First β-decay spectroscopy of 135In and new β-decay branches of 134In

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ First β-decay spectroscopy of 135In and new β-decay branches of 134In © Authors, 2021 Published version Piersa-Siłkowska, M.; Korgul, A.; Benito, J.; Fraile, L. M.; Adamska, E.; Andreyev, A. N.; Álvarez-Rodríguez, R.; Barzakh, A. E.; Benzoni, G.; Berry, T.; Borge, M. J. G.; Carmona, M.; Chrysalidis, K.; Correia, J. G.; Costache, C.; Cubiss, J. G.; Day, Goodacre T.; De Witte, H.; Fedorov, D. V.; Fedosseev, V. N.; Fernández-Martínez, G.; Fijałkowska, A.; Fynbo, H.; Galaviz, D.; Galve, P.; García-Díez, M.; Greenlees, Paul T.; Grzywacz, R.; Harkness-Brennan, L. J.; Henrich, C.; Huyse, M.; Ibáñez, P.; Illana, A.; Janas, Z.; Johnston, K.; Jolie, J.; Judson, D. S.; Karanyonchev, V.; Kicińska-Habior, M.; Konki, Joonas; Koszuk, Ł.; Kurcewicz, J.; Lazarus, I.; Lică, R.; López-Montes, A.; Mach, H.; Madurga, M.; Marroquín, I.; Marsh, B.; Martínez, M. C.; Mazzocchi, C.; Miernik, K.; Mihai, C.; Mărginean, N.; Mărginean, R.; Negret, A.; Nácher, E.; Ojala, Joonas; Olaizola, B.; Page, R. D.; Pakarinen, Janne; Pascu, S.; Paulauskas, S. V.; Perea, A.; Pucknell, V.; Rahkila, Panu; Raison, C.; Rapisarda, E.; Rezynkina, K.; Rotaru, F.; Rothe, S.; Rykaczewski, K. P.; Régis, J.-M.; Schomacker, K.; Siłkowski, M.; Simpson, G.; Sotty, C.; Stan, L.; Stănoiu, M.; Stryjczyk, Marek; Sánchez-Parcerisa, D.; Sánchez-Tembleque, V.; Tengblad, O.; Turturică, A.; Udías, J. M.; Van Duppen, P.; Vedia, V.; Villa, A.; Viñals, S.; Wadsworth, R.; Walters, W. B.; Warr, N.; Wilkins, S. G. Piersa-Siłkowska, M., Korgul, A., Benito, J., Fraile, L. M., Adamska, E., Andreyev, A. N., ÁlvarezRodríguez, R., Barzakh, A. E., Benzoni, G., Berry, T., Borge, M. J. G., Carmona, M., Chrysalidis, K., Correia, J. G., Costache, C., Cubiss, J. G., Day, G. T., De Witte, H., Fedorov, D. V., . . . Wilkins, S. G. (2021). First β-decay spectroscopy of 135In and new β-decay branches of 134In. Physical Review C, 104(4), Article 044328. https://doi.org/10.1103/PhysRevC.104.044328 2021 PHYSICAL REVIEW C 104, 044328 (2021) First β-decay spectroscopy of 135In and new β-decay branches of 134In M. Piersa-Siłkowska ,1,*A. Korgul,1,†J. Benito,2L. M. Fraile,2,3E. Adamska,1A. N. Andreyev,4R. Álvarez-Rodríguez,5 A. E. Barzakh,6G. Benzoni,7T. Berry,8M. J. G. Borge,3,9M. Carmona,2K. Chrysalidis,3J. G. Correia,3,10 C. Costache,11 J. G. Cubiss,3,4T. Day Goodacre,3,12 H. De Witte,13 D. V. Fedorov,6V. N. Fedosseev,3G. Fernández-Martínez,14 A. Fijałkowska,1H. Fynbo,15 D. Galaviz,16 P. Galve,2M. García-Díez,2P. T. Greenlees,17,18 R. Grzywacz,19,20 L. J. Harkness-Brennan,21 C. Henrich,22 M. Huyse,13 P. Ibáñez,2A. Illana,13,23 Z. Janas,1K. Johnston,3J. Jolie,24 D. S. Judson,21 V. Karanyonchev,24 M. Kici´ nska-Habior,1J. Konki,17,18 Ł. Koszuk,1J. Kurcewicz,3I. Lazarus,25 R. Lic˘ a,3,11 A. López-Montes,2H. Mach,26 M. Madurga,3,19 I. Marroquín,9B. Marsh,3M. C. Martínez,2C. Mazzocchi,1K. Miernik,1 C. Mihai,11 N. M˘ arginean,11 R. M˘ arginean,11 A. Negret,11 E. Nácher,27 J. Ojala,17 B. Olaizola,28,29,3R. D. Page,21 J. Pakarinen,17 S. Pascu,11 S. V. Paulauskas,19 A. Perea,9V. Pucknell,25 P. Rahkila,17,18 C. Raison,4E. Rapisarda,3 K. Rezynkina,13 F. Rotaru,11 S. Rothe,3K. P. Rykaczewski,20 J.-M. Régis,24 K. Schomacker,24 M. Siłkowski,1G. Simpson,30 C. Sotty,11,13 L. Stan,11 M. St˘ anoiu,11 M. Stryjczyk,1,13,17 D. Sánchez-Parcerisa,2V. Sánchez-Tembleque,2O. Tengblad,9 A. Turturic˘ a,11 J. M. Udías,2P. Van Duppen,13 V. Vedia,2A. Villa,2S. Viñals,9R. Wadsworth,4 W. B. Walters,31 N. Warr,24 and S. G. Wilkins3 (IDS Collaboration) 1Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland 2Grupo de Física Nuclear and IPARCOS, Universidad Complutense de Madrid, CEI Moncloa, E-28040 Madrid, Spain 3CERN, CH-1211 Geneva 23, Switzerland 4Department of Physics, University of York, York, YO10 5DD, United Kingdom 5Escuela Tecnica Superior de Arquitectura, Universidad Politécnica de Madrid, E-28040 Madrid, Spain 6Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia 7Istituto Nazionale di Fisica Nucleare, Sezione di Milano, I-20133 Milano, Italy 8Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom 9Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain 10C2TN, Centro de Ciências e Tecnologias Nucleares, Instituto Superior Técnico, Universidade de Lisboa, Portugal 11“Horia Hulubei” National Institute of Physics and Nuclear Engineering, RO-077125 Bucharest, Romania 12School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom 13KU Leuven, Instituut voor Kernen Stralingsfysica, Celestijnenlaan 200D, 3001 Leuven, Belgium 14Institut für Kernphysik, Technische Universität zu Darmstadt, 64289 Darmstadt, Germany 15Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark 16LIP, and Faculty of Sciences, University of Lisbon, 1000-149 Lisbon, Portugal 17University of Jyväskylä, Department of Physics, P.O. Box 35, FI-40014, Jyväskylä, Finland 18Helsinki Institute of Physics, University of Helsinki, FIN-00014 Helsinki, Finland 19Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA 20Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 21Oliver Lodge Laboratory, The University of Liverpool, Liverpool, L69 7ZE, United Kingdom 22Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany 23Instituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy 24Institut für Kernphysik, Universität zu Köln, 50937 Köln, Germany 25STFC Daresbury, Daresbury, Warrington WA4 4AD, United Kingdom 26National Centre for Nuclear Research, BP1, PL 00-681 Warsaw, Poland 27Instituto de Física Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain 28Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G 2W1 29TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada 30Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS/Université Grenoble Alpes, Grenoble Cedex F-38026, France 31Department of Chemistry, University of Maryland, Maryland 20742, USA (Received 20 July 2021; accepted 28 September 2021; published 26 October 2021) *Corresponding author: [email protected] †[email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. 2469-9985/2021/104(4)/044328(19) 044328-1 Published by the American Physical Society M. PIERSA-SIŁKOWSKA et al. PHYSICAL REVIEW C 104, 044328 (2021) The βdecay of the neutron-rich 134In and 135In 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 β-delayed γ-ray spectroscopy measurement was performed at the ISOLDE facility at CERN, where indium isotopes were selectively laser-ionized and on-line mass separated. Three β-decay branches of 134In were established, two of which were observed for the first time. Population of neutron-unbound states decaying via γrays was identified in the two daughter nuclei of 134In, 134Sn and 133Sn, at excitation energies exceeding the neutron separation energy by 1 MeV. The β-delayed oneand two-neutron emission branching ratios of 134In were determined and compared with theoretical calculations. The β-delayed one-neutron decay was observed to be dominant β-decay branch of 134In even though the Gamow-Teller resonance is located substantially above the two-neutron separation energy of 134Sn. Transitions following the βdecay of 135In are reported for the first time, including γrays tentatively attributed to 135Sn. In total, six new levels were identified in 134Sn on the basis of the βγγ coincidences observed in the 134In and 135In βdecays. A transition that might be a candidate for deexciting the missing neutron single-particle 13/2+state in 133Sn was observed in both βdecays and its assignment is discussed. Experimental level schemes of 134Sn and 135Sn are compared with shell-model predictions. Using the fast timing technique, half-lives of the 2+,4 +,and6 +levels in 134Sn 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. DOI: 10.1103/PhysRevC.104.044328 I. INTRODUCTION The region around 132Sn, the heaviest doubly magic nucleus far from the valley of βstability, 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/Zratio becomes large, such as evolution of shell structure [1–4] and rare processes of β-delayed multiple-neutron emission [5–8]. Properties of nuclei around 132Sn are also important for modeling the rapid neutron capture nucleosynthesis process (rprocess), since the A≈130 peak in the r-process abundance pattern is linked to the N=82 shell closure [9–12]. Due to the robust nature of the 132Sn 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 132Sn 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 [14–16]. The 133Sn nucleus, with only one neutron outside the doubly magic 132Sn, is the heaviest odd-Atin isotope for which excited states were reported so far [13,15,17–22]. 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 ν1i13/2s. p. state in 133Sn remains unknown. Recently, states having dominant twoparticle one-hole (2p1h) neutron configurations with respect to the 132Sn core were identified in 133Sn [20,22]. In the case of even-Atin isotopes above N=82, information on excited states was obtained for 134Sn, 136Sn, and 138Sn [14,16,23,24]. All members of the two-neutron ν2f7/2(ν2f2 7/2) multiplet were reported in these isotopes. An additional state belongingtotheν2f7/21h9/2configuration is known in 134Sn [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 β-decay study of 134In and 135In nuclei that provide new experimental insights into tin isotopes above N=82. In an r-process sensitivity study, 134In and 135In 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]. Moreover, for neutron densities around 1025 cm−3, where the r-matter flow has already broken through the N= 82 shell, the 135In nuclide acts as an important waiting point [26]. The neutron-rich isotopes 134In and 135In represent rare cases of experimentally accessible nuclei for which the βdelayed three-neutron (β3n) decay is energetically allowed [6,27]. Therefore, these isotopes are representative nuclei to investigate competition between β-delayed 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 Snwas observed in 133Sn [20,22]. As reported in Ref. [20], the main factor that hinders the neutron emission from highly excited 2p1h states in 133Sn is the small overlap of the wave functions of the states involved in the βndecay. It is expected that similar nuclear structure effects play a role for other nuclei southeast of 132Sn, including 134In and 135In [20]. So far, the βdecay of 134In was investigated via β-delayed γ-ray spectroscopy in only one measurement, which provided the first information about neutron s. p. states in 133Sn [15,17]. The population of excited states in other tin isotopes was not observed. The βnemission probability Pnwas estimated to be around 65% and a β-decay half-life of 138(8) ms was reported for 134In [6,15]. Later, the measurement of β-delayed neutrons from 134In yielded the more precise value of 141(5) ms [26]. Recently, a half-life of 126(7) ms was obtained at RIKEN for 134In [30]. In the case of the 135In βdecay, no information on the population of states in tin isotopes existed prior to this work. The β-decay half-life of 135In was measured in 044328-2 FIRST β-DECAY SPECTROSCOPY … PHYSICAL REVIEW C 104, 044328 (2021) 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 134In. Transitions following the 135In βdecay, including those belonging to the βγ-, β1nand β2n-decay branches, were also established for the first time. II. EXPERIMENTAL DETAILS The 134In and 135In nuclei were produced at the ISOLDECERN 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 134In and 225 ms for 135In. 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 134In beam in which the tape was moved after each proton pulse. Surface-ionized isobaric contaminants, 134Cs and 135Cs, were present in the A=134 and A=135 ion beams, respectively. In the case of the A=135 measurements, the isomeric state of 135Cs 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 laser-off mode, only surface-ionized elements reached the IDS, while in the laseron mode, RILIS-ionized indium was additionally present in the beam. To detect βparticles, 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 LaBr3(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 time-to-amplitude converters (TACs), which provided the time difference between coincident signals from plastic and LaBr3(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 [36–38]. The Nutaq digital data-acquisition system [39] was used to record and sample energy signals from all detectors along with outputs from TACs and the 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 152Eu, 140Ba - 140La, and 133Ba radioactive sources as well as 88Rb and 138Cs samples produced online. High-energy γrays 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 LaBr3(Ce) detector, an efficiency of around 1% at 1 MeV was obtained. Time-response calibrations of LaBr3(Ce) detectors for full-energy 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. [38,40–42]. III. RESULTS A. βdecay of 134In Transitions following the βdecay of 134In 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 γrays in daughter nuclei are enhanced when this time window is limited to a few hundred milliseconds. Figure 1shows 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 134mCs contaminant, was subtracted from the data presented. Apart from γrays that can be assigned to the 134In βdecay, neutron-induced background arising from inelastic scattering of fast neutrons [44–48], which were emitted from 134In 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 134In [15,17]. They were assigned to the 133Sn nucleus as transitions depopulating the 3/2−,(9/2−), and 5/2−states, respectively. These assignments were confirmed later in one-neutron transfer reactions [13,18,19]. The most intense transition at 1561 keV was used to determine the β-decay half-life of 134In. From the time distribution relative to the proton pulse, shown in Fig. 2,the half-life was deduced to be 118(6) ms. This value is consistent with the 134In 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 134In is expanded with three transitions, all of which depopulate states above Snin 133Sn, 2398.7(27) keV [27]. The peak visible in 044328-3 M. PIERSA-SIŁKOWSKA et al. PHYSICAL REVIEW C 104, 044328 (2021) x3 132Sb 134Cs (n,n' γ) ○ * 134Sn 133Sn 132Sn 3512 4110 3563 4351 1976 SE 1606 1666 2004 2434 354 511 563 * DE 596 * 834 * 843 * 1015 * 1039 * 1205 * 1561 SE 174 300 347 375 726 854 992 ○ 197 * 4041 (4039) 127 2026& 1427 (508) Pb X rays # # 3599 + SE 3816& 4283 3251& 3840& 3763 3824& FIG. 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 134In 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 134In βdecay 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 133Sn [43]. Triangularshaped peaks arising from inelastic neutron scattering in the HPGe detectors [44–48] 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 remain unidentified. Fig. 1at 3563 keV corresponds to the transition depopulating the (11/2−) state in 133Sn. A 3570(50)-keV γray was first identified in 133Sn via one-neutron knockout from 134Sn [20]. This was confirmed in a β-decay study of 133In that provided improved precision of its energy, 3563.9(5) keV [22]. The peak visible in Fig. 1at 4110 keV can be associated with the 4110.8(3)-keV γray, which was seen previously in the βdecay of 133In [40], but the absence of βγγ coincidence relations hindered its assignment to a particular daughter nucleus. An observation of this line in the βdecays of both 133In and 134In provides support for its assignment to the 133Sn nucleus. In the energy range corresponding to the predicted excitation energy of the 13/2+state in 133Sn, 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 134Sn or 132Sn unlikely and thus providing an argument for its assignment to 133Sn. The 2792-keV transition, discussed in Ref. [19]asapossible candidate for γrays depopulating the 13/2+state in 133Sn, was not observed in the βdecay of 134In. Among the known low-lying levels in 133Sn, only the 1/2−state [13,19,22] was not seen in the 134In βdecay. The 354-keV transition that was identified in the previous β-decay study of 134In but remained unassigned despite 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 134In was also reported in Refs. [15,17] was not present in our spectra. We now turn to the βγ-decay branch of 134In, leading to the population of states in 134Sn, which was observed for the first time in this work. Figure 1shows clearly the presence of the 174-, 347and 726-keV transitions that were assigned to the yrast 6+→4+→2+→0+ g.s.cascade in 134Sn from the 248Cm fission data [16,23]. The 1262-keV γray deexciting the (8+) state in 134Sn [23] was not observed in the 134In βdecay. 044328-4 FIRST β-DECAY SPECTROSCOPY … PHYSICAL REVIEW C 104, 044328 (2021) T1/2 = 118(6) ms Time (ms) 134In decay: gate on β-1561 keV FIG. 2. Time distributions relative to the proton pulse of the 1561-keV transition (blue circles) and the background area (red diamonds) observed in coincidence with βparticles at A=134 when RILIS was applied to ionize indium. A function composed of an exponential decay and a constant background was fit (solid line) in the 510–1200 ms time range. The curve corresponding to the background component is also presented (dashed line). A Bayesian approach was applied in the statistical analysis of the data [49]. Analysis of βγγ coincidences reveals three new transitions in 134Sn. The 1666-, 3512and 3763-keV lines are seen in spectra of γrays in coincidence with previously known transitions in this nucleus. Figures 3(a)–3(c) displays the γ-ray spectra in coincidence with new transitions assigned to the daughter nucleus produced in the βγ-decay branch of 134In. Two of them depopulate neutron-unbound states at excitation energies exceeding the S1nof 134Sn, 3631(4) keV [27], by more than 1 MeV. The β2n-decay branch of 134In, leading to the population of states in 132Sn, was observed for the first time. Transitions depopulating the 2+,3 −,4 +, and 6+states in 132Sn [52], with energies of 4041, 4351, 375, and 300 keV, respectively, were identified (see Fig. 1). Coincidence relationships observed for γrays in the daughter nucleus produced in the β2n-decay branch of 134In are shown in Fig. 3(d). Transitions assigned to the βγ-, β1n-, and β2n-decay branches of 134In are summarized in Table I. Several additional transitions were observed with a time pattern consistent with the 134In 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 134In. These transitions are also listed in Table I. The β-decay scheme of 134In established in the present work is shown in Fig. 4. The previously reported scheme [15] is now complemented by the βγand β2n-decay branches, with thirteen new transitions assigned to this βdecay. Neutron-unbound states decaying via γrays were identified in two daughter nuclei, 134Sn and 133Sn. It should be emphasized that presumably only a partial β-decay scheme is established in this work, since the β-decay energy of 134In is large (Qβ≈ 14.5MeV[27]) and, as we have presented, the contribution of γray deexcitation to the decay of neutron-unbound states in 134Sn and 133Sn is significant. 174 347 726 1666 keV 3512 keV 3763 keV (a) (b) (c) 174 347 726 174 347 726 4041 keV 300 375 (d) FIG. 3. Background-subtracted γ-ray spectra in coincidence with the (a) 1666-, (b) 3512-, and (c) 3763-keV transitions that depopulate new levels in 134Sn following the βγ decay of 134In. Vertical dotted lines indicate energies of previously known transitions in 134Sn. (d) Background-subtracted γ-ray spectrum in coincidence with the 4041-keV transition in 132Sn observed in the β2ndecay of 134In. Relative intensities of transitions following the 134In βdecay were determined from the β-gated γ-ray spectrum. These intensities, normalized to the most intense 1561-keV γray, agree with those reported in the previous β-decay study of 134In [15,17]. For the γrays involved in the 174-347-726 keV cascade decaying from the 6+isomeric state in 134Sn, a correction to the intensity extracted from the β-gated γray spectrum due to an isomer half-life of 81.7(12) ns (see Sec. IIIC) 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 134Sn are not fed directly in the βdecay of 134In 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 174and 726-keV lines 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 134Sn 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 β1nand β2nemission from 134In were determined from the ratio of daughter nuclei produced in a 044328-5 M. PIERSA-SIŁKOWSKA et al. PHYSICAL REVIEW C 104, 044328 (2021) TABLE I. Energies and relative intensities of the transitions observed in the 134In βdecay. Total γ-ray and internal-conversion intensities are normalized to the intensity of the 1561-keV transition, for which the absolute intensity is deduced to be 10.8(6)% per βdecay of 134In. Decay Daughter Energy Relative branch nucleus (keV) intensity βγ 134Sn 173.8(3) 4.9(3)a βγ 134Sn 347.4(3) 4.9(3)a βγ 134Sn 725.6(3) 4.9(4) βγ 134Sn 1665.5(3) 0.6(1) βγ 134Sn 3512.3(3) 2.7(3) βγ 134Sn 3763(1) 0.5(1) β1n133Sn 854.0(3) 10.4(7) β1n133Sn 1561.1(3) 100(5) β1n133Sn 2003.8(3) 3.7(3) β1nb133Sn 2434.2(3) 1.4(2) β1n133Sn 3563(1) 0.6(2) β1n133Sn 4110(1) 0.7(2) β2n132Sn 299.5(3) 0.4(2) β2n132Sn 375.0(3) 0.48(7) β2n132Sn 4041.0(5) 0.9(2) β2n132Sn 4351(1) 0.5(1) Unassigned: Energy Relative Energy Relative (keV) intensity (keV) intensity 354.3(3) 1.5(2) 3599(2) 0.4(1)c 1427.4(3) 0.7(2) 3816(1)d<0.4 1605.8(3) 1.0(2) 3824(1)d<0.4 1976.3(3) 0.8(1) 3840(1)d<0.4 2026(1)d<0.5 4283(1) 0.5(1) 3251(1)d<0.4 aRelative intensities were corrected for internal conversion assuming E2 character: αtot(174 keV)=0.227(4) and αtot(347 keV)= 0.0221(4) [53]. bSee the discussion section for more details on this assignment. cUpper limit, this intensity includes a contribution from the SE peak. dThe identification is uncertain due to low statistics. given β-decay branch to the total number of daughter nuclei, using γrays emitted in their decays. The following transitions and their absolute intensities were used: 872 keV in 134Sb from the 134Sn βdecay with 6(3)% [54], 341 keV in 132Sb from the 132Sn βdecay with 48.8(12)% [55,56], and 962 keV in 133Sb from the 133Sn βdecay with 12(2)% [43]. For the latter, both the βdecay of 133Sn and the βndecay of 134Sn contribute to the intensity. For the βn-decay branch of 134Sn we use the 1.4% feeding of the 962-keV state in 133Sb 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 βdecay of 134In: P0n=2.2(15)%, P1n=89(3)%, and P2n=9(2)%. The P1nvalue obtained in our estimate is larger than the βn-decay branching ratio evaluated from the previous β-decay study of 134In, Pn≈65% [6,15,57]. B. βdecay of 135In Spectra acquired at A=135 are dominated by the decay of the surface-ionized 135Cs. Figure 5shows a comparison of the β-gated γ-ray spectra measured in laser-on and laser-off modes. Despite strong isobaric contamination of the RILISionized beam, we were able to identify for the first time transitions following the 135In βdecay. 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 γrays in 134Sn. The β-decay half-life of 135In was determined from the time distributions of the 347and 726keV transitions which yielded T1/2=89(10) ms and 90(9) ms, respectively. The decay curve of the 347-keV γray 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-Aindium isotopes, a β-decaying isomer in 135In 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 135In βdecay. 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 135mCs [59]. The second approach was to study γrays observed in coincidence with the highestenergy deposit in the plastic detector in order to preferentially select 135In βdecay. Figure 7shows the γ-ray spectra built using two different β-gating conditions. By comparing these spectra, transitions following the 135In βdecay were established. Their energies and relative intensities, which were determined from the β-gated γray spectrum, are listed in Table II. Figure 8shows the β-decay scheme of 135In established in this work. The most intense transitions observed in the 135In βdecay belong to 134Sn. Three lines that can be attributed to the previously known γrays in 133Sn were also identified. The 2434-keV transition, which was seen in the 134In βdecay, was also observed in the 135In βdecay and is a plausible candidate for a new transition in 133Sn. As for the possible β3n-decay branch of 135In, 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 132Sn [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 135In. Using βγγ coincidence data, new transitions were identified in 134Sn. Figure 9displays the β-gated γ-ray spectra in coincidence with the 347and 726-keV transitions that reveal three new γrays in 134Sn with energies of 857, 1094, and 1405 keV. These transitions were placed in the level scheme of 134Sn as depopulating levels at excitation energies of 1930, 044328-6 FIRST β-DECAY SPECTROSCOPY … PHYSICAL REVIEW C 104, 044328 (2021) 0 4041 4351 4416 4716 4041.0 4351 375.0 299.5 132Sn 0+ 2+ 3– 4+ 6+ 0 854 1561 2004 3563 4110 854.0 2003.8 3563 4110 133Sn 7/2– 3/2– (9/2–) 5/2– (11/2–) S3n Sn S2n Sn 1561.1 0 3.6 6.0 1 3.4 14.5 (MeV) ( 6–,7– ) T1/2=118(6) ms 134Sn 50 84 50 83 50 82 134In 49 85 0 726 1073 1247 2912 4759 5010 725.6 347.4 173.8 1665.5 3512.3 3763 0+ 2+ 4+ 6+ Sn S2n (6, 7, 8) (6, 7, 8) (6+,7+,8+) 2434 2434.2 (13/2+) P0n = 2.2(15) % P1n = 89(3) % P2n = 9(2) % FIG. 4. Decay scheme of 134In established in the present work. 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 134In was proposed based on our experimental findings. Shell-model predictions and systematics discussed in Sec. IVA favor the 7−assignment. The left vertical scale (in MeV) shows the excitation energy and (multi-) neutron separation energies with respect to the 134Sn ground state. The shaded regions represent energy windows for population of (multi-) neutron-unbound states. The Qβ,Sn,S2n,andS3nvalues are taken from Ref. [27]. Counts / keV 10 101 102 103 104 105 Energy (keV) 0 200 400 600 800 1 000 RILIS: on, off Cs X rays Pb X rays ■ 347 668 726 787 818 846 857 872 ■ ■ d FIG. 5. The β-gated γ-ray spectrum obtained at A=135 when RILIS was applied to ionize indium (upper blue curve) and when one of the RILIS lasers was blocked (lower red curve). Some of the most prominent transitions are labeled with their energies (in keV). Peaks present in both spectra originate from the contaminants, while those appearing only in the RILIS-on mode can be attributed to the βdecay of 135In (square) or its daughter nucleus (marked with “d”). 2167, and 2478 keV, respectively (see Fig. 8). Tentative assignment to 134Sn 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 βdecays of the lighter indium isotopes, were seen in the 135In βdecay. They are listed in Table II. Based on the available experimental information on daughter nuclei produced in the β1nand β2n-decay branches of 135In, at least two of them can be considered as transitions in 135Sn. For 134Sn, identification of new levels below the excitation energy of the 6+state (at 1247 keV) is unlikely [16,23,24]. For 133Sn, new levels below 2004 keV are also not expected [15,17–22]. Therefore, the 950and 1221-keV lines, being the most intense in the considered energy range and for which no coincident γrays were observed, were attributed to deexcitations in 135Sn. Due to the higher excitation energies of other transitions as well 044328-7 M. PIERSA-SIŁKOWSKA et al. PHYSICAL REVIEW C 104, 044328 (2021) T1/2 = 89(10) ms 135In decay: gate on β-347 keV Time (ms) FIG. 6. Time distribution relative to the proton pulse of the 347keV transition (blue circles) and the background area (red diamonds) observed in coincidence with βparticles at A=135 in the laser-on mode. A function composed of an exponential decay and a constant background was fit (solid line) in the 230–1200 ms time range. The curve corresponding to the background component is also presented (dashed line). A Bayesian approach was applied in the statistical analysis of the data [49]. as the lack of βγγ and γγ coincidences for them, it was not possible to attribute them to 135Sn or 134Sn. Due to the overwhelming long-lived background in the singles and β-gated γ-ray spectra, evaluation of the intensities of γrays following βdecays of tin isotopes was not possible. Thus, absolute intensities of transitions assigned to the 135In βdecay could not be determined. Based on relative transition intensities, it can be concluded that the 135In βdecay is dominated by the β1nemission. C. Lifetime measurements for 134Sn For the three lowest excited states in 134Sn, it was possible to measure their lifetimes using data from both the 134In and 135In βdecays. The fast-timing analyses of these two βdecays have their own limitations. In the case of 134In, acquiring high statistics for transitions in 134Sn was limited by the large P1n=89(3)% and P2n=9(2)% values for the parent nucleus. For this reason, it was beneficial to include in the lifetime analysis the data collected for 135In, despite the beam-contamination problems and over an order of magnitude fewer implanted ions of 135In than 134In. The statistics obtained in these two βdecays precluded the use Counts / keV Energy (keV) ■ 1405 1373 cc 1349 2434 c c 857 ■ 726 ■ 1094 ■ 950 ccc ■ 347 c 1221 ■ 174 962 d c cc c c 872 d c c c 2118 2003 1721 1562 Counts / keV 1824 854 1854 174 347 726 c d c 857 (a) (b) 2259 c c c c c cccc c 134Sn 133Sn ■ FIG. 7. 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. [(a), (b), top panels] 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 panel (a) shows a portion of the spectrum with an increased energy threshold for βparticles. [(a), (b), bottom panels] 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 β1n-andβ2n-decay branches of 135In are marked with squares and diamonds, respectively. Peaks that can be attributed to γ rays following 135In βdecay are indicated by energy only, while those assigned to activities of the daughter or contaminant nuclei are marked with “d”and“c,” respectively. 044328-8 FIRST β-DECAY SPECTROSCOPY … PHYSICAL REVIEW C 104, 044328 (2021) Yuan2016 [86] 134Sn Expt. 0 726 1073 1247 1321 1930 2167 2478 2509 2912 4759 5010 Sn = 3631(4) 725.6 347.4 173.8 595 857.2 1093.8 1404.8 1261.5 1665.5 3512.3 3763 ( ) ( 6, 7, 8 ) ( 6, 7, 8 ) 6 +, 7 +, 8 + ( ) (keV) Energy Jin2011 [75] 12 ν 2f7/2 1h9/2 ν 2f7/2 3p3/2 –1 ν 2f7/2 1h11/2 3 ν 2 f7/2 2 Cov2011 [87] ν 2f7/2 1h9/2 ν 3p3/2 2 ν 2f7/2 3p1/2 ν 2f7/2 3p3/2 Kart2007 [77] ν 1h9/2 2 (keV) (c)(a) (d)(b) Refs.: SM: FIG. 12. Experimental (Expt.) level scheme of 134Sn along with the results of the shell-model calculations (SM) (a) including neutron-core excitations, Jin2011 from Ref. [75], as well as employing 132Sn as a closed core: (b) Kart2007 fromRef.[77], (c) Yuan2016 from Ref. [86], and (d) Cov2011 fromRef.[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 134Sn were taken from Refs. [16,23]. The Snvalue for 134Sn was taken from Ref. [27]. 2. 135Sn Shell-model calculations for 135Sn [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 135Sn, being a member of the ν2f3 7/2multiplet. 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 133Sn nucleus, with a7/2−ground state [13]. The 5/2−and 3/2−levels are predicted to be the lowestlying excited states in 135Sn [77,78,86,88,92]. Given the expected 9/2+ground-state spin-parity for 135In, their population in the 135In βdecay is unlikely. States populated in 135Sn via ff transitions most likely have spins and parities 7/2−,9/2−,or11/2−. Figure 14 displays the calculated excitation energies for low-lying 7/2−,9/2−, and 11/2−levels in 135Sn. Shell-model calculations support the tentative assignment of the 950and 1221-keV transitions to 135Sn as ground-state transitions, since states with such spin values are expected in a comparable energy range [77,78,86,88,92]. Theoretical predictions tend to disagree when we consider levels at higher excitation energies in 135Sn, arising from the ν2f3 7/2,2f2 7/23p3/2and ν2f2 7/21h9/2configurations (see Fig. 14)[77,78,86,88,92]. 044328-15 M. PIERSA-SIŁKOWSKA et al. PHYSICAL REVIEW C 104, 044328 (2021) (W. u.) B(E2, 2+→ 0+)B(E2, 4+→ 2+)B(E2, 6+→ 4+) Expt.SM S. Sarkar, M. S. Sarkar (2004) [88]. C. Yuan et al. (2016) [86]. M. P. Kartamyshev et al. (2007) [77]. C. T. Zhang et al. (1997) [16]. J. R. Beene et al. (2004) [60]. This work A. K. Jain, B. Maheshwari (2017) [89]. Coraggio et al. (2002) [78]. D. Kameda et al. (2012) [24]. FIG. 13. Comparison of predicted (SM) and experimental (Expt.) reduced transition probabilities B(E2) (in W.u.) for E2 transitions in 134Sn. Presented data are taken from Refs. [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. V. SUMMARY AND CONCLUSIONS We report on new γ-ray spectroscopy results from the ISOLDE facility at CERN on the βdecay of the neutronrich 134In and 135In nuclei, populating excited states in tin isotopes with N⩾82. Due to the relatively simple structure of daughter nuclei, these βdecays provide unique conditions for the simultaneous investigation of oneand two-neutron excitations as well as states formed by couplings of valence neutrons to excitations of the 132Sn core. The βγand β2n-decay branches of 134In have been observed for the first time. The β-decay scheme of 134In was supplemented by thirteen transitions, of which three depopulate new levels in 134Sn and two depopulate new levels in 133Sn. Although the prevalent ν1g7/2→π1g9/2GT transition feeds neutron-unbound states at excitation energies exceeding S2nof 134Sn, the 134In βdecay is dominated by β1nemission, with a probability of P1n=89(3)%. Among the available global calculations of βnbranching ratios, only the QRPA + HF [71] and EDM [8,69] models predict the predominance of this β-decay branch for 134In. These two theoretical approaches take into account the competition between oneand multiple-neutron emission as well as γ-ray deexcitation in the decay of neutron-unbound states, which is not included in the other models considered. A significant contribution of γ-ray emission from neutronunbound states populated in the two daughter nuclei, 133Sn and 134Sn, at excitation energies exceeding S1nby 1 MeV was observed in this work. The competition of γ-ray deexcitation with neutron emission well above S1ncan be explained by the weak overlap of the wave functions of states involved in βnemission. Neutron-unbound states emitting γrays in 134Sn are formed by couplings of valence neutrons to core excitations, while the low-lying levels in 133Sn arise from oneparticle excitations of valence neutron. In the energy range consistent with the predicted excitation energy of the 13/2+ state in 133Sn, a 2434-keV transition was observed, which is proposed as a candidate for a γray depopulating the missing ν1i13/2s. p. state in 133Sn. Transitions following the βdecay of 135In were identified for the first time and the partial β-decay scheme of this nucleus was established. Three new transitions were assigned to 134Sn based on βγγ coincidences. Two transitions were tentatively attributed to 135Sn. Their placement in the level scheme of 135Sn is supported by shell-model calculations. Several other γrays were observed in the 135In βdecay 950.3 1220.9 (7/2 ,9/2 ,11/2 ) (7/2 ,9/2 ,11/2 ) (7/2 ) Cor2002 (d) [78] Yuan2016 (c) [86] Kart2007 (b) [77] Sar2004 (a) [88] Refs.: SM: 135Sn Expt. FIG. 14. Excited states in 135Sn tentatively proposed in this work (Expt.). Calculated excitation energies (SM) for the 7/2−,9/2−,and 11/2−states in 135Sn reported in (a) Sar2004 [88], (b) Kart2007 [77], (c) Yuan2016 [86], and (d) Cor2002 [78] are also presented. Excitation energies relative to the 135Sn ground state are given in keV. The ground-state spin-parity assignment for 135Sn, based on systematic trends in neighboring nuclei, was taken from Ref. [59]. 044328-16 FIRST β-DECAY SPECTROSCOPY … PHYSICAL REVIEW C 104, 044328 (2021) 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 134Sn was supplemented in total by six new excited states, populated either through ff decays of 134In or via β1nemission from neutron-unbound states in 135Sn. Data from these two βdecays also allowed us to determine the lifetimes of the previously known 2+,4 +, and 6+states in 134Sn. Experimental excitation energies and reduced transition probabilities were compared with the shell-model calculations for 134Sn. New levels appear at excitation energies for which existence of the ν2f7/23p3/2and ν2f7/21h9/2multiplets is predicted. Calculations including core excitations reproduce well the energies of the two neutron-unbound states identified in 134Sn that are most likely populated in the ff ν1h11/2→ π1g9/2decays of 134In. ACKNOWLEDGMENTS M.P.-S. acknowledges the funding support from the Polish National Science Center under Grants No. 2019/33/N/ST2/03023 and No. 2020/36/T/ST2/00547 (Doctoral scholarship ETIUDA). J.B. acknowledges support from the Universidad Complutense de Madrid under the Predoctoral Grant No. CT27/16CT28/16. This work was partially funded by the Polish National Science Center under Grants No. 2020/39/B/ST2/02346, No. 2015/18/E/ST2/00217, and No. 2015/18/M/ST2/00523, by the Spanish government via Projects No. FPA2017-87568-P, No. RTI2018-09886 8-B-I00, No. PID2019-104390GB-I00, and No. PID2019-104714GB-C21, by the U.K. Science and Technology Facilities Council (STFC), the German BMBF under Contract No. 05P18PKCIA, by the Portuguese FCT under the Projects No. CERN/FIS-PAR/0005/2017, and No. CERN/FIS-TEC/0003/2019, and by the Romanian IFA Grant CERN/ISOLDE. The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 654002. M.Str. acknowledges the funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 771036 (ERC CoG MAIDEN). J.P. acknowledges support from the Academy of Finland (Finland) with Grant No. 307685. 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