Detailed spectroscopy of doubly magic 132 Sn
J. Benito, L.M. Fraile, A.Korgul, M. Piersa, E.Adamska, A.N. Andreyev, R. Álvarez-Rodríguez, A.E. Barzakh, G. Benzoni, T. Berry, M.J.G. Borge, M. Carmona, K. Chrysalidis, C. Costache, J.G. Cubiss, T. Day Goodacre, H. De Witte, D. V. Fedorov, V. N. Fedosseev, G. Fernández-Martínez, A. Fijałkowska, M. Fila, H. Fynbo, D. Galaviz, P. Galve, M. García-Díez, P.T. Greenlees, R. Grzywacz, L.J. Harkness-Brennan, C. Henrich, M. Huyse, P. Ibáñez, A. Illana, Z. Janas, J. Jolie, D.S. Judson, V. Karayonchev, M. Kicinska-Habior, J.Konki, J. Kurcewicz, I. Lazarus, R. Lica, A. López-Montes, M. Lund, H. Mach, M. Madurga, I. Marroquín, B. Marsh, M.C. Martínez, C. Mazzocchi, N. Marginean, R. Marginean, K. Miernik, C. Mihai, R.E. Mihai, E. Nácher, A. Negret, B. Olaizola, R.D.Page, S.V.Paulauskas, S.Pascu, A.Perea, V. Pucknell, P. Rahkila, C. Raison, E. Rapisarda, J.-M. Régis, K. Rezynkina, F. Rotaru, S. Rothe, D. Sánchez-Parcerisa, V. Sánchez-Tembleque, K. Schomacker, G. S. Simpson, Ch. Sotty, L. Stan, M. Stanoiu, M. Stryjczyk, O.Tengblad, A.Turturica, J.M. Udías, P.Van Duppen, V.Vedia, A. Villa-Abaunza, S. Viñals, W.B.Walters, R.Wadsworth, N.Warr
DDetailed spectroscopy of doubly magic Sn J. Benito, ∗ L.M. Fraile, † A. Korgul, M. Piersa, E. Adamska, A.N. Andreyev,
3, 4
R. Álvarez-Rodríguez, A.E. Barzakh, G. Benzoni, T. Berry, M.J.G. Borge,
9, 10
M. Carmona, K. Chrysalidis, C. Costache, J.G. Cubiss,
9, 3
T. Day Goodacre,
9, 12
H. De Witte,
9, 13
D. V. Fedorov, V. N. Fedosseev, G. Fernández-Martínez, A. Fijałkowska, M. Fila, H. Fynbo, D. Galaviz, P. Galve, M. García-Díez, P.T. Greenlees,
17, 18
R. Grzywacz,
19, 20
L.J. Harkness-Brennan, C. Henrich, M. Huyse, P. Ibáñez, A. Illana,
13, 23, ‡ Z. Janas, J. Jolie, D.S. Judson, V. Karayonchev, M. Kicińska-Habior, J. Konki,
17, 18, § J. Kurcewicz, I. Lazarus, R. Lică,
9, 11
A. López-Montes, M. Lund, H. Mach, ¶ M. Madurga,
9, 19
I. Marroquín, B. Marsh, M.C. Martínez, C. Mazzocchi, N. Mărginean, R. Mărginean, K. Miernik, C. Mihai, R.E. Mihai, E. Nácher, A. Negret, B. Olaizola, R.D. Page, S.V. Paulauskas, S. Pascu, A. Perea, V. Pucknell, P. Rahkila,
17, 18
C. Raison, E. Rapisarda, J.-M. Régis, K. Rezynkina, F. Rotaru, S. Rothe, D. Sánchez-Parcerisa,
1, 29
V. Sánchez-Tembleque, K. Schomacker, G. S. Simpson, Ch. Sotty,
13, 11
L. Stan, M. Stănoiu, M. Stryjczyk,
2, 13
O. Tengblad, A. Turturica, J.M. Udías, P. Van Duppen, V. Vedia, A. Villa-Abaunza, S. Viñals, W.B. Walters, R. Wadsworth, and N. Warr (IDS collaboration) Grupo de Física Nuclear & IPARCOS, Universidad Complutense de Madrid, CEI Moncloa, E-28040 Madrid, Spain Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland Department of Physics, University of York, York, YO10 5DD, United Kingdom Advanced Science Research Center (ASRC), Japan Atomic Energy Agency, Tokai-mura, Japan Escuela Técnica Superior de Arquitectura, Universidad Politécnica de Madrid, E-28040 Madrid, Spain Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia Istituto Nazionale di Fisica Nucleare, Sezione di Milano, I-20133 Milano, Italy Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom CERN, CH-1211 Geneva 23, Switzerland Instituto de Estructura de la Materia, CSIC, E-28040 Madrid, Spain “Horia Hulubei" National Institute of Physics and Nuclear Engineering, RO-077125 Bucharest, Romania School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium Institut für Kernphysik, Technische Universität Darmstadt, Germany Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark LIP, and Faculty of Sciences, University of Lisbon, 1000-149 Lisbon, Portugal University of Jyväskylä, Department of Physics, P.O. Box 35, FI-40014 Jyväskylä, Finland Helsinki Institute of Physics, University of Helsinki, FIN-00014 Helsinki, Finland Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Department of Physics, Oliver Lodge Laboratory,University of Liverpool, Liverpool L69 7ZE, United Kingdom Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany Instituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy Institut für Kernphysik, Universität zu Köln, D-50937 Köln, Germany STFC Daresbury, Daresbury, Warrington WA4 4AD, United Kingdom National Centre for Nuclear Research, PL 02-093 Warsaw, Poland Instituto de Física Corpuscular, CSIC - Universidad de Valencia, E-46071 Valencia, Spain TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 Canada Sedecal Molecular Imaging, E-28110 Algete (Madrid), Spain LPSC, IN2P3-CNRS/Université Grenoble Alpes, Grenoble Cedex F-38026, France Department of Chemistry, University of Maryland, Maryland 20742, USA (Dated: July 8, 2020)The structure of the doubly magic Sn has been investigated at the ISOLDE facility at CERN,populated both by the β − decay of In and β − -delayed neutron emission of In. The levelscheme of
Sn is greatly expanded with the addition of 68 γ -transitions and 17 levels observedfor the first time in the β decay. The information on the excited structure is completed by new γ -transitions and states populated in the β -n decay of In. Improved delayed neutron emissionprobabilities are obtained both for
In and
In. Level lifetimes are measured via the AdvancedTime-Delayed βγγ (t) fast-timing method. An interpretation of the level structure is given basedon the experimental findings and the particle-hole configurations arising from core excitations bothfrom the N = 82 and Z = 50 shells, leading to positive and negative parity particle-hole multiplets.The experimental information provides new data to challenge the theoretical description of Sn. a r X i v : . [ nu c l - e x ] J u l I. INTRODUCTION
The
Sn nucleus is one of the bastions of our under-standing of nuclear structure in the framework of the nu-clear shell model. With 50 protons and 82 neutrons it isone of the most exotic doubly-magic nuclei within reachof current experimental facilities. One of the signaturesof its doubly-magic nature is the high lying first-excitedstate at 4041.6 keV [1–3]. This value, once scaled by afactor of A / to account for the size of the nucleus, islarge in comparison to other doubly magic nuclei suchas Pb and O, which points to a strong double shellclosure. The
Sn doubly magic structure is also man-ifested by the almost pure single-particle nature of thelevels in
Sn. This nature was probed by a trans-fer reaction in inverse kinematics [4] yielding very largespectroscopic factors.The region of the nuclear chart around
Sn playsan important role in the astrophysical rapid neutron-capture process (r-process), which impacts elementalabundances in the solar system. Recently, the identi-fication of the nucleosynthesis site for neutron-rich nu-clei around N = 82 has been reported [5, 6] associatedto a "kilonova" [7], observed by multimessenger astron-omy. The robustness of the N = 82 neutron shell is oneof the important parameters when modeling r-processnucleosynthesis and describing light curves arising fromcompact object mergers. The shell structure in this re-gion is also necessary to understand the role of fission inthe r-process [8].From the point of view on nuclear structure the nu-clei with a valence particle or hole around Sn are rel-evant for investigating single-particle states and tran-sition probabilities. They provide observables that arethe main ingredients in state-of-the-art large scale shell-model calculations to understand the nuclear structurein the region. The single-particle states in the regionare represented in Figure 1 following the procedure de-scribed in [9], and employing binding energies from [10]and the excitation spectra from
Sn,
Sn,
Sb and
In. In particular, the neutron single-particle orbitsabove the N = 82 shell gap have been taken from low-lying states in Sn: the νf / ground state and the νp / , νp / , νh / and νf / states at 854, 1367, 1561and 2005 keV excitation energy [4, 11–16]. The νi / single-particle state has not been experimentally iden-tified to date [17]. These single particle states are notonly relevant for Sn but also for neutron-rich nucleiin its vicinity.Experimental data on
Sn is essential for the shell- ∗ [email protected] † [email protected] ‡ Present address: University of Jyväskylä, Department ofPhysics, P.O. Box 35, FI-40014 Jyväskylä, Finland § Present address: CERN, CH-1211 Geneva 23, Switzerland ¶ Deceased. -7.5-5.0-2.50.02.55.07.5 π ν -7.5-5.0-2.50.02.55.07.5 π ν E s p - Δ E C - λ F [ M e V ] π d π d π g π s π h -7.23-8.70-9.67?-6.87 π g π p π p π f -15.81-16.11-17.10? ν d ν h ν s ν d ν g -7.35-7.42-7.68-9.01-9.79 ν i ν f ν h ν p ν p ν f ?-0.39-0.84-1.04-1.54-2.40 FIG. 1. Experimental single-particle and single-hole ener-gies for neutrons ( ν ) and protons ( π ) in the doubly-magicnucleus Sn. Following [9] the energy origin is set in thecenter of the shell gap ( λ F ) in order to remove Coulomb en-ergy differences ∆ E C . Binding energies are taken from [10].The absolute single-particle energies are given in MeV. model description of the exotic nuclear region around N = 82 and to provide insight into particle-hole cou-plings for both protons and neutrons. Most of the ex-cited levels in Sn correspond to particle-hole (p-h)configurations where a proton or a neutron is promotedacross the closed shell. The coupling of single particleand single hole configurations (Figure 1) leads to mul-tiplets of excited states with an expected low admix-ture of other configurations. The particle-hole residualinteraction makes the level energies within a multipletnon-degenerate. The identification of these multipletsprovides information on the nuclear two-body matrixelements to first order. Experimentally measured tran-sition rates between states within a multiplet, and alsobetween states of different multiplets, give importantknowledge of the underlying single particle structure.The investigation of the doubly-magic
Sn is thus es-sential for theoretical models aiming at the understand-ing neutron-rich nuclei in the region. The developmentof these models is furthermore needed for the descriptionof r-process nuclei that are at present experimentally outof reach.The excited structure of
Sn has been experimen-tally investigated since the 1970s. Beta decay ex-periments were carried out at OSIRIS [1, 18–20] andISOLDE [2, 21], as well as fission experiments performedat the JOSEF facility [22, 23] and the Argonne NationalLaboratory [24].The most complete β -decay experiment was per-formed by Fogelberg et al. [18–20] at the OSIRIS fa-cility in the 1990s, where the level scheme of Sn wasexpanded to 21 excited levels, including negative andpositive parity states up to the neutron separation en-ergy. Proton particle-hole states were identified for thefirst time, and the 4352-keV J π = 3 − state was con-firmed to have an octupole vibrational character. Life-time measurements of the excited states down to the psrange were performed, and spin and parities assignmentswere made for the levels below 5 MeV.Despite all the detailed studies on Sn attainedthrough the β -decay and fission experiments, manyof the expected particle-hole multiplet states remainwithout experimental identification. Beta decay isthe ideal tool to investigate the excited structure of Sn, both directly from
In (7 − ) g.s. and viabeta-delayed neutron emission from the In (9/2 + )g.s. and the (1/2 − ) 330-keV beta-decaying isomer.This is due to the large energy window availablefor the decay, of Q β ( In) = 14140(60) keV and Q βn ( In) = 11010(200) keV (from systematics) [10],respectively, and due to the high spin of the parent nu-clei that makes it possible to feed many states in
Sn.In this work we focus on the investigation of the ex-cited structure of
Sn populated in β and β -n decay.Taking advantage of the enhanced yield and selectivityachieved at the ISOLDE facility at CERN some of themissing particle-hole multiplet states have been identi-fied. In addition, lifetimes of excited states in Snhave been measured using fast-timing techniques. Theresults from the β decay study of the In isomers havebeen partially covered in [16]. Details on the experi-mental method used in the present work are providedin Section II. The experimental results are presented inSection III and discussed in Section IV. Conclusions aredrawn in Section V.
II. EXPERIMENTAL DETAILS
The experiment was carried out at the ISOLDE fa-cility at CERN. It was performed in two separate data-taking campaigns in 2016 and 2018, where the excitedstructure in
Sn was populated in the β decay of Inand in the β -n decay of the In (9/2 + ) and (1/2 − )states. The In and
In isotopes were produced bythe bombardment of a UC x target equipped with a neu-tron converter by 1.4-GeV protons from the CERN PS-Booster (PSB). The indium ions thermally diffused outof the target and were ionized using the ISOLDE reso-nance ionization laser ion source (RILIS) [25]. The useof RILIS granted isomeric selectivity, by taking advan-tage of the difference in the hyperfine splitting of theisomer and ground state. More details on the isomerselection can be found in [26]. Following the ionization,indium ions were extracted and accelerated by a 40-kVpotential difference, mass analyzed [27] and implantedon an aluminized mylar tape located at the center of ourdetector setup at the ISOLDE Decay Station (IDS) [28].The ions reached the IDS following the time structure ofthe PSB supercycle whereby proton pulses were groupedinto sets of 34 or 35 pulses, out of which around half ofthem are delivered to the ISOLDE target-unit separatedin time by multiples of 1.2 s. The beam was collectedon the tape for a fixed time varying from 200 to 400ms after the impact of each proton pulse. Once every supercycle the tape was moved in order to reduce theactivity of long-lived daughter nuclides. The averagebeam intensity at the experimental station was of theorder of 4 · and 2 · ions per second for In and
In, respectively. Data were collected for 20 hours foreach mass.The IDS setup consists of a set of detectors aimedat measuring the β and γ radiation emitted after the β -decay of the implanted isotopes. They are arrangedin close geometry surrounding the implantation point.The setup can be divided in two branches. The firstbranch is composed of four clover-type HPGe detec-tors for γ -ray spectroscopy, with a combined full-energypeak efficiency of 4 % at 1173 keV. The second branchis aimed at lifetime measurement of excited states usingthe Advanced Time-Delayed βγγ ( t ) (fast timing) tech-nique [29–31]. It consists of two LaBr (Ce) crystals withthe shape of truncated cones [32] coupled to fast photo-multiplier tubes (PMTs) [33], with 1 % of total efficiencyat 1 MeV each, and an ultrafast 3-mm thick NE111Aplastic scintillator used as a β detector, with a ∼ % efficiency. The energy and fast-timing signals are takenfrom the PMT dynode and anode outputs, respectively.The timing signals are processed by analog constantfraction discriminators and introduced in pairs in time-to-amplitude converter (TAC) modules that provide thetime difference between them. In this experiment, timedifferences between the β and the two LaBr (Ce) de-tectors as well as between the two LaBr (Ce) detectorswere recorded. More details on the setup are providedin [31, 34].All the signals from both branches were read and dig-itized by the Nutaq digital data acquisition system [35].Logic signals, such as the time of arrival of the protonpulse on target and the tape movement, were also digi-tized. Data were collected in a triggerless mode. Eventswere built during the offline analysis where they weresorted in coincidence windows, and correlated with theproton arrival time. At this stage, the energy calibra-tion for each detector was applied, as well as add-backcorrections for the clover detectors. Due to the large en-ergy of the Sn γ rays, a precise efficiency calibration isneeded in a wide energy range. Therefore, Eu,
Cs,
Ba and
Ba radioactive sources were used to buildthe energy calibration. The calibration was extended upto 7.6 MeV by including high-energy γ rays originatingfrom the capture of thermal neutrons produced at theISOLDE target station, mainly in iron (IDS frame) andgermanium (HPGe detectors).For the timing measurements, the calibration of theLaBr (Ce) time response for full-energy peaks (FEP) asa function of energy, the FEP walk curve, is required. Itwas built for each LaBr (Ce) detector using βγ (t) and γγ (t) coincidences with Ba/
La and Eu γ -raysources, Cs and Rb on-line sources and by includ-ing several transitions in
Sb as an internal calibrationsource. In this way, we obtained FEP time responsecurves for each LaBr (Ce) detector in the energy range100 keV to 2.6 MeV, with an average one-sigma errorof 3 ps. A similar procedure was implemented to buildthe Compton walk curve in order to take care of thecorrections due to Compton events. III. EXPERIMENTAL RESULTS
The excited structure of
Sn was populated throughthe β decay of In (7 − ), and from the β -n decay of the In (9/2 + ) g.s. and the (1/2 − ) isomer. The largedifferences in the spin and parity of the parent nucleiresult in distinct feeding patterns for each decay, whichprovides information on the spin and parity of the levelsfed.Owing to the large difference in the β -decay half-livesof In and
Sn, of 200(2) ms and 39.7(8) s [3], respec-tively, the time distribution relative to the arrival of theproton on target makes it possible to identify whether a γ ray has been emitted during the β decay of In orfrom the daughters. A similar situation occurs for the β decay of In. Apart from the time distribution, theidentification of the γ -rays belonging to Sn is basedon γ - γ coincidences with previously-known transitions. A. Beta decay of In The Q β in In is 14140(60) keV, while the neutronseparation energy in
Sn is 7353(4) keV [10]. Hence,the feeding of excited states up to ≈ γ -rays may be observed.The excited structure populated in the In β decay isvery complex. The high spin of the parent, (7 − ) [36],favors the population of high spin (6-8) excited statesin the energy range from 4 to 7 MeV. Those levels canonly de-excite to the ground state by means of γ -raycascades of 3 or more transitions. As discussed before,due to the doubly magic nature of Sn, the first excitedstate appears at a very high energy, 4041 keV.Therefore,it is not expected to find new levels in this decay thatcan de-excite directly to the g.s. with an energy below4 MeV.The energy spectra recorded by the HPGe clover de-tectors, setting a time window of 30-530 ms after protonimpact are depicted in Figure 2. This condition was im-posed in order to reduce the contribution of the differ-ent contaminants. The contribution of neutron-inducedbackground coming from the target is suppressed by re-moving the first 30 ms of the time window. An upperlimit of the time window at 530 ms was chosen to re-duce the contribution of the long-lived daughters, whilekeeping most of the statistics.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 C oun t s / k e V Energy(keV)5.0·10 D E SE D E SE FIG. 2. Singles γ -ray energy spectrum recorded by theHPGe detectors following the In decay. This histogramwas built using the events measured during the 30-530 mstime interval after proton pulse. The strongest peaks ob-served in the spectra are labeled with their energies in keV.The SE and DE labels indicates single escape and doubleescape peaks. The inset zooms in the 2400-4450 keV region.
1. Half-life of
In ground state
The half-life of
In was measured by fitting the timedistribution of the 10 strongest γ rays (labeled in Fig. 2except for the 4416 keV). Since the activity at the exper-imental station is pulsed by the proton beam structureand the release from the target, the time distributionis fitted to an exponential decay function with a con-stant background after the end of the implantation. Thebackground contribution was estimated by analyzing thetime range from 2400 to 3600 ms after proton impact.Due to the high count rates, dead time effects are sizable,
0 500 1000 1500 2000 C oun t s / m s Time since the last pp(ms)
375 keV T =203.1(5) ms 4042 keV T =200.5(9) ms 2268 keV T =201.6(18) ms4352 keV T =200.5(16) msfit
FIG. 3. Decay curves of the 375-, 4042-, 2268- and 4352-keV γ -rays recorded in singles in the HPGe detectors. Theregion considered for the fit goes from 700 ms, marked witha dark-blue dashed line, up to 2400 ms. This region has beenadjusted in order to minimize dead-time effects. mainly during implantation, but also at the beginning ofthe decay. In each HPGe crystal an average count rateof 3 · counts per seconds (cps) was observed, how-ever, during the implantation time the count rate couldrise up to 1.5 · cps. To account for this effect the be-ginning of the fit range was shifted by a few half-livestowards higher times and a χ fit test was performed toverify that the expected exponential decay behavior wasrecovered. The lifetime measurement was performed in-dependently for each of the two data sets of In decaymeasured in the two experimental campaigns. The anal-ysis made use of single events recorded in the HPGe de-tectors. The contribution of the Compton backgroundunder full-energy peaks was subtracted. This investi-gation furnishes 20 independent values for the
In, 10from each data set, which are all statistically compatiblewith each other. The final value of the
In half-life wasadopted as the weighted average of these measurementsyielding T / =202.2(2) ms. The statistical uncertaintyof the weighted average is calculated and increased bymultiplying by the χ obtained. No systematic error isincluded. This half-lifes is in agreement with, but moreprecise than, the value reported in the latest evaluation,T / =200(2) ms [3]. In Figure 3 the decay curves for 4of the γ rays under consideration, from the 2016 dataset, are shown.
2. Identification of new γ -rays in Sn The analysis of γ - γ coincidences was done using thefull statistics independently for the two data sets fromeach campaign. The assignments were cross-checked byrequiring coincidences with the β detector and/or a timerange since proton impact from 30 to 530 ms. Figure4 shows the γ rays in coincidence with the 6 + → + Sn. The spectrum illustratesthe amount of statistics and the quality of the γ -raycoincidence spectra.The level scheme of Sn has been greatly expandedwith the addition of 57 new γ transitions and 11 newlevels, observed following the direct In β decay. Thelevel scheme is shown in Figure 5. A list of the γ rays isprovided in Table I.The states located at 5766 and 5446 keV were pre-viously observed in the β -delayed neutron emission of In [16]. The assignment is confirmed in this workwith the uncovering of new cascades in the
In decayinvolving both levels.A new level is found at 5754 keV defined by the 1457-1038 keV γ cascade. This sequence had already beenobserved by Fogelberg et al. [18], however the order ofthe γ rays they proposed was inverted, giving rise toan excited level at 6173 keV with suggested (6 + ) spin-parity. This level has been ruled out in our analysisdue to the finding of another γ -ray that de-excites the5754-keV state, confirmed by γ - γ coincidences.The 5280-keV level was already reported in Cm fis-sion studies [24], and tentatively identified as the (9 + )state that arises from the particle-hole νf / h − / con-figuration. That level is confirmed in this work by theobservation of the de-exciting 431.8-keV transition in de- layed coincidence with the 132-keV γ -ray that de-excitesthe 8 + β feeding to states in Sn was determinedfrom the balance between feeding and de-exciting γ raysto each level. The intensities of the γ rays were ob-tained from the measured HPGe singles with neithercoincidence nor condition on the time from the impactof protons on target. Theoretical internal conversion co-efficients have been taken from [37] if required. The β feeding to the states should be understood as upper lim-its and the log f t values as lower limits due to possiblemissing transitions. β -delayed neutron branches in In The β -delayed one neutron emission of In has beenconfirmed by the observation of γ rays belonging to theexcited structure of Sn. Two transitions have beenidentified in this decay, specifically, the 2435.0(3) keVand 4273.6(5) keV with an absolute intensity of 0.11(1) % and 0.04(1) % respectively. The P n value has been ob-tained from the analysis of the γ -ray intensities of the β and β -n branches, following the β decay of the Sn and
Sn daughters. For the Sn → Sb decay branch,the intensities of the 5 most intense γ rays were con-sidered. The absolute intensities for those transitionswere adopted from [38]. Previous measurements of the Sn → Sb decay [39] were not able to disentanglethe decay of the
In isomers. Besides, in our analy-sis we observed that the intensity of the γ rays emittedin this decay mainly originate from the population oflevels with high spin (11/2, 13/2, 15/2). This indicatesthat the In isotopes that decay by β -n mostly feed the11/2 − isomer in Sn directly, which is strongly favoredagainst the 3/2 + g.s. due to the angular momentum dif-ference.The total intensity from Sn → Sb decay was cal-culated from the analysis of the γ rays from Sb ob-served in this data set. An absolute intensity of 69(7) % has been estimated for the most intense transition, of1226 keV. This value was obtained by making two as-sumptions: firstly that In β -n decay mainly populatesthe (11/2 − ) isomer, which is consistent with our obser-vations, and secondly that no direct intensity was lostdue to direct population of Sn to the
Sb g.s. Thisis to be expected in order to be consistent with the firstassumption due to the large spin difference (11/2 − → + transition). The 7 % uncertainty in the value takesinto account these assumptions.Finally, the number of decays calculated for each tinisotope was corrected to account for the movement ofthe tape at the end of each super-cycle, considering thedifferent half-lives of each isotope and for dead time ef-fects. From this analysis a P n =12(2) % value was foundfor the In β -n decay, which is notably higher thanthe 6.8(14) % in [40] but in good agreement with the10.7(33) % from [41].
0 500 1000 1500 2000 2500 3000 3500 4000 4500 D E SE D E SE * * * * * * * * * * * * C oun t s / k e V Energy(keV)
FIG. 4. Compton-subtracted γ - γ energy spectrum gated on the 6 + → + γ transition in Sn. The previously-known γ rays are labeled with their energies in black. New transitions identified in this work are labeled in red with an asterisk.The negative peaks in the spectrum arise from background subtraction, due to Compton scattering between two HPGe cloverdetectors.TABLE I: List of γ rays observed in the β decay of Into
Sn, including transition energies and intensities. Theinitial and final levels for each connecting transition are alsogiven.E i (keV) J Π i E f (keV) J Π f E γ (keV) I aγ + + − + + + + + − + + − − + + + + + + b + + + b − − + + − − ) 4830.5(4) 4 − b − b + b + ) 4848.3(5) 8 + b − ) 4351.6(3) 3 − − − − ) 437.2(4) 0.23(2)5398.9(5) (6 + ) 4715.9(4) 6 + + ) 4416.6(3) 4 + + ) 4848.3(5) 8 + + ) 4715.9(4) 6 + Continued on next table
TABLE I: (Continued)E i (keV) J Π i E f (keV) J Π f E γ (keV) I aγ + + + ) 229.8(3) 0.65(5)5478.4(6) (8 + ) 150.3(3) 0.29(3) b + ) 4416.6(3) 4 + + b + b + ) 4715.9(4) 6 + + ) 354.3(3) 0.58(4)5766.3(3) (5 + ) 4416.6(3) 4 + + + − + ) 4715.9(4) 6 + b + + + ) 609.4(4) 0.37(5)6235.5(3) (7 + ) 4715.9(4) 6 + b + + ) 836.3(4) 0.64(6)5753.9(4) (6 + ) 481.8(3) 0.53(6)6296.6(5) (5 − ) 4830.5(4) 4 − b + ) 4715.9(4) 6 + + + ) 987.7(3) 0.14(4) b − ) 4830.5(4) 4 − − + ) 5398.9(5) (6 + ) 1093.9(3) 0.73(5)6526.2(5) (6-8 + ) 5628.9(3) (7 + ) 897.3(3) 0.32(4)6598.5(5) (6 − ) 4942.4(4) 5 − + ) 1199.6(5) 0.036(10) b + ) 4715.9(4) 6 + + Continued on next table
TABLE I: (Continued)E i (keV) J Π i E f (keV) J Π f E γ (keV) I aγ + + ) 1231.9(4) 0.27(3) b − ) 4918.8(5) 7 + − b + ) 4416.6(3) 4 + + b + ) 4918.8(5) 7 + + ) 1496.8(3) 0.37(3)6997.1(3) (7 + ) 4715.9(4) 6 + + + ) 1519.2(5) 0.14(2) b + ) 1368.2(5) 0.43(5) b − − + + − − ) 1823.2(3) 1.41(10)5398.9(5) (6 + ) 1812.6(6) 0.12(1)5628.9(3) (7 + ) 1582.1(3) 1.16(9)5697.7(3) (5 + ) 1513.8(3) 0.34(3)5753.9(4) (6 + ) 1456.9(3) 1.44(11)5766.3(3) (5 + ) 1445.1(3) 0.49(4)6008.2(4) (7 + ) 1202.4(6) 0.024(7) b + ) 975.6(3) 1.4(2) b − ) 913.9(4) 0.121(14) b + ) 777.4(3) 0.15(2) b − ) 733.5(3) 0.38(3)6598.5(5) (6 − ) 612.6(3) 0.42(3)6709.7(4) (6 − ) 501.8(4) 1.7(4)6630.6(4) (6 + ) 580.8(5) 0.09(2) b − + + − + ) 1845.3(3) 0.46(3)5478.4(6) (8 + ) 1766.2(3) 3.2(3) b + ) 1489.4(4) 0.084(11)6235.5(3) (7 + ) 1008.1(5) 0.11(2)6492.8(3) (6,7 + ) 751.3(3) 0.124(12) a Relative γ intensities normalized to 100 units for the4 + −→ + b Intensity from γ - γ coincidences. Given the two-neutron separation energy in the
SnS n ( Sn)=12557.0(27) keV [10], there is a 1583 keVenergy window, within Q β ( In), that makes the de-cay via a β -delayed two neutron branch possible. Wehave searched for γ rays belonging to the A = 130 masschain. Nevertheless, no evidence has been found thatwould point to the existence of a β -2n decay branch in In. This is consistent with expectations, since theonly levels in
Sn that could be populated are the 0 + g.s. and 2 + at 1221 keV [42]. Assuming a (7 − ) spin-parity assignment for the In g.s. [36], this decay willbe highly suppressed. B. β -delayed neutron decay of In The large Q β =13.4(2) MeV value along with the lowneutron separation energy in Sn, S n =2.399(3) MeV[10], favor the In decay via β -delayed neutron emis-sion to Sn. This gives rise to the large P n values forboth In β -decaying isomers [16]. The lower spin of the In (9/2 + ) ground state and (1/2 − ) isomer, in compar-ison with In (7 − ), is expected to favor the populationof low spin p-h excited states that are not fed in the β decay of In due to the large spin of the parent (7 − ).The population of Sn excited levels in the β decay of In was already reported in [16], where the β decay of In was investigated focusing on the excited structureof
Sn. In the present work, we concentrate on resultsof the β -n decay of In to
Sn, discuss excited statesin
Sn and report new transitions following the β -ndecay branch of In.
1. Feeding of excited states in Sn Gamma rays emitted after the β decay of In can beclearly distinguished from the background by their timedistribution following the impact of protons on target.Nevertheless, the decay curve does not allow the sepa-ration of the transitions that belong to
Sn from thoseof
Sn, neither from the background induced by β -delayed neutrons from In β -n decay.The identification of new γ rays that belong to Snis based on γ - γ coincidences. Gamma rays with ener-gies below 4 MeV are always a part of a cascade sincethey cannot directly feed the g.s. The analysis allows toidentify several levels and γ rays in Sn that are notobserved in the
In decay, see Figure 6. Among themwe confirm the states at 4965, 5131, 5431 and 5790 keV.
479 597 * * * * C oun t s / k e V Energy(keV)
FIG. 6. γ - γ spectrum observed in the β decay of In,gated on the 4352-keV transition in
Sn. The contributionfrom Compton events beneath the 4352-keV peak has beensubtracted. Newly-observed γ transitions are labeled in redwith an asterisk. FIG. 5. Level scheme of
Sn observed following the β decay of In. Note that the energy gap from the g.s. to the 2 +1 state is not to scale. The positive-parity states are shown on the left-hand side and the negative parity ones on the right-handside. The high-lying 7 − and 6 − states feed states of both parities. Levels and transitions previously observed in this decay arecolored in black, while those observed for the first time are highlighted in red. Levels previously-known from Cm fission orfrom In β -n decay and observed here in the β -decay of In are colored in blue.
TABLE II: List of observed states in
Sn following the β -n decay of the In (9/2 + ) g.s. (>95% pure), labeled g In, and the beam with enhanced content of the (1/2 − )isomeric state, with a contamination of ∼
30% of g In, la-beled m In.E i J Π i E f J Π f E γ I crel I drel (keV) (keV) (keV) g In m In4041.6(3) 2 + + − + + + + + − b b + + − − + a + + a + + + a <1.6 a + + + b b − − a b + + b b − b − )4830.5(4) 4 − − a a + + )4416.6(3) 4 + a − a + − )4351.6(3) 3 − + − )4351.6(3) 3 − − b b − b b − )437.2(4) 0.7(2) b b + )4715.9(4) 6 + + − a + a a + )4416.6(3) 4 + + )4848.3(5) 8 + + )4715.9(4) 6 + a + b <0.3 b + b <0.2 b + )229.8(3) 0.10(2) b <0.05 b + )150.3(3) 0.047(8) b <0.03 b + )4416.6(3) 4 + b + a + b b + )4715.9(4) 6 + a a + )354.3(3) 0.6(2) b b + )4416.6(3) 4 + a + a + − b a + )4416.6(3) 4 + a − Continued on next table
TABLE II: (Continued)E i J Π i E f J Π f E γ I crel I drel (keV) (keV) (keV) g In m In6296.6(5) (5 − )4830.5(4) 4 − a <0.5 a − )4830.5(4) 4 − a <0.5 a − b <0.1 ba Intensity obtained from γ - γ coincidences. b Not observed in this decay, intensity calculated from
In decay data. c Relative γ intensities normalized to 100 units for the4042-keV transition.For intensity per 100 decays multiply by 0.049(5). d Relative γ intensities normalized to 100 units for the4042-keV transition.For intensity per 100 decays multiply by 0.043(5). The low spin of the states to which they can de-excitesuggests a small spin value (2-4) for these levels, whichmakes them good candidates for the remaining particle-hole states with low spin expected in this energy range.In Figure 7 the level-scheme of
Sn in the β -n decay of In is depicted. The direct feeding to each level (I β − n )is measured by analyzing the γ -ray intensities calculatedseparately for each isomer. The indium beams for eachisomer were separated taking advantage of the isomer se-lectivity provided by RILIS. However the separation wasnot complete, and the m In beam contained a contri-bution of ∼
30% of g In [16]. The amount of m In inthe g In beam is below 5%. The total feeding has beencalculated using the intensities of the γ -rays emitted bythe daughters. The observed states in Sn followingthe β -n decay of the In (9/2 + ) g.s. and (1/2 − ) iso-meric state are listed in Table II.
2. High energy γ -rays Another interesting feature observed in the β -decayof In is the presence of several γ rays at very highenergies, above 5 MeV, with a time behavior compatiblewith the decay of g,m In. The existence of those γ rays was already reported in [16], where the 6088-keVtransition was assigned to Sn. Some other γ -rays werediscussed in [16] as being emitted in the decay of In,however the lack of γ - γ coincidences does not allow toidentify the daughter tin isotopes they belong to.The high energy γ lines observed in the g,m In de-cays are shown in Figure 8. As it can be seen, the ob-served peaks differ notably depending on the selected β -decaying indium state. In the decay of the g In(9/2 + ) g.s. there are two predominant γ -rays, the one at6088 keV mentioned above, and another one at 6019 keV.Although the 6019-keV peak has the same energy as atransition in Fe produced by the neutron backgroundas discussed in [16] its intensity is only a small fractionof the total γ -ray intensity from the excited 7647-keVlevel in Fe, while the other, more intense transitions,are not observed. Therefore the 6019-keV transition is0
FIG. 7. Level scheme of
Sn observed following the β -n decay of the In (9/2 + ) ground state and (1/2 − ) isomer. Notethat the energy gap from the g.s. to the 2 +1 state is not to scale. The positive parity states on the left-hand side and thenegative parity states to the right. The isomer observed feeding to levels in Sn is provided separately for each decay. Notecontributions coming from beam impurity cannot be excluded in the (1/2 − ) decay. Levels and transitions observed for the firsttime in the β -decay of In are highlighted in red. β -decay of In, andpredominantly from the (9/2 + ) g.s. ? 6463 ? C oun t s / k e V Energy(keV)
In (1/2 - ) decay 0 10 20 30 40 50 SE SE D E C oun t s / k e V In (9/2 + ) decay FIG. 8. Beta-gated γ -ray spectra from the β decay of Inisomers highlighting the energy range above 5 MeV. Only theevents recorded in the time window from 10 to 600 ms sincethe arrival of the proton pulse are used.
In the decay of the m In (1/2 − ), the 6088- and 6019-keV transitions are suppressed, but several other peaks,which are absent in the decay of the g In, can be iden-tified. Those peaks appear at the energies of 5440, 5712,5770, 5952, and 6067 keV. Two more tentative peaks, atthe detection limit of the HPGe detectors, are seen at6220 and 6463 keV. Some of these γ lines may be com-patible with escape peaks from other γ rays (for instancesingle and double escape peaks from 6463 keV), but itis not possible to make a consistent identification forall of the energies. It is interesting to observe transi-tions having this energy from the decay of the (1/2 − )isomer, as there are unidentified members of particle-hole multiplets in Sn, such as ν p / d − / , π g / g − / and ν p / s − / , that can give rise to low spin levels. Itis very unlikely to populate them in the decay of Inwith (7 − ). However, the feeding of such levels would bestrongly favored in the β -n decay of the (1/2 − ) state in m In. All of this points towards these transitions likelyoriginating from the de-excitation of such p-h multipletstates.It is worth mentioning that a 5131-keV peak can beseen in both the g In and m In decays. This γ rayhas been firmly identified to belong to Sn since itsenergy perfectly matches the de-excitation of the new5131-keV level proposed in this work. In addition, theexistence of a transition to the 0 + g.s. supports thetentative assignment of this level to the 2 − state of the ν f / d − / multiplet.For the sake of completeness, the γ -rays observed inthe In decay that have not been assigned to any decaybranch are listed in Table III.
TABLE III. Gamma rays observed in the
In decay thatcould not been assigned to any specific decay branch. Inten-sities are given relative to the 4042-keV γ -ray intensity. Thelabel g In refers to the
In (9/2 + ) g.s., with an estimatedpurity above 95%, while the label m In is used for the beamwith enhanced content of the (1/2 − ) isomeric state, with acontamination of ∼
30% of g In.E γ I arel I brel (keV) g In (9/2 + ) m In (1/2 − )1116(2) 2.5(4) 4.6(8)1529.7(7) - 2.6(7)1649.9(4) - 7(1)4110.8(3) 8(1) 8(2)5439.6(4) d - 4(2)5711.6(9) e - 3.7(12) c c d - 6(2) c c c c ca For I abs multiply by 0.049(5). b For I abs multiply by 0.043(5). c Intensity obtained from β -gated spectrum. d Energy compatible with the escape peaks from thetentative 6463-keV γ -ray. e Energy compatible with the single escape peak fromthe tentative 6220-keV γ -ray. β -delayed neutron emission from In We have used the same procedure described above for
In to determine the β -delayed neutron emission prob-abilities from the In (9/2 + ) ground state and (1/2 − )isomer. The most intense γ rays have been considered inthe analysis. For Sn → Sb decay, the absolute in-tensity of 12(2) % for the 962-keV transition was adoptedfrom [43], while for the Sn → Sb an absolute inten-sity of 48.8(12) % for the 340-keV transition was takenfrom [38]. The relative decay activity of the tin daughternuclei was corrected for the tape movement. In particu-lar, the supercycle structure of the proton beam has tobe considered for the evaluation of the unobserved ac-tivity. Our analysis yields P n =90(3) % for the decay ofthe In 9/2 + g.s., and P n =93(3) % for the decay of the(1/2 − ) isomer. The results differ from those previouslyreported by us in [16], which were obtained from thesame dataset but where the supercycle structure wasnot fully taken into account. The re-evaluated resultsare in agreement with the P n =85(10) % value in [11]. C. Lifetime measurements
Lifetimes of excited levels in
Sn have been investi-gated by means of the Advanced Time-Delayed βγγ (t)fast-timing method [29–31]. The lifetimes were mainlyobtained from the time differences between the fast β (Ce) detectors. A coincidence condition onthe HPGe detectors is applied. The HPGe detectors donot participate in the timing information, but are es-sential in this complex level scheme due to their energyresolution to obtain the required γ -ray selectivity.The use of two different LaBr (Ce) detectors gives usthe possibility to obtain two independent measurementsfor the same lifetime, one per β -LaBr (Ce) combina-tion. In addition, γγ (t) time differences between thetwo LaBr (Ce) detectors are used when possible. To il-lustrate the analysis and the results here obtained, wediscuss the half-life of the 4416-keV 4 + and 4831-keV 4 − levels, depicted in Figure 9 and Figure 10 respectively.To measure the 4416-keV 4 + level half-life using βγγ (t) events a time distribution was generated by se-lecting the 526- and 375-keV transitions in the HPGeand LaBr (Ce) detectors respectively. Corrections wereincluded to account for the contribution of Comptonbackground. The 4416-keV 4 + state lifetime is free fromthe influence of other long-lives states and shows up asan exponential tail which can be fitted to measure thehalf-life. The analysis was done separately for each ofthe two LaBr (Ce) as well as for each of the two avail-able data sets. In the case of γγ (t) events, the 299-keVand 375-keV transitions are selected. Here no extra gatein the HPGe energies is needed thanks to the large peakto background ratio. The lifetime is measured from timedifference distributions with the direct and reversed en-ergy selection on the LaBr (Ce) detectors, giving twoindependent measurements for each of the two data sets.Using the two experimental data sets, our analysis yields8 independent measurements for the half life, 4 from βγ (t) events and another 4 from γγ (t), all of them con-sistent with each other. The final value is obtained fromthe weighted average from these measurements, yieldinga final value of 3.99(2) ns, which is in good agreementwith the 3.95(13) ns reported by Fogelberg et al. [19].Shorter lifetimes were measured using the centroidshift method. In Figure 10, the analysis to extract thelifetime of the 4830-keV 4 − level is is illustrated for βγγ (t) events for one of the LaBr (Ce) detectors. Inthis case the mean life is derived from the centroid shiftof the time distribution with respect to a prompt cas-cade, corrected by the FEP time response calibration.The analysis has been repeated for both LaBr (Ce)detectors and both data sets, and also using the γγ (t)method, yielding six independent values for the 4830-keV 4 − level mean-life. The weighted average ofT / =27(2) ps is adopted as the final result. The half-life is in very good agreement with the 26(5) ps reportedby Fogelberg et al. [19]. It should be noted that the un-certainties in [18] are too small to be compatible with afast-timing measurement; the values within brackets in[19] are actually the errors in ps [44], so the uncertaintiesfrom [19] are adopted.The lifetime of the 4848-keV 8 + level is beyond thefast-timing time range, but it can be investigated us-ing βγ (t) coincidences between the plastic scintillator
10 20 30 40 50LaBr =4.05(5)nsLaBr =4.06(5)ns C oun t s / T A C C hanne l s Time(ns) LaBr FIG. 9. Time delay spectra between the β and each ofthe two LaBr (Ce) detectors for βγγ (t) events. These dis-tribution are built by selecting the events when the 526-keVtransition in the HPGe detectors and the 375-keV transitionin the LaBr (Ce) detector. The lifetime is obtained by a χ fit of the whole time distribution to a exponential decay con-voluted with a Gaussian function plus a constant backgroundto account for the random background. -500 0 500 1000 1500 2000 2500 C oun t s Time (ps) Δ C=271(5) ps τ =44(9) ps C en t r o i d ( p s ) Energy(keV)
FEP walk Δ FEP=227(8) ps
FIG. 10. Time delayed βγγ (t) spectra used to measure thelifetime of the 4830-keV 4 − excited level. The blue spectradepicts the prompt time distribution used as reference, whichis obtained by gating on the 479 and 2380-keV transitions inthe HPGe and the LaBr (Ce) detectors respectively. The redone correspond to events obtained after reversing the gates,the 2380 keV one applied to the HPGe and the 479 keV oneto the LaBr (Ce). The shift measured between the centroidposition of each distribution ∆ C is caused by the lifetime ofthe level, but also due the time walk ∆ FEP between bothenergies. The lifetime τ is obtained by subtracting to thecentroid shift the contribution due to the FEP time response. and the HPGe detectors. Three β -HPGe(t) time differ-ences spectra were obtained by selecting the 132-, 299-and 375-keV γ rays, respectively. The half-life was mea-sured by fitting the delayed slope of the spectra in along time range of ∼ µ s. The contribution of ran-dom coincidences to the time spectra in this range hadto be carefully taken into account. Our analysis yieldsT / =2.108(14) µ s for the 4848-keV level in agreementwith the value of 2.080(17) µ s reported in the latest eval-3uation [3].The analysis procedures were extended to the otherobserved levels, provided sufficient statistics were avail-able. The data sets from the two experimental runs havebeen combined for the analysis. The lifetimes of 7 differ-ent states were measured. In addition, upper limits foradditional 7 levels were obtained. The results obtainedin this work for level lifetimes in Sn are compiled inTables IV and compared to the previous β -decay studies.The overall agreement is quite good, with the excep-tion of the 4919-keV 7 + level whose half-life is 104(4) ps,much higher than the value of 62(7) ps reported earlier[18], which was measured using BaF scintillator detec- tors. Since this level can only be measured by analyzingthe time distribution of the 203-keV γ -ray, where thecontribution of Compton background is very important,the difference may stem from time corrections in thisdifficult energy range.The reduced transition probabilities for de-exciting γ -transitions in Sn have been determined using themeasured lifetimes, branching ratios and energies, andusing theoretical internal conversion coefficients [37].The most likely spin-parity assignments are employed(see Section IV). The transition rates are calculated as-suming a pure multipolarity character of the transitions.
TABLE IV: Half-lives and reduced transition probabilities of the transitions in
Sn. The B(X λ ) values have been derivedfrom the lifetimes and branching ratios obtained from In decay in this work I, as well as the theoretical internal conversioncoefficients, calculated using Bricc [37]. Transition rates have been calculated assuming a pure multipolarity character of thetransitions, using the assignments from [18]. For those levels where no previous assignment had been made, the B(X λ ) valuescorresponding to the most likely multipolarities are presented.E i (keV) Config i J Π i T / T / (literature) E f (keV) Config f J Π f E γ (keV) X λ B(X λ ) (W.u.)4351.6 Octupole 3 − <5 ps <5 ps [18] 0 g.s. 0 + c >7.1vibration 3.4( +20 − ) ps [45] b νf / h − / + c >1.2 · − νf / h − / + + νf / h − / + c − · − νf / h − / + νf / h − / + c νf / d − / − a − c · − νf / h − / + · − νf / h − / + µ s 2.080(17) µ s [3] 4715.9 νf / h − / + c νf / h − / + <30 ps <40 ps [18] 4416.6 νf / h − / + · − E2 >194715.9 νf / h − / + · − E2 >944918.8 νf / h − / + a νf / h − / + · − νf / h − / + · − νf / d − / − a − νf / h − / + c · − νf / h − / + · − νp / h − / − · − νf / s − / ) (4 − ) <17 ps 4351.6 Octupole vibration 3 − · − E2 >0.54830.5 νf / d − / − · − E2 >0.94942.4 νf / d − / − · − E2 >5.14949.0 νf / d − / (3 − ) 437.2 M1 >1.7 · − E2 >5.65398.9 ( πg / g − / ) (6 + ) <17 ps 4715.9 νf / h − / + · − E2 >5.65478.4 ( πg / g − / ) (8 + ) <14 ps 4848.3 νf / h − / + · − E2 >105628.9 ( πg / g − / ) (7 + ) 9(3) ps 13(4) ps [18] a νf / h − / + +9 − ) · − E2 1.5( +7 − )4848.3 νf / h − / + +6 − ) · − E2 1.4( +6 − ) Continued on next page TABLE IV: (Continued)E i (keV) Config i J Π i T / T / (literature) E f (keV) Config f J Π f E γ (keV) X λ B(X λ ) (W.u.)4918.8 νf / h − / + +3 − ) · − E2 0.9( +4 − )5398.9 ( πg / g − / ) (6 + ) 229.8 M1 6( +3 − ) · − E2 76( +34 − )5478.4 ( πg / g − / ) (8 + ) 150.3 M1 9( +4 − ) · − E2 215( +95 − )5753.9 ( νp / h − / ) (6 + ) <20 ps 4715.9 νf / h − / + · − E2 >0.45398.9 ( πg / g − / ) (6 + ) 354.3 M1 >5.5 · − E2 >286235.5 (7 + ) <10 ps 4715.9 νf / h − / + · − E2 >0.044918.8 νf / h − / + · − E2 >0.055398.9 ( πg / g − / ) (6 + ) 836.3 M1 >1.1 · − E2 >1.05753.9 ( νp / h − / ) (6 + ) 481.8 M1 >4.8 · − E2 >136709.7 (7 − ) <13 ps 4918.8 νf / h − / + · − νf / d − / − a The uncertainties are taken from [19] since those in [18] contain several typographical errors [44]. b Calculated from the B(E3) rate measured in Coulomb excitation [45] c Assigned multipolarity in [18]
IV. DISCUSSION
All new levels in
Sn observed in this investiga-tion are candidates for the remaining unidentified stateswithin the particle-hole multiplets. In Figure 11 theenergies for the 24 particle-hole multiplets in
Sn ex-pected to appear below the neutron separation energyare represented. The energies and the splitting of the dif-ferent levels for the same multiplet are estimated by tak-ing into account the single particle energies from neigh-boring nuclei, and the analogous particle-hole states in
Pb, taken from [19, 46, 47], where a A − / scale isintroduced to take into account the nuclear potentialdepth. These empirical calculations provide guidancefor the location of the p-h states, which allows to pro-pose spin-parity assignments to the new levels found inthis work.The other piece of information is provided by the vastnumber of new transitions which connect the new statesto known levels. By assuming that the transitions arepredominantly of dipole character (mainly of M1 mul-tipolarity) and using the electromagnetic selection rulesit is possible to make tentative spin-parity assignmentsof the newly-identified levels. The transition rates ob-tained from the measured lifetimes and lifetime limits ofthe new levels also provide constraints. Together withthe information from the systematics of p-h states ten-tative configurations for the new levels are proposed. Inthe level schemes presented above, the tentative spin andparity assignments are already shown. A. Low energy neutron particle-hole states
The unique identification of every observed state in
Sn with a specific state from a given p-h multipletis a very complex task. In previous β -decay stud-ies [2, 18] the tentative assignment of several stateswas done by considering the analogies between the In [( π g / ) − ν f / ] decay and its two neighbors In[ πg − / ] and Sn [ νf / ] decays. The 6 − and 7 − lev-els observed above 7 MeV, attributed to the νf / g − / configuration, receive the main fraction of the total β -feeding intensity. This strong transition would be equiv-alent to the Gamow-Teller transition in the In decay πg − / → νg − / [48]. Keeping up with the In decayanalogy, the second strongest decay branch correspondsto the first-forbidden transition πg − / → νh − / . In the In decay the equivalent transition would populate the νf / h − / multiplet. Consequently the positive paritystates that appear below 5 MeV are suggested to bemembers of this configuration. On the other hand, thestrong 2435-keV γ transition in Sn that connects thesingle hole states νg − / → νd − / would be analogue tothe 2380-keV and 2268-keV transitions in Sn, whichindicates that the 4 − and 5 − found below 5 MeV areindeed members of the νf / d − / p-h multiplet.In this way there are two neutron p-h multiplets iden-tified within this energy range. However, several of theexpected levels from those configurations lack experi-mental identification. Specifically the 3 + and 8 + levels5 ν f (h ) -1 π g (g ) -1 ν p (h ) -1 ν f (h ) -1 π d (g ) -1 ν h (h ) -1 ν (f ) (h ) -2 E ne r g y [ M e V ] Positive Parity J Π ν s (h ) -1
0 1 2 3 4 5 6 7 4567 0 1 2 3 4 5 6 7 ν f (d ) -1 ν f (s ) -1 ν p (d ) -1 ν f (g ) -1 ν p (s ) -1 ν p (d ) -1 ν p (s ) -1 ν h (d ) -1 ν f (d ) -1 π g (p ) -1 ν f (d ) -1 ν h (s ) -1 π g (p ) -1 π d (p ) -1 ν f (s ) -1 (Octupole vibration) E ne r g y [ M e V ] Negative Parity J Π FIG. 11. Calculated energies for the different particle-hole multiplet states in
Sn, adopted from J. Blomqvist [46, 47]. Theenergies and energy splitting within a given multiplet are estimated by scaling the analogous particle-hole states in
Pb andtaking into account single particle energies from neighboring nuclei. Previously identified levels are plotted with continuouslines. The experimental energies from our work are shown for the newly identified states. The levels whose energies appearbetween brackets correspond to tentative assignments. from the νf / h − / coupling, as well as the 2 − and 3 − levels from the νf / d − / multiplet, which are expectedto be found at excitation energies around 5 MeV, re-main unseen. In a previous investigation from the Cmspontaneous fission [24], a level at 5280 keV was sug-gested to be the missing νf / h − / + level. On thecontrary, in our work we observe the population of thislevel in the In decay, which de-excites by a γ ray tothe 4848-keV state. This level has a very large apparentlog f t value, around 7.2, as it would be expected for ahigh spin such as 9 + , which suggests its identification asthe missing 9 + level.The remaining three levels found within that energyrange are the 4949-, 4965- and 5131-keV states. Theyare directly populated in the β -n decay of g,m In, butnot directly fed from the
In (7 − ) decay. The 4949-keV level is observed in the In decay, but indirectlypopulated by a γ -transition from the 5387 keV (4 − ) levelwithout any noticeable direct β feeding. The β -n feedingfrom the (1/2 − ) and (9/2 + ) In states points towardsa low spin value for these three levels. Specifically the5131-keV state is populated more favorably in the β -ndecay of the (1/2 − ) isomer, which, along with the γ tran- sition which connects that level with the g.s., suggests alower spin for that level than for the other ones. This isan indication that the 5131-keV state is very likely the2 − member of the νf / d − / multiplet. The systematicsof the transitions that de-excite the 4949- and 4965-keVlevels suggests angular momenta J =3. Therefore one ofthem would correspond to the 3 + state from νf / h − / and the other matches the 3 − from ν f / (p / ) − . Thereis no direct information to determine their parity, sinceboth of them are linked to positive and negative paritylevels. However, there are analogies between the 4949keV and the 5 − νf / s − / (4 − ), with similar intensities. Secondly bothlevels have a transition to the 4352-keV 3 − collectivestate, and another one to the νf / d − / − level whoseintensity ratio is about 10:1 in both cases. Those sim-ilarities strongly suggest that 4949-keV level is indeedthe 3 − member from the νf / d − / multiplet, and there-fore the 4965 keV can only be the 3 + member of the νf / h − / p-h configuration.The new assignments are shown in Figure 11.6 B. Particle-hole states from 5 to 6 MeV
In the investigation by Fogelberg et al. [18, 19], the5399-keV (6 + ), 5478-keV (8 + ) and 5629-keV (7 + ) levelswere identified as members of the proton p-h πg / g − / multiplet. This assignment was supported by the in-tense feeding of the 5629 keV (7 + ) state, which wouldbe the equivalent to the strongest transition in the Sndecay, ν f / → π g / . Within this region we have found7 new levels with expected angular momenta from 4 to8. In addition to the proton πg / g − / p-h levels, statesfrom the neutron νp / h − / and νf / s − / configura-tions are also expected. All the levels found from 5.3to 6 MeV could be related to p-h levels from those mul-tiplets. There is not much information apart from γ -ray intensities and the lifetimes and lifetime limits thatpoint towards dominant M1 transitions. This, togetherwith the possibility that the configurations are mixed,hinders a clearer assignment. Nevertheless several con-clusions about them can be drawn.For the 5431-keV level, observed only in the In de-cay, a J = 3 spin assignment can be assumed based onthe γ transitions systematics. Thus, this level can beeither identified with the 3 + state of the πg / g − / orwith the 3 − of the νf / s − / configuration.At similar excitation we expect two 4 + states be-longing to the two positive parity multiplets mentionedabove. In our analysis two levels have been found withinthis energy range with a tentative angular momenta J =4. There is a level at 5446 keV (4 + ), populated indirectlyby γ transitions in In and directly in the β -n decayof g,m In. This level is a good candidate to be a mem-ber of the proton πg / g − / multiplet, but it can also beinterpreted as the 4 + level from the neutron νp / h − / configuration. At 5790 keV another level was identified,this one can be only observed in the In β -n decay, andits de-exciting transitions point towards a spin of (3,4).Therefore, this level can be identified either as the 4 + from the νp / h − / particle-hole coupling expected inthis region, or the 3 + from πg / g − / .The (5 + ) levels at 5698 keV and 5766 keV, which areobserved in this work in both the In and
In decays,can be related to the 5 + states from the πg / g − / andthe νp / h − / multiplets. The two remaining levels inthis region are the 5754-keV (6 + ) and the 6008-keV (7 + )ones, which we tentatively suggest as members of the νp / h − / particle-hole configuration.These tentative assignments are reflected in Figure 11. C. States from 6 to 7 MeV
Moving up to the next energy interval the identifi-cation becomes even more complicated, due to all thepossible p-h multiplets that are expected in this region, and the likely admixture of configurations. Neverthe-less, since most of these levels are populated only in thedirect β -decay of In, they are constrained by the se-lective nature of β decay that favors, in this case, stateswith a large spin (6-8). Because there are not so manyp-h multiplets at this energy that could give rise to lev-els with such a large spin (Figure 11) we can draw someconclusions about them.Regarding the negative parity states, there are twohigh-lying levels with most likely (6 − ) assignments ob-served only in the In decay, at 6598 and 6709keV. Only two neutron multiplets, the νh / d − / and νf / d − / have a negative parity member with J = 6,and therefore these two levels can only be related tothose. The remaining two negative parity levels appear-ing at 6297 and 6476 keV are present in both the Inand In β decays. The systematics of the transitionsthat de-excite and populate them suggest a (5 − ) spin-parity and therefore they are likely to be members ofthe νh / d − / and νf / d − / multiplets as well.On the positive parity side the situation is more in-volved due to the larger amount of multiplets predictedat these high energies. There are 8 different states withan assumed positive parity. These were only observedin the direct β decay of In, out of which 5 have beenidentified in this work for the first time. Relying onthe systematics of the transitions between these levels,along with the selectivity of the β -decay population fromthe (7 − ) g.s. in In, they can have angular momentafrom 5 to 8. Four different positive parity p-h multipletsare predicted in this energy range, three of them ex-pected to arise from neutron configurations ( νh / h − / , νf / h − / and νp / h − / ), and another one comingfrom the proton πd / g − / coupling. Almost all of themcan be give rise to (5,6,8) + states, which hampers theiridentification. Moreover the states are probably mixed.The only noticeable difference observed among thepositive parity levels is the larger feeding measured forthe 6631-keV state, around 1 % with a log f t of the orderof 6.4 (Figure 5). This enhanced population can be inter-preted on the grounds of the equivalence mentioned be-fore between the In and
Sn decays. In
Sn, the β decay is dominated by the first forbidden ν f / → π g / transition populating the g.s. in Sb with 86 % of thetotal β intensity and log f t ≈ πg / g − / multiplet in the Indecay. Moreover, the second strongest transition foundin
Sn decay corresponds to the νf / → πd / transi-tion, receiving 11 % of the total feeding with log f t ≈ πd / g − / configuration in the In β -decay. Comparing the population of the 6631-keV levelwith the population of 5629-keV level, identified as the(7 + ) state of the πg / g − / multiplet, we can see thatthey keep the 8:1 β intensity ratio, and similar log f t values for the level at 5629 keV. Such a large popula-7tion might be an indication of a predominant πd / g − / configuration for the 6631 keV (6 + ) state. V. CONCLUSIONS
Experimental information about the
Sn structureplays a crucial role in the shell-model interpretation ofnuclei around N = 82, because it provides direct knowl-edge about the particle-hole couplings for both protonsand neutrons. In this work the properties of excitedstates in Sn have been studied from the β decay of In. By taking advantage of the isomer selectivity ca-pabilities of the ISOLDE RILIS, independent investiga-tions of the β -decay of the In g (9/2 + ) g.s. and the In (1/2 − ) isomer were performed as well. Thanksto both decay modes, the knowledge of the Sn struc-ture has been largely expanded in this work. A total of17 new levels and 68 new γ -transitions have been added(including those already quoted in the previous publica-tion [16] derived from the same experiment). A completefast-timing investigation of the excited levels in Snhas been performed as well, confirming and extendingprevious results.An interpretation of the level structure is provided interms of particle-hole configurations arising from corebreaking states both from the N = 82 and Z = 50 shellsacross the gap. The interpretation is based on empiricalcalculations [19, 46, 47] leading to positive and negativeparity particle-hole multiplets, where the energies areobtained from the single-particle energies from neighbor-ing nuclei and from the analogous particle-hole states in Pb. These empirical calculations, together with theexperimental information on the β and β -n feeding, thelevel lifetimes and the γ decay branches provide guid-ance for the identification of the levels as proton-holemembers of the multiplets, facilitating tentative spin-parity assignments to the new levels.The number of states is consistent with the one cal-culated from the angular momentum couplings. Theidentification of all remaining missing levels from the νf / h − / and νf / d − / neutron-hole configurationshas been completed. A tentative interpretation has beenprovided for the rest of observed states, where we have been able to observe most of the expected p-h levels withangular momenta close to 7.Most of the missing information is related to the antic-ipated low spin states, which are very unlikely to be pop-ulated in the In (7 − ) β -decay. However, the identifi-cation of many γ -rays around 7 MeV from the g,m In β -decay strongly suggests feeding of those missing low-spin multiplet states. Enhanced statistics for this decaywill be beneficial to provide more firm assignments.In conclusion the knowledge about states in the dou-bly magic Sn has been largely expanded by the inves-tigation of the β -decay of In and β -n decay of Inperformed at the ISOLDE facility at CERN. The identi-fication of particle-hole multiplets both for protons andneutrons and the transition rates connecting different p-h configurations and states within multiplets may pro-vide input on the two-body matrix elements and singleparticle states. The new data challenges the theoreticaldescription of
Sn, which is relevant for the under-standing of nuclear structure in the region.
VI. ACKNOWLEDGMENTS
We acknowledge the support of the ISOLDE Col-laboration and the ISOLDE technical teams, and bythe European Union Horizon 2020 research and inno-vation programme under grant agreement No 654002.This work was partially funded by the Spanish gov-ernment via FPA2015-65035-P, FPA-64969-P, FPA2017-87568-P and RTI2018-098868-B-I00 projects, the PolishNational Science Center under Contracts No. UMO-2015/18/E/ST2/00217, UMO-2015/18/M/ST2/00523and UMO-2019/33/N/ST2/03023, the Portuguese FCTvia CERN/FIS-NUC/0004/2015 project, the GermanBMBF under contract 05P18PKCIA, the Romanian IFAGrant CERN/ISOLDE and by grants from the U.K. Sci-ence and Technology Facilities Council, the ResearchFoundation Flanders (FWO, Belgium), the Excellence ofScience program (EOS, FWO-FNRS, Belgium), and theGOA/2015/010 (BOF KU Leuven). J.B. acknowledgessupport by the Universidad Complutense de Madrid un-der the predoctoral grant CT27/16-CT28/16. [1] A. Kerek, G. B. Holm, L. E. De Geer, and S. Borg,Physics Letters B , 252 (1973).[2] T. Björnstad, M. J. G. Borge, J. Blomqvist, R. D.Von Dincklage, G. T. Ewan, P. Hoff, B. Jonson,K. Kawade, A. Kerek, O. Klepper, G. Lövhöiden,S. Mattsson, G. Nyman, H. L. Ravn, G. Rudstam,K. Sistemich, and O. Tengblad, Nuclear Physics A ,463 (1986).[3] Y. Khazov, A. Rodionov, S. Sakharov, and B. Singh,Nuclear Data Sheets , 497 (2005). [4] K. L. Jones, A. S. Adekola, D. W. Bardayan, J. C. Black-mon, K. Y. Chae, K. A. Chipps, J. A. Cizewski, L. Erik-son, C. Harlin, R. Hatarik, R. Kapler, R. L. Kozub,J. F. Liang, R. Livesay, Z. Ma, B. H. Moazen, C. D.Nesaraja, F. M. Nunes, S. D. Pain, N. P. Patterson,D. Shapira, J. F. Shriner, M. S. Smith, T. P. Swan, andJ. S. Thomas, Nature , 454 (2010).[5] J. Barnes, D. Kasen, M.-R. Wu, and G. Martínez-Pinedo, The Astrophysical Journal (2016),10.3847/0004-637X/829/2/110. [6] P. S. Cowperthwaite, E. Berger, V. A. Villar, B. D.Metzger, M. Nicholl, R. Chornock, P. K. Blanchard,W. Fong, R. Margutti, M. Soares-Santos, K. D. Alexan-der, S. Allam, J. Annis, D. Brout, D. A. Brown, R. E.Butler, H. . Y. Chen, H. T. Diehl, Z. Doctor, M. R.Drout, T. Eftekhari, B. Farr, D. A. Finley, R. J. Foley,J. A. Frieman, C. L. Fryer, J. García-Bellido, M. S. S.Gill, J. Guillochon, K. Herner, D. E. Holz, D. Kasen,R. Kessler, J. Marriner, T. Matheson, E. H. Neilsen,E. Quataert, A. Palmese, A. Rest, M. Sako, D. M. Scol-nic, N. Smith, D. L. Tucker, P. K. G. Williams, E. Bal-binot, J. L. Carlin, E. R. Cook, F. Durret, T. S. Li,P. A. A. Lopes, A. C. C. Lourenço, J. L. Marshall,G. E. Medina, J. Muir, R. R. Muñoz, M. Sauseda,D. J. Schlegel, L. F. Secco, A. K. Vivas, W. Wester,A. Zenteno, Y. Zhang, T. M. C. Abbott, M. Banerji,K. Bechtol, A. Benoit-Lévy, E. Bertin, E. Buckley-Geer,D. L. Burke, D. Capozzi, A. Carnero Rosell, M. Car-rasco Kind, F. J. Castander, M. Crocce, C. E. Cunha,C. B. D’Andrea, L. N. d. a. Costa, C. Davis, D. L. De-Poy, S. Desai, J. P. Dietrich, A. Drlica-Wagner, T. F.Eifler, A. E. Evrard, E. Fernandez, B. Flaugher, P. Fos-alba, E. Gaztanaga, D. W. Gerdes, T. Giannantonio,D. A. Goldstein, D. Gruen, R. A. Gruendl, G. Gutier-rez, K. Honscheid, B. Jain, D. J. James, T. Jeltema,M. W. G. Johnson, M. D. Johnson, S. Kent, E. Krause,R. Kron, K. Kuehn, N. Nuropatkin, O. Lahav, M. Lima,H. Lin, M. A. G. Maia, M. March, P. Martini, R. G.McMahon, F. Menanteau, C. J. Miller, R. Miquel, J. J.Mohr, E. Neilsen, R. C. Nichol, R. L. C. Ogando, A. A.Plazas, N. Roe, A. K. Romer, A. Roodman, E. S. Rykoff,E. Sanchez, V. Scarpine, R. Schindler, M. Schubnell,I. Sevilla-Noarbe, M. Smith, R. C. Smith, F. Sobreira,E. Suchyta, M. E. C. Swanson, G. Tarle, D. Thomas,R. C. Thomas, M. A. Troxel, V. Vikram, A. R. Walker,R. H. Wechsler, J. Weller, B. Yanny, and J. Zuntz,The Astrophysical Journal (2017), 10.3847/2041-8213/aa8fc7.[7] B. D. Metzger, G. Martínez-Pinedo, S. Darbha,E. Quataert, A. Arcones, D. Kasen, R. Thomas, P. Nu-gent, I. V. Panov, and N. T. Zinner, Monthly Noticesof the Royal Astronomical Society , Monthly Notices ofthe Royal Astronomical Society , 2650 (2010).[8] G. Martínez-Pinedo, D. Mocelj, N. T. Zinner, A. Ke-lić, K. Langanke, I. Panov, B. Pfeiffer, T. Rauscher,K. H. Schmidt, and F. K. Thielemann,
InternationalWorkshop on Nuclear Physics 28th Course , Progress inParticle and Nuclear Physics , 199 (2007).[9] H. Grawe, K. Langanke, and G. Martínez-Pinedo, Re-ports on Progress in Physics , 1525 (2007).[10] M. Wang, G. Audi, F. G. Kondev, W. Huang, S. Naimi,and X. Xu, Chinese Physics C , 030003 (2017).[11] P. Hoff, P. Baumann, A. Huck, A. Knipper, G. Wal-ter, G. Marguier, B. Fogelberg, A. Lindroth, H. Mach,M. Sanchez-Vega, R. B. E. Taylor, P. Van Duppen,A. Jokinen, M. Lindroos, M. Ramdhane, W. Kurcewicz,B. Jonson, G. Nyman, Y. Jading, K.-L. Kratz, A. Wöhr,G. Løvhøiden, T. F. Thorsteinsen, and J. Blomqvist(ISOLDE Collaboration), Phys. Rev. Lett. , 1020(1996).[12] P. Hoff, P. Baumann, A. Huck, A. Knipper, G. Wal-ter, G. Marguier, B. Fogelberg, A. Lindroth, H. Mach,M. Sanchez-Vega, R. Taylor, P. van Duppen, A. Jokinen,M. Lindroos, M. Ramdhane, W. Kurcewicz, B. Jonson, G. Nyman, Y. Jading, K.-L. Kratz, A. Wöhr, G. Løvhøi-den, T. Thorsteinsen, and J. Blomqvist, Hyperfine In-teractions , 141 (2000).[13] K. L. Jones, F. M. Nunes, A. S. Adekola, D. W. Bar-dayan, J. C. Blackmon, K. Y. Chae, K. A. Chipps, J. A.Cizewski, L. Erikson, C. Harlin, R. Hatarik, R. Kapler,R. L. Kozub, J. F. Liang, R. Livesay, Z. Ma, B. Moazen,C. D. Nesaraja, S. D. Pain, N. P. Patterson, D. Shapira,J. F. Shriner, M. S. Smith, T. P. Swan, and J. S.Thomas, Phys. Rev. C , 034601 (2011).[14] J. M. Allmond, A. E. Stuchbery, J. R. Beene,A. Galindo-Uribarri, J. F. Liang, E. Padilla-Rodal, D. C.Radford, R. L. Varner, A. Ayres, J. C. Batchelder,A. Bey, C. R. Bingham, M. E. Howard, K. L. Jones,B. Manning, P. E. Mueller, C. D. Nesaraja, S. D. Pain,W. A. Peters, A. Ratkiewicz, K. T. Schmitt, D. Shapira,M. S. Smith, N. J. Stone, D. W. Stracener, and C.-H.Yu, Phys. Rev. Lett. , 172701 (2014).[15] V. Vaquero, A. Jungclaus, P. Doornenbal, K. Wim-mer, A. Gargano, J. A. Tostevin, S. Chen, E. Nácher,E. Sahin, Y. Shiga, D. Steppenbeck, R. Taniuchi, Z. Y.Xu, T. Ando, H. Baba, F. L. B. Garrote, S. Franchoo,K. Hadynska-Klek, A. Kusoglu, J. Liu, T. Lokotko,S. Momiyama, T. Motobayashi, S. Nagamine, N. Nakat-suka, M. Niikura, R. Orlandi, T. Saito, H. Sakurai, P. A.Söderström, G. M. Tveten, Z. Vajta, and M. Yalcinkaya,Phys. Rev. Lett. , 202502 (2017).[16] M. Piersa, A. Korgul, L. M. Fraile, J. Benito,E. Adamska, A. N. Andreyev, R. Álvarez-Rodríguez,A. E. Barzakh, G. Benzoni, T. Berry, M. J. G. Borge,M. Carmona, K. Chrysalidis, J. G. Correia, C. Costache,J. G. Cubiss, T. Day Goodacre, H. De Witte, D. V. Fe-dorov, V. N. Fedosseev, G. Fernández-Martínez, A. Fi-jałkowska, M. Fila, H. Fynbo, D. Galaviz, P. T. Green-lees, R. Grzywacz, L. J. Harkness-Brennan, C. Henrich,M. Huyse, A. Illana, Z. Janas, K. Johnston, D. S. Jud-son, V. Karanyonchev, M. Kici ńska Habior, J. Konki,J. Kurcewicz, I. Lazarus, R. Lică, H. Mach, M. Madurga,I. Marroquín, B. Marsh, M. C. Martínez, C. Mazzoc-chi, N. Mărginean, R. Mărginean, K. Miernik, C. Mi-hai, E. Nácher, A. Negret, B. Olaizola, R. D. Page,S. Paulaskalas, S. Pascu, A. Perea, V. Pucknell, P. Rahk-ila, E. Rapisarda, J.-M. Régis, F. Rotaru, S. Rothe,V. Sánchez-Tembleque, G. Simpson, C. Sotty, L. Stan,M. Stănoiu, M. Stryjczyk, O. Tengblad, A. Turturica,J. M. Udías, P. Van Duppen, V. Vedia, A. Villa,S. Viñals, R. Wadsworth, W. B. Walters, and N. Warr(IDS Collaboration), Phys. Rev. C , 024304 (2019).[17] A. Korgul, P. Ba¸czyk, W. Urban, T. Rza¸ca Urban, A. G.Smith, and I. Ahmad, Phys. Rev. C , 027303 (2015).[18] B. Fogelberg, M. Hellström, D. Jerrestam, H. Mach,J. Blomqvist, A. Kerek, L. O. Norlin, and J. P.Omtvedt, Phys. Rev. Lett. , 2413 (1994).[19] B. Fogelberg, M. Hellström, D. Jerrestam, H. Mach,J. Blomqvist, A. Kerek, L. O. Norlin, and J. P.Omtvedt, Physica Scripta T56 , 79 (1995).[20] H. Mach and B. Fogelberg, Physica Scripta
T56 , 270(1995).[21] T. Björnstad, L.-E. D. Geer, G. Ewan, P. Hansen,B. Jonson, K. Kawade, A. Kerek, W.-D. Lauppe,H. Lawin, S. Mattsson, and K. Sistemich, Physics Let-ters B , 35 (1980).[22] K. Kawade, K. Sistemich, G. Battistuzzi, H. Lawin,K. Shizuma, and J. Blomqvist, Zeitschrift für Physik A Atoms and Nuclei , 33 (1982).[23] J. Dehesa, W. Lauppe, K. Sistemich, and J. Speth,Physics Letters B , 309 (1978).[24] P. Bhattacharyya, P. J. Daly, C. T. Zhang, Z. W.Grabowski, S. K. Saha, R. Broda, B. Fornal, I. Ah-mad, D. Seweryniak, I. Wiedenhöver, M. P. Carpenter,R. V. F. Janssens, T. L. Khoo, T. Lauritsen, C. J. Lis-ter, P. Reiter, and J. Blomqvist, Phys. Rev. Lett. ,062502 (2001).[25] V. Fedosseev, K. Chrysalidis, T. D. Goodacre, B. Marsh,S. Rothe, C. Seiffert, and K. Wendt, Journal of PhysicsG: Nuclear and Particle Physics , 084006 (2017).[26] M. Piersa et al. , Proceedings, 35th Mazurian Lakes Con-ference on Physics: Exotic Nuclei - Laboratories forFundamental Laws of Nature: Piaski, Poland, Septem-ber 3-9, 2017 , Acta Phys. Polon.
B49 , 523 (2018).[27] R. Catherall, W. Andreazza, M. Breitenfeldt, A. Dor-sival, G. J. Focker, T. P. Gharsa, T. J. Giles, J.-L.Grenard, F. Locci, P. Martins, S. Marzari, J. Schipper,A. Shornikov, and T. Stora, Journal of Physics G: Nu-clear and Particle Physics , 094002 (2017).[28] “The IDS collaboration”, http://isolde-ids.web.cern.ch/isolde-ids/ .[29] H. Mach, R. Gill, and M. Moszyński, Nucl. Instrum.Meth. A , 49 (1989).[30] M. Moszyński and H. Mach, Nuclear Instruments andMethods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment , 407 (1989).[31] L. M. Fraile, Journal of Physics G: Nuclear and ParticlePhysics , 094004 (2017).[32] V. Vedia, M. Carmona-Gallardo, L. M. Fraile, H. Mach,and J. M. Udías, Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrom-eters, Detectors and Associated Equipment , 98(2017).[33] L. M. Fraile, H. Mach, V. Vedia, B. Olaizola, V. Paziy,E. Picado, and J. Udías, Nuclear Instruments and Meth-ods in Physics Research Section A: Accelerators, Spec-trometers, Detectors and Associated Equipment ,235 (2013).[34] R. Lică, G. Benzoni, A. I. Morales, M. J. G. Borge, L. M.Fraile, H. Mach, M. Madurga, C. Sotty, V. Vedia, H. D.Witte, J. Benito, T. Berry, N. Blasi, A. Bracco, F. Cam-era, S. Ceruti, V. Charviakova, N. Cieplicka-Oryńczak,C. Costache, F. C. L. Crespi, J. Creswell, G. Fernández-Martínez, H. Fynbo, P. Greenlees, I. Homm, M. Huyse,J. Jolie, V. Karayonchev, U. KĂśster, J. Konki,T. KrĂśll, J. Kurcewicz, T. Kurtukian-Nieto, I. Lazarus,S. Leoni, M. Lund, N. Marginean, R. Marginean, C. Mi-hai, R. Mihai, A. Negret, A. Orduz, Z. Patyk, S. Pascu,V. Pucknell, P. Rahkila, J. M. Regis, F. Rotaru, N. Saed-Sami, V. Sánchez-Tembleque, M. Stanoiu, O. Tengblad,M. Thuerauf, A. Turturica, P. V. Duppen, and N. Warr,Journal of Physics G: Nuclear and Particle Physics ,054002 (2017).[35] “Nutaq data acquisition systems”, . [36] A. Jungclaus, A. Gargano, H. Grawe, J. Taprogge,S. Nishimura, P. Doornenbal, G. Lorusso, Y. Shimizu,G. S. Simpson, P.-A. Söderström, T. Sumikama, Z. Y.Xu, H. Baba, F. Browne, N. Fukuda, R. Gernhäuser,G. Gey, N. Inabe, T. Isobe, H. S. Jung, D. Kameda,G. D. Kim, Y.-K. Kim, I. Kojouharov, T. Kubo,N. Kurz, Y. K. Kwon, Z. Li, H. Sakurai, H. Schaffner,K. Steiger, H. Suzuki, H. Takeda, Z. Vajta, H. Watan-abe, J. Wu, A. Yagi, K. Yoshinaga, S. Bönig, L. Cor-aggio, J.-M. Daugas, F. Drouet, A. Gadea, S. Ilieva,N. Itaco, T. Kröll, A. Montaner-Pizá, K. Moschner,D. Mücher, H. Nishibata, A. Odahara, R. Orlandi, andA. Wendt, Phys. Rev. C , 041301 (2016).[37] T. Kibédi, T. Burrows, M. Trzhaskovskaya, P. David-son, and C. Nestor, Nuclear Instruments and Methodsin Physics Research Section A: Accelerators, Spectrom-eters, Detectors and Associated Equipment , 202(2008).[38] C. A. Stone, S. H. Faller, and W. B. Walters, Phys.Rev. C , 1963 (1989).[39] H. Huck, M. L. Pérez, J. J. Rossi, and H. M. Sofía,Phys. Rev. C , 2227 (1981).[40] E. Lund, P. Hoff, K. Aleklett, O. Glomset, and G. Rud-stam, Zeitschrift für Physik A Atoms and Nuclei ,233 (1980).[41] G. Rudstam, K. Aleklett, and L. Sihver, Atomic Dataand Nuclear Data Tables , 1 (1993).[42] B. Singh, Nuclear Data Sheets , 33 (2001).[43] J. Blomqvist, A. Kerek, and B. Fogelberg, EuropeanPhysical Journal A - EUR PHYS J A , 199 (1983).[44] H. Mach, Private Communication (2014).[45] D. Rosiak, M. Seidlitz, P. Reiter, H. Naïdja, Y. Tsun-oda, T. Togashi, F. Nowacki, T. Otsuka, G. Colò,K. Arnswald, T. Berry, A. Blazhev, M. J. G. Borge,J. Cederkäll, D. M. Cox, H. De Witte, L. P. Gaffney,C. Henrich, R. Hirsch, M. Huyse, A. Illana, K. John-ston, L. Kaya, T. Kröll, M. L. L. Benito, J. Ojala,J. Pakarinen, M. Queiser, G. Rainovski, J. A. Ro-driguez, B. Siebeck, E. Siesling, J. Snäll, P. Van Dup-pen, A. Vogt, M. von Schmid, N. Warr, F. Wenander,K. O. Zell, MINIBALL, and H.-I. Collaborations, Phys-ical Review Letters , 252501 (2018).[46] H. Mach, B. Fogelberg, M. Hellström, D. Jerrestam,J. Blomqvist, A. Kerek, L. Norlin, J. Omtvedt,K. Erokhina, and V. Isakov, Nuclear Physics A ,c179 (1995), proceedings of the Fifth International Sym-posium on Physics of Unstable Nuclei.[47] J. Blomqvist, Private Communication (1998).[48] B. Fogelberg, H. Gausemel, K. A. Mezilev, P. Hoff,H. Mach, M. Sanchez-Vega, A. Lindroth, E. Ramström,J. Genevey, J. A. Pinston, and M. Rejmund, Phys. Rev.C , 034312 (2004).[49] M. Sanchez-Vega, B. Fogelberg, H. Mach, R. B. E.Taylor, A. Lindroth, J. Blomqvist, A. Covello, andA. Gargano, Phys. Rev. C60