV transition, which was found in coincidence with that at 726 keV, but was not observed in the γ-ray spectra sorted with two different β-gating conditions (see Fig. 7). Several new lines, which were not observed in the β decays of the lighter indium isotopes, were seen in the 135 In β decay. They are listed in Table II. Based on the available experimental information on daughter nuclei produced in the β1n-and β2n-decay branches of 135 In, at least two of them can be considered as transitions in 135 Sn. For 134 Sn, identification of new levels below the excitation energy of the 6 + state (at 1247 keV) is unlikely [16,23,24]. For 133 Sn, new levels below 2004 keV are also not expected [15,[17][18][19][20][21][22]. Therefore, the 950-and ■ Figure 7: (Color online) The β-gated γ-ray spectra obtained at A = 135 in the laser-on mode in which different conditions on time with respect to the proton pulse were applied. [Top panels of (a) and (b):] The orange (gray) curve shows the spectrum gated at times later than 600 ms relative to the proton pulse, while the black curve shows the spectrum without any condition imposed on the time of the event with respect to the proton pulse. The inset in (a) shows a portion of the spectrum with an increased energy threshold for β particles. [Bottom panels of (a) and (b):] The β-gated γ-ray spectrum recorded in the first 400 ms relative to the proton pulse from which long-lived background was subtracted. Transitions assigned to the β1nand β2n-decay branches of 135 In are marked with squares and diamonds, respectively. Peaks that can be attributed to γ rays following 135 In β decay are indicated by energy only, while those assigned to activities of the daughter or contaminant nuclei are marked with "d " and "c", respectively. 1221-keV lines, being the most intense ones in the considered energy range and for which no coincident γ rays were observed, were attributed to deexcitations in 135 Sn. Due to the higher excitation energies of other transitions as well as the lack of βγγ and γγ coincidences for them, it was not possible to attribute them to 135 Sn or 134 Sn.
Due to the overwhelming long-lived background in the singles and β-gated γ-ray spectra, evaluation of the intensities of γ rays following β decays of tin isotopes was not possible. Thus, absolute intensities of transitions assigned to the 135 In β decay could not be determined. Based on relative transition intensities, it can be concluded that the 135 In β decay is dominated by the β1n emission.

C. Lifetime measurements for 134 Sn
For the three lowest excited states in 134 Sn, it was possible to measure their lifetimes using data from both the 134 In and 135 In β decays. The fast-timing analy-ses of these two β decays have their own limitations. In the case of 134 In, acquiring high statistics for transitions in 134 Sn was limited by the large P 1n = 89(3)% and P 2n = 9(2)% values for the parent nucleus. For this reason, it was beneficial to include in the lifetime analysis the data collected for 135 In, despite the beam contamination problems and over an order of magnitude fewer implanted ions of 135 In than 134 In. The statistics obtained in these two β decays precluded the use of triple coincidences βγγ(t). Nevertheless, by investigating the time response of the background and introducing relevant corrections [38,40], half-lives were determined using double-coincidence events [42].
The half-life of the 6 + 1247-keV state in 134 Sn was previously reported as 80(15) ns [16] and, more recently, as 86 +8 −7 ns [24]. Such a long half-life can be measured using the timing information from the HPGe detectors. Figure 10a shows the β − γ HP Ge (t) time distributions gated on the 174-, 347-and 726-keV transitions forming the 6 + → 4 + → 2 + → 0 + g.s cascade from which the halflife of the 6 + level was determined to be 81.7 (12) ns. This value is in agreement with those previously reported, but has a significantly-improved precision.
Determination of the lifetime for the 4 + 1073-keV level in 134 Sn requires the use of fast γ ray detectors. The γ LaBr3(Ce) − γ LaBr3(Ce) (t) coincidences observed in the 134 In β decay between two scintillation detectors were used to obtain the time difference between the 174-keV transition feeding the 4 + state at 1073 keV and the 347-keV transition depopulating it. Figure 10b displays the resulting delayed and antidelayed time distributions. In the 135 In β decay, the 6 + isomeric state in 134 Sn is weakly populated and the same approach was not pos-sible. In this case, the lifetime was derived by analyzing the β − γ LaBr 3 (Ce) (t) time distributions gated on the 347-and 726-keV γ rays depopulating the 4 + and 2 + states in 134 Sn, respectively. By combining the results from both β decays, the half-life of the 4 + state in 134 Sn was measured for the first time and determined to be 1183 (40) ps.
For the 2 + 726-keV state in 134 Sn, the lifetime has not been directly measured to date. A half-life of 49(7) ps was deduced from B(E2; 0 + → 2 + ) = 0.029(5) e 2 b 2 obtained in a Coulomb excitation measurement [60]. To ex- tract the half-life of the 2 + state, the γ LaBr 3 (Ce) − γ LaBr 3 (Ce) (t) coincidences between the 347-and 726-keV γ rays were analyzed. Due to the limited statistics, this was only feasible using the 134 In β-decay data. The determined centroid positions suffered from low statistics. Figure 10c shows the time distributions for the 347 − 726 keV delayed and antidelayed coincidences from which a half-life of 53(30) ps was determined for the 2 + state. This value is consistent with the one deduced from the Coulomb excitation measurement [60].

IV. DISCUSSION
A. β decay of 134 In The ground-state configuration of 134 In, with Z = 49 and N = 85, is based on the coupling of the proton hole in the π1g 9/2 orbital and three neutrons in the ν2f 7/2 orbital (see Fig. 11). The 134 In ground-state spin and parity have not been determined experimentally yet. However, in the previous β-decay study of 134 In, it was possible to restrict the expected spin-parity values to a range from 4 − to 7 − , with 7 − being favored, based on the observed β-decay feeding to excited states in 133 Sn and on systematics [15]. The observation of the β-decay feeding to only one member of the ν2f 2 7/2 multiplet in 134 Sn, the one with maximum spin value of 6 + , is another argument for a high ground-state spin of the parent nucleus, which can be 6 − or 7 − . For the analogous configuration π1g −1 9/2 ν2f 7/2 in 132 In, the 7 − state is the lowest-lying member of the multiplet [52,62]. Thus, the 7 − ground state can also be expected in 134 In. This ground-state spin-parity assignment is supported by shell-model calculations that reproduce the recently identified 3.5(4)µs isomer in 134 In decaying by an E2 transition [63]. Shell-model calculations with two different interactions consistently predict 7 − as the 134 In ground state, while the 6 − state is expected to lie above the 5 − isomer [63]. Therefore, we consider 7 − as the most likely ground-state spin-parity assignment for 134 In.
The β decay of 134 In is dominated by the Gamow-Teller (GT) ν1g 7/2 → π1g 9/2 transition [64]. Since this GT decay involves deeply-bound neutrons in the N = 82 132 Sn core, it populates neutron-unbound states in the daughter nucleus (see Fig. 11). These are expected in 134 Sn at excitation energies comparable to the energy of the 6 − state in 132 Sn (7211 keV), arising from the ν1g −1 7/2 2f 7/2 configuration, which is populated in the GT decays of 132 In [40,52]. This implies that the prevalent β-decay feeding is located well above the S 2n of 134 Sn, 6030(4) keV [27]. As a result, the 134 In β decay proceeds mainly through βn-emission branches. The observed population of the 6 + 4716-keV state in the β2n-decay daughter nucleus 132 Sn indicates that there is significant β-decay feeding to neutron-unbound states in 134 Sn at excitation energies exceeding 10 MeV. This βdecay strength most likely originates from GT transitions involving proton particle-hole excitations across the Z = 50 shell gap (see Fig. 11).
The obtained β1n-and β2n-decay branching ratios for 134 In allow for verification of the predictions of the models used for calculating β-delayed particle emission, which are employed in r-process nucleosynthesis modeling. There are presently only two known β2n emitters in the 132 Sn region for which P 2n have been measured [6,65]: 136 Sb with P 2n = 0.14(3)% [66] and 140 Sb  with P 2n = 7.6(25)% [67].

Method
P1n ( Table III). For the QRPA, it is possible to compare three successively extended models, some of which take into account not only GT transitions but also first-forbidden (ff ) transitions and competition between all available decay branches of neutron-unbound states. The inclusion of ff transitions in the QRPA-2 model [70] leads to an increase in the β1n-decay branching ratio by a factor of about ten with respect to the previous model, QRPA-1, in which only GT transitions were considered [68]. A larger contribution of the β1n emission from 134 In is predicted by RHB+RQRPA [7], which accounts for both GT and ff transitions. However, in the RHB+RQRPA calculations, the total probability of βn emission (P n,tot ) is lower (≈ 66%) than in the two first variants of the QRPA calculations, where P n,tot exceeds 90%. Besides, the predicted branching ratio of the β1n decay remains lower than the experimental result.
The dominant contribution of the β1n emission is predicted by the most recent QRPA calculations in which the statistical Hauser-Feshbach (HF) model [28] is incorporated to address competition between γ-ray, oneand multiple-neutron emission in the decay of neutronunbound states (QRPA+HF) [71]. The P 1n value predicted by the QRPA+HF model, which also accounts for ff transitions, is the closest to the experimental value among the models considered. In the case of the P 2n , the experimental value is well reproduced only by the EDM. This approach also accounts for the competition between one-and multiple-neutron emission as well as γ-ray emission above S n . If the cutoff method is applied to the EDM, so that the decay of states above S 1n (S 2n ) proceeds only via emission of one (two) neutron(s), the calculated probabilities change significantly, P 1n = 28% and P 2n = 39% [8].
A comparison of the different P 1n,2n calculations shows that the best reproduction of the experimental values for 134 In is achieved when ff transitions and all possible deexcitation paths of neutron-unbound states are taken into account. Indeed, the inclusion of competi- tion between the emission of one and multiple neutrons as well as γ rays following the 134 In β decay is relevant, as in this work the β1n-decay branch of 134 In was observed to be dominant even though the GT resonance is located substantially above S 2n of 134 Sn. Moreover, neutron-unbound states decaying via γ rays were observed in the two daughter nuclei, 134 Sn and 133 Sn. In the one-neutron knockout reaction from 134 Sn, it was estimated that around 25% − 35% of the decay of neutronunbound states populated in 133 Sn proceeds via γ-ray emission [20]. The enhanced γ-ray emission from states above S n was explained by the small spectroscopic overlap between states involved in neutron emission.
A similar nuclear structure effect is expected to play a role in the β decay of 134 In, both in βγ-and β1n-decay branches. The GT decays of neutrons from the N = 82 132 Sn core result in population of states in 134 Sn formed by couplings of the valence neutrons to core excitations (ν −1 ν 3 or ππ −1 ν 2 , see Fig. 11). The wave functions of the states populated following neutron emission have small spectroscopic overlaps with the low-lying states in 133 Sn, having a single-particle nature [13]. For this reason, γ rays are able to compete with neutron emission well above S 1n . Similar structure effects leading to hindrance of neutron emission were identified in other βn emitters [72][73][74]. The QRPA+HF calculations estimate a minor change, below 3%, in the calculated βn emission probability if an increase of one order of magnitude to the γ-ray strength function is assumed [28]. However, such enhancement of γ-ray emission would have a larger effect on the neutron capture rates of neutronrich nuclei.
The population of states below the excitation energy of 7 MeV in 134 Sn is due to ff β decays of 134 In. One of these, the ν1h 11/2 → π1g 9/2 transition, which involves neutrons from the N = 82 132 Sn core, feeds neutron-unbound states located below the GT resonance (see Fig. 11). The two new states identified in 134 Sn at excitation energies around 5 MeV are most likely members of the ν1h −1 11/2 2f 3 7/2 multiplet. This assignment is supported by shell-model calculations with core excitations, which predict the first state from this multiplet at around 5 MeV (see Fig. 12) [75]. An analogous (11/2 − ) state in 133 Sn, resulting from the coupling of a neutron hole in the ν1h 11/2 orbital and two neutrons in the ν2f 7/2 orbital, was identified at 3564 keV [15,20,22]. The 1.26-MeV neutrons [15] and 3564-keV γ rays [22] were assigned to the decay of the (11/2 − ) state in 133 Sn in β-decay studies of 133 In. The observation of a 3563(1)-keV transition in this work implies that this neutron-unbound (11/2 − ) state is also populated via the β1n decay of 134 In. A certain analogy can be noted to the population pattern observed in the βn decay of 132 In, which proceeds primarily through the high-spin (11/2 − ) isomer in 131 Sn [40,76]. In the β decay of 134 In, states with configurations involving neutron hole in the ν1h 11/2 orbital are populated in each observed β-decay branch. These states are neutron-unbound in both 134 Sn and 133 Sn. However, γ-ray deexcitation has a significant contribution to their decay. This means that states populated following neutron emission, with hole in the ν1h 11/2 orbital, have little overlap with low-energy states in the corresponding βndecay daughter nuclei, which correspond to excitations of valence neutrons in the N = 82 − 126 shell.
The large P 1n = 89(3)% value and the expected 7 − ground-state spin and parity for 134 In set favorable conditions to search for the missing ν1i 13/2 s. p. state in 133 Sn. The high excitation energies of the predicted multiplets in 134 Sn involving the ν1i 13/2 orbital are also advantageous. The lowest-lying state arising from the ν2f 7/2 1i 13/2 configuration is expected at an excitation energy of around 4−5 MeV [77] or 3.2 MeV [78], where negative-parity particle-hole excitations are also expected to appear. Due to the negative parity of states involving the ν1i 13/2 orbital and the expected high density of such levels in 134 Sn [78], there is a chance that they are mixed with other neutron-unbound states of negative parity. Such admixtures would increase the overlap of the wave functions of states involved in the β1n decay in which the 13/2 + state in 133 Sn can be populated. Since there is a wide range of spins, from 3/2 − to (11/2 − ), for the states populated in 133 Sn following the 134 In β decay, the population of the 13/2 + state does not seem to be hindered in terms of the angular momentum for neutron emission.
The excitation energy of the first 13/2 + level in 133 Sn was estimated to be 2511(80) keV [50] or between 2360 and 2600 keV [51]. The 2434-keV transition, which is the only one registered in the energy range from 2100 to 3500 keV that can be attributed to the β decay of 134 In (see Fig. 1), is therefore a natural candidate for a transition deexciting the 13/2 + state in 133 Sn. Due to the large difference between the 134 In and 134 Sn groundstate spins, direct or indirect feeding of an excited state in 134 Sn that decays to the 0 + ground state is unlikely in the 134 In β decay. The 2434-keV transition is also observed in the 135 In β decay, in which other states in 133 Sn are populated in the β2n-decay branch.
The decay of the 13/2 + state to the 7/2 − ground state in 133 Sn can proceed via an E3 transition with an expected lifetime of around 2 ns. In the analogous nucleus in the 208 Pb region with one neutron above the core, 209 Pb, a 15/2 − level corresponding to the ν1j 15/2 s. p. state decays via an E3 transition to the 9/2 + ground state (ν2g 9/2 ) and via an M 2 transition to the 11/2 + excited state (ν1i 11/2 ) [79,80]. The observed relative intensities of these two transitions are 100(2) and 11(1), respectively. Relying on the similarity of the corresponding excitations in the 132 Sn and 208 Pb regions [43,50,[81][82][83][84], the E3 transition is anticipated to dominate the decay of the 13/2 + state in 133 Sn. It is worth mentioning that a transition with energy of 2434 keV was identified in 131 Sn [85]. However, an excited state with that energy cannot be populated in 131 Sn following the 134 In β decay due to an insufficient β-decay energy window.
For the three newly identified states in 134 Sn, pop-ulated by the 134 In β decay, it is possible to propose their spins taking into account the observed γ-ray depopulation pattern and the favored 7 − ground-state spinparity assignment for the parent nucleus. Spin values for the 2912-, 4759-and 5010-keV levels can be limited to a range from 6 to 8, since their decay to the 6 + state at 1247 keV was observed, while the γ-ray decay branch to the 4 + level at 1073 keV was not identified. For the state at 2912 keV, a positive parity can also be proposed. Due to the nature of the low-lying neutron s. p. orbitals in the N = 82 − 126 shell, the bound states in 134 Sn can be populated solely via ff decays of 134 In (see Fig. 11).
A particular remark should be made about the 354-keV transition, which is confirmed in this work as following the β decay of 134 In [15]. Due to the lack of βγγ or γγ coincidence relations, its assignment to one of the daughter nuclei is not possible. A state decaying directly to the ground state cannot be placed at such a low excitation energy in the level scheme of the 132-134 Sn isotopes. In view of the enhanced contribution of electromagnetic transitions above S n in 133 Sn and 134 Sn, one might consider the possibility that the 354-keV γ rays are emitted from a neutron-unbound state for which the centrifugal barrier hinders neutron emission. Once a γ ray has been emitted with the associated angular-momentum transfer, the level that has been fed could subsequently decay via neutron emission.

B. β decay of 135 In
The β-decay feeding pattern of the N = 86 135 In is expected to be similar to that observed in the β decay of the N = 84 133 In [22]. The ground state of 133 In has a π1g −1 9/2 ν2f 2 7/2 configuration, while for the ground state of 135 In, an additional pair of neutrons occupies the ν2f 7/2 orbital. Based on systematics of the Z = 49 isotopes [59], a 9/2 + ground-state spin-parity assignment is expected for both 133 In and 135 In. For the 133 In nucleus, this spin value is supported by the observed βdecay feeding to levels in 133 Sn [22] with well-established spins and parities [13,19].
As discussed in the previous section for 134 In, the β decays of neutron-rich indium isotopes with N > 82 are dominated by the GT ν1g 7/2 → π1g 9/2 transition populating states above S 1n in the daughter nuclei. Therefore, the 135 In β decay is also dominated by the βn-decay branches, as was observed in this work. The analogous state attributed to this GT decay was proposed in 133 Sn at an excitation energy of around 6 MeV [22]. The lowestlying states populated via the ν1g 7/2 → π1g 9/2 β decay can be expected in 135 Sn at comparable energies, being close to the S 2n of 5901(4) keV [27]. Based on the observations from the β decay of 134 In, other GT transitions involving deeply-bound orbitals in the 132 Sn core also contribute, which enhances the β1n-and β2n-decay branches of 135 In.
While the states populated via the dominant GT decays of 135 In are mainly due to particle-hole excitations across the N = 82 shell gap, levels at low excitation energies in 135 Sn can be interpreted as excitations involving neutron orbitals in the N = 82 − 126 shell. In analogous β decay of the (9/2 + ) 133 In ground state, only two bound states in 133 Sn are populated: the 7/2 − (ν2f 7/2 ) ground state and the (9/2 − ) (ν1h 9/2 ) excited state [22]. Since the structure of the three valence-particles nucleus 135 Sn is more complex than the one valence-particle nucleus 133 Sn, more bound states can be populated via ff transitions in 135 Sn than in 133 Sn. If we make an analogy to the 133 In β decay [22], then the population of states arising from the ν2f 3 7/2 and ν2f 2 7/2 1h 9/2 configurations in 135 Sn is expected in the 135 In β decay. Taking into account the most probable (9/2 + ) ground-state spin of 135 In, the ff -type β decay should favor the population of 7/2 − , 9/2 − and 11/2 − states in 135 Sn. Therefore, the 950-and 1221-keV transitions observed in the 135 In β decay are assigned as deexciting states in 135 Sn with proposed spin-parity values of 7/2 − , 9/2 − or 11/2 − .

C. Comparison with shell-model calculations
134 Sn Shell-model predictions for 134 Sn are compared with the excited states observed in this nucleus in Fig. 12. The previously reported states in 134 Sn, belonging to the ν2f 2 7/2 multiplet and one corresponding to the ν2f 7/2 1h 9/2 configuration, are well reproduced by available shell-model calculations.
The experimental information obtained in this work resulted in a significant expansion of the level scheme of 134 Sn, including seven new states, of which one is tentatively proposed. Four levels were placed in the range of 2 − 3 MeV, where calculations indicate the existence of members of the ν2f 7/2 3p 3/2 and ν2f 7/2 1h 9/2 multiplets [75,77,86,87]. The interpretation of levels at excitation energies around 5 MeV differs for the various calculations. These differences are mainly due to the chosen model space. The calculations presented in Ref. [75] (shown in Fig. 12a) do not include the ν1i 13/2 orbital in the model space, but they do include core excitations by considering the ν1h 11/2 and ν2d 3/2 orbitals below the N = 82 shell gap. Excited states predicted above 5 MeV belong to core-excited states with a dominant ν2f 3 7/2 h −1 11/2 configuration. These are out of the model spaces of Refs. [77,78,86,87], which adopt a neutron valence space consisting of orbitals above the N = 82 shell gap only. At excitation energies exceeding 3.   [75], as well as employing 132 Sn as a closed core: (b) Kart2007 from Ref. [77], (c) Yuan2016 from Ref. [86] and (d) Cov2011 from Ref. [87]. The newly identified states are indicated in red. The level shown by the dashed line is proposed tentatively. The (8 + ) state at 2509 keV [23] was not observed in this work. The experimental spin-parity assignments for previously known states in 134 Sn were taken from Refs. [16,23]. The Sn value for 134 Sn was taken from Ref. [27].   [16,24,60,77,78,86,88,89]. Uncertainties of the previously reported experimental results and the one obtained in this work are shown by the gray and orange areas, respectively.
of the 2 + , 4 + and 6 + levels. Figure 13 shows the comparison of the determined values with those reported previously and with theoretical predictions. The obtained B(E2; 2 + → 0 + ) = 1.3 +1.7 −0.5 W. u., is in agreement with the previously reported, more precise, B(E2) value from the Coulomb excitation [60], which is well reproduced by the shell-model calculations. The experimental B(E2; 4 + → 2 + ) = 2.25(7) W. u., which was measured for the first time in this work, is not reproduced by any of the available calculations, which consistently predict a value of about 1.6 W.u., similar to the B(E2; 2 + → 0 + ) rate. In the case of the 6 + → 4 + transition, the precision of the new experimental result, B(E2; 6 + → 4 + ) = 0.870(13) W. u., is significantly improved compared with earlier results [16,24]. For this transition rate, agreement was obtained with various variants of the shell-model predictions (see Figure 13).
If we review the experimental and predicted trends of B(E2) values for successive transitions between members of the ν2f 2 7/2 multiplet in 134 Sn, we find that the calculations do not predict such an increase in B(E2) for the 4 + → 2 + transition as it was observed. A similar trend, although more pronounced, occurs for E2 transitions connecting states belonging to the analogous mul-tiplet in the 208 Pb region, ν2g 2 9/2 in 210 Pb [90,91].
135 Sn Shell-model calculations for 135 Sn [77,78,86,88,92] provide guidance in the interpretation of the first experimental results on excited states for this nucleus. They predict a 7/2 − spin-parity for the ground state of 135 Sn, being a member of the ν2f 3 7/2 multiplet. This prediction is also supported by the systematics of excitation energies in the N = 85 isotones [93] as well as by the expected analogy to the 133 Sn nucleus, with a 7/2 − ground state [13].

V. SUMMARY AND CONCLUSIONS
We report on new γ-ray spectroscopy results from the ISOLDE facility at CERN on the β decay of the neutron-rich 134 In and 135 In nuclei, populating excited states in tin isotopes with N ≥ 82. Due to the relatively simple structure of daughter nuclei, these β decays provide unique conditions for the simultaneous investigation of one-and two-neutron excitations as well as states formed by couplings of valence neutrons to excitations of the 132 Sn core.
tion in the decay of neutron-unbound states, which is not included in the other models considered.
A significant contribution of γ-ray emission from neutron-unbound states populated in the two daughter nuclei, 133 Sn and 134 Sn, at excitation energies exceeding S 1n by 1 MeV was observed in this work. The competition of γ-ray deexcitation with neutron emission well above S 1n can be explained by the weak overlap of the the wave functions of states involved in βn emission. Neutron-unbound states emitting γ rays in 134 Sn are formed by couplings of valence neutrons to core excitations, while the low-lying levels in 133 Sn arise from one-particle excitations of valence neutron. In the energy range consistent with the predicted excitation energy of the 13/2 + state in 133 Sn, a 2434-keV transition was observed, which is proposed as a candidate for a γ ray depopulating the missing ν1i 13/2 s. p. state in 133 Sn.
Transitions following the β decay of 135 In were identified for the first time and the partial β-decay scheme of this nucleus was established. Three new transitions were assigned to 134 Sn based on βγγ coincidences. Two transitions were tentatively attributed to 135 Sn. Their placement in the level scheme of 135 Sn is supported by shell-model calculations. Several other γ rays were observed in the 135 In β decay but could not be assigned to a specific β-decay branch of the parent nucleus. Due to their low energies and lack of βγγ coincidence relations, they cannot be placed in the level scheme of any other daughter nuclei.
The level scheme of 134 Sn was supplemented in total by six new excited states, populated either through ff decays of 134 In or via β1n emission from neutron-unbound states in 135 Sn. Data from these two β decays also allowed us to determine the lifetimes of the previously known 2 + , 4 + and 6 + states in 134 Sn. Experimental excitation energies and reduced transition probabilities were compared with the shell-model calculations for 134 Sn. New levels appear at excitation energies for which existence of the ν2f 7/2 3p 3/2 and ν2f 7/2 1h 9/2 multiplets is predicted. Calculations including core excitations reproduce well the energies of the two neutron-unbound states identified in 134 Sn that are most likely populated in the ff ν1h 11/2 → π1g 9/2 decays of 134 In.