Ground-state and decay properties of neutron-rich 106Nb
A. J. Mitchell, R. Orford, G. J. Lane, C. J. Lister, P. Copp, J. A. Clark, G. Savard, J. M. Allmond, A. D. Ayangeakaa, S. Bottoni, M. P. Carpenter, P. Chowdhury, D. A. Gorelov, R. V. F. Janssens, F. G. Kondev, U. Patel, D. Seweryniak, M. L. Smith, Y. Y. Zhong, S. Zhu
GGround-state and decay properties of neutron-rich Nb A. J. Mitchell,
1, a
R. Orford,
2, 3, b
G. J. Lane, C. J. Lister, P. Copp,
4, c
J. A. Clark, G. Savard,
3, 5
J. M. Allmond, A. D. Ayangeakaa,
7, 8
S. Bottoni,
3, d
M. P. Carpenter, P. Chowdhury, D. A. Gorelov,
3, 9
R. V. F. Janssens,
7, 8
F. G. Kondev, U. Patel,
1, e
D. Seweryniak, M. L. Smith,
1, f
Y. Y. Zhong, and S. Zhu
3, g Department of Nuclear Physics, Research School of Physics,The Australian National University, Canberra, ACT 2601, Australia Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada Physics Division, Argonne National Laboratory, Argonne, IL 60439 Department of Physics and Applied Physics, University of Massachusetts Lowell, Lowell, MA 01854 Department of Physics, University of Chicago, Chicago, IL 60637 Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830 Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3255 Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27708-2308 Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada (Dated: February 9, 2021)The ground-state properties of neutron-rich
Nb and its β decay into Mo have been studiedusing the CARIBU radioactive-ion-beam facility at Argonne National Laboratory. Niobium-106 ionswere extracted from a
Cf fission source and mass separated before being delivered as low-energybeams to the Canadian Penning Trap, as well as the X-Array and SATURN β -decay-spectroscopystation. The measured Nb ground-state mass excess of -66202.0(13) keV is consistent with arecent measurement but has three times better precision; this work also rules out the existence of asecond long-lived, β -decaying state in Nb above 5 keV in excitation energy. The decay half-life of
Nb was measured to be 1.097(21) s, which is 8 % longer than the adopted value. The level schemeof the decay progeny, Mo, has been expanded up to ≈ Mo of J ≥ emphasises the need to revise theadopted J π = 1 − ground-state spin-parity assignment of Nb; it is more likely to be J ≥ . PACS numbers: 23.40.-s, 21.60.Fw, 23.20.LvKeywords: nuclear mass, β decay, γ decay, radiation detection, neutron-rich nuclei I. INTRODUCTION
Atomic nuclei that bridge the chart of nuclides betweenthe so-called ‘valley of stability’ and ‘neutron drip-line’play diverse roles in nuclear science. As well as providingimportant tests of fundamental nuclear-structure theory,quantitative measurements of their ground-state and de-cay properties provide highly valued constraints of stellarnucleosynthesis models [1] and decay-heat calculationsfor the nuclear energy sector [2].The flow of r -process nucleosynthesis across theneutron-rich landscape is largely dictated by the near-parabolic shape of the valley of stability. Variations inbinding energy per nucleon along isobaric chains deter-mine both the extreme limit of the neutron drip-line and a Email: [email protected] b Present address: Nuclear Science Division, Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, USA. c Present address: Physics Division, Argonne National Laboratory,Argonne, IL 60439 d Present address: Universita’ degli Studi di Milano, InstitutoNazionale di Fisica Nucleare, Milano 20133, Italy e Present address: Department of Physics, Duke University,Durham, North Carolina 27701 f Present address: Australian Nuclear Science and Technology Or-ganisation, Lucas Heights, NSW 2234, Australia g Present address: Brookhaven National Laboratory, Upton, NY11973 each nuclide’s Q -value for β decay back towards stabil-ity, thereby modulating the timescale of the entire pro-cess. To a large extent, this parabolic shape is a resultof the bulk properties of nuclear matter and is capturedby even the simplest liquid drop models. However, wheninspected in detail, nuclear structure plays a significantrole in modulating r -process isotope production [3].The most prominent structure effects are the majorshell closures at N = 50, 82, and 126, which cause bot-tlenecks in the r -process flow and enhanced abundance ofelements produced at these locations [4]. Beyond that,smaller effects, like shell-driven areas of large deforma-tion, shape coexistence, nuclear isomers, and anoma-lously slow β decays (caused by large spin differences,or poor overlap of parent and daughter wave functions)result in more modest modulations in the final r -processstable-isotope production. The exact locus of the r -process is still not accurately known, and most nucleion the expected path are yet to be produced and mea-sured. Experimental study of these nuclei is a major goalof new, ‘next-generation’ radioactive-beam facilities cur-rently under construction. Many important cases are re-fractory elements, whose production is suppressed withcurrent Isotope Separation On-Line (ISOL) techniques.However, a growing number of recent results have yieldeda wealth of nuclear-structure information and consider-able progress is being made in pushing into this neutron-rich region with existing infrastructure, motivated by a r X i v : . [ nu c l - e x ] F e b both astrophysical and nuclear-structure reasons.This specific research is aimed at clarifying the massand spin of highly deformed Nb, and at seeking along-lived, low-lying β -decaying isomer, similar to thosefound in , , Nb. Such isomers are ubiquitous inodd-odd nuclei in the region; a consequence of near-degenerate structures of pure pf -shell, or g -shell, parent-age. The structure of the progeny, Mo, has beenwell investigated through prompt-fission-fragment γ -rayspectroscopy, but our β -decay study populated a wealthof new low-spin levels and offers access to particle-holestates not seen in prompt fission. During the preparationof this manuscript, a similar β -decay study performed atthe RIKEN RI Beam Factory was published [5]. Theresults presented below are in broad agreement with thefindings of the RIKEN work, although some details differ,both in the data and in their interpretation. II. EXPERIMENT DETAILS
This work was performed at the CAlifornium RareIsotope Breeder Upgrade (CARIBU) facility at ArgonneNational Laboratory. Here, neutron-rich radioactive nu-clei produced in the spontaneous fission of
Cf are ex-tracted and thermalised in the CARIBU gas catcher. Thespecies of interest is mass-selected by an isobar separa-tor, bunched, and delivered to the required experimentalarea. Details relevant to the reported experiments areprovided below. For a more detailed description of theCARIBU facility, we refer the reader to existing litera-ture, for example Ref. [6]. Here, we report on the firstdedicated inspection of the ground-state and decay prop-erties of
Nb via complementary nuclear mass measure-ments and β -delayed γ -ray spectroscopy. A. CANADIAN PENNING TRAP
A mass measurement was performed using the Cana-dian Penning Trap (CPT) [7] to confirm the accuracy ofthe reported
Nb ground-state mass [8]. At CARIBU,
Nb ions were extracted from the gas catcher in a 2 + charge state, and a bunched beam was produced at arepetition rate of 10 Hz. To remove unwanted contami-nant ions from the beam, the new Multi-Reflection Time-Of-Flight (MR-TOF) mass separator [9] was employed.Ion bunches were captured in the MR-TOF and allowedto isochronously cycle between the two ion mirrors fora duration of 10 ms, wherein a mass resolving powerof R = m/ ∆ m > , was achieved. A Bradbury-Nielsen Gate [10] at the MR-TOF exit was used to se-lectively transfer Nb ions to the low-energy experi-mental area, while suppressing other A = 106 isobars byseveral orders of magnitude.The resulting ion bunches were collected in a cryogeniclinear RFQ trap, where they were cooled and re-bunchedfor injection into the Penning trap. The mass mea- surement was conducted using the Phase-ImagingIon-Cyclotron-Resonance (PI-ICR) technique [11]. Inthis method, a position-sensitive micro-channel plate isused to infer the phase of the orbital motion of trappedions at some given time. The cyclotron frequency ( ν c )is determined by measuring the change in phase duringa period of excitation-free accumulation ( t acc ). Aftertime t acc in the Penning trap, the ions are ejectedand the position of the ions at the detector plane ismeasured. Ions acquire a mass-dependent phase duringthe accumulation time and form clusters (or spots ) atsome radius from the projected trap centre. The anglebetween these spots and a mass-independent referencespot is measured ( φ c ) and the cyclotron frequency isgiven by: ν c = φ c + 2 πN πt acc , (1)where N is the integer number of revolutions during thetime t acc . The technique provides high sensitivity andresolution, and is therefore also well-suited to search forlow-lying or weakly produced isomers. A 1-s accumula-tion time results in a mass resolution of R ≈ . × .Details of the implementation of this measurement tech-nique at the CPT are introduced in Refs. [12, 13]. B. X-ARRAY AND SATURNDECAY-SPECTROSCOPY STATION
The β -decay properties of Nb were investigated us-ing the X-Array and SATURN decay-spectroscopy sta-tion [14]. The decay-spectroscopy station consists of upto five high-efficiency High-Purity Germanium (HPGe)clover-style γ -ray detectors, and a plastic scintillator of-fering almost complete solid-angle coverage. The systemhas been demonstrated to be a powerful spectroscopydevice with low-intensity, radioactive-ion beams [15]. Alow-energy beam of mass-separated Nb ions, bunchedand delivered at 100-ms intervals, was deposited on amovable aluminized-mylar tape located in the geometriccentre of the array at a rate of 100-200 ions/second. TheX-Array configuration described in Ref. [14] was modifiedslightly for this experiment. The clover detector locatedon the left-hand-side of the X-Array, as observed by theoncoming beam particles, was removed and replaced withfive unshielded LaBr scintillators. The purpose here wasto test the capacity of the modified X-Array to measureexcited-state lifetimes. Unfortunately, due to the highlevel of room-background, no useful information was ex-tracted from the LaBr detector data, and so these arenot discussed any further here.Despite the MR-TOF described above not being avail-able at the time, the beam delivered for this experi-ment consisted primarily of mass-selected Nb ions.Small contributions from neighbouring isobars,
Zr and
Mo, may be expected due to the small mass differencesand the maximum achievable mass resolution of the iso-bar separator at the time of this experiment. However,the presence of
Zr is effectively suppressed due to therelative proportion of its spontaneous fission branch andthe low intensity of the radioactive-ion beam. There areno known γ rays associated with Zr → Nb β de-cay for identification. Six Nb γ -ray transitions withrelative intensities > % are known from prompt-fissionspectroscopy [16]; these were undetectable in both the γ -ray singles and coincidence data. Any beam contami-nation leading directly to Mo → Tc decay would besuppressed along with the other long-lived isobaric con-tamination by the repeating beam cycle, described below,that was applied throughout the experiment.Data were collected in two modes of repeating tape-movement cycles: one lasted for 14.0 s; the other for7.5 s. The growth-and-decay collection cycle of alter-nating ‘beam on’ and ‘beam off’ periods was achievedby switching an electrostatic beam deflector with theSATURN logic control system. The implantation tapewas moved at the end of each cycle to suppress accu-mulation of activity from long-lived decay products atthe collection site. The longer cycle was used to mea-sure the
Nb decay half-life; this technique was suc-cessfully demonstrated in the earlier work of Ref. [17].The shorter cycle was adopted to maximise the collec-tion rate for
Nb decay. While isobaric contaminationof the γ -ray spectra was suppressed by the moving tapecycle, the relatively short half-lives involved meant thatsome level of contamination was unavoidable. Over time,activity build-up on the tape led to contribution of iso-baric β decay from Mo → Tc (T / = 8.73(12) s)and Tc → Ru (T / = 35.6(6) s). Since the half-lifeof Ru is T / = 371.8(18) days [16], this was effectivelythe end of the decay chain over the days-long timescale ofthis experiment. The photopeak of the most-intense γ -ray transition observed in Mo is five-to-six times largerthan the corresponding transitions in
Tc and
Ru.In many cases, it was possible to confirm assignments ofnew γ rays to the appropriate isobar by measuring theassociated β -decay half-life.Standard γ -ray sources of Am, Co,
Eu, and
Ta were used to calibrate the detection efficiency of theX-Array up to ≈ γ rays were also used to obtain an energy calibration ex-ceeding the range of interest for this experiment (whichwas E γ ≈ γ rays pro-duced from ( n , γ ) reactions, a consequence of the highneutron flux emitted from the CARIBU Cf source,were used to confirm the appropriate use of a linear cal-ibration. Photopeaks of these γ rays appear in the γ -ray singles data, but are removed by applying a β - or γ -coincidence condition in offline data sorting. System-atic uncertainty of the energy calibration was found to be < ∼ γ -ray energiesquoted in this work include the systematic uncertainty,as well as the statistical uncertainty associated with thefitting routines of the gf software package [18]. The Phase projection ( ) C o un t s (b) MoH
22+ 106 Nb (a) Nb X (mm) Y ( mm ) MoH y ( mm ) y (mm) -8 -6 -4 -2 0 2 4160120804000 C oun t s Nb Nb
2+ 104
MoH Nb MoH
50 Phase projection (deg) 200 250100 150
FIG. 1. Example CPT spectra acquired using the PI-ICR technique with t acc = 190 ms. (a) Ions acquire amass-dependent phase, forming characteristic ‘ spots ’, duringthe collection time in the trap; the Nb and molecular MoH are identified. (b) Corresponding phase projec-tion of Nb and the MoH contaminant. measured energy resolution of the X-Array in this workwas 2.5 keV at 1000 keV, 3.7 keV at 2000 keV and 4.2 keVat 3000 keV.Data were collected using a digital acquisition system(DAQ) that applied a free-running trigger. Signals fromthe individual clover crystals and tape-cycle reset triggerwere input directly in the DAQ. The outputs of threeHammamatsu PMTs associated with the BC-408 plastic-scintillator detector in SATURN were coupled togetherand amplified before being delivered to the DAQ. Datawere sorted offline into a combination of singles spectraand coincidence matrices that were used in the subse-quent analyses discussed below.
III. GROUND-STATE PROPERTIES OF
NBA. GROUND-STATE MASS
The CPT system was calibrated by measuring the cy-clotron frequency of Cr + , which is readily available atCARIBU and has a precisely known mass [8]. To re- x10 M a ss r e s o l v i ng po w e r PI-ICR extrapolation TOF-ICR PI-ICR data
Measurement accumulation time (ms)200 400 800 1000 1200 14006000.0 R e s o l v a b l e Δ m ( k e V ) FIG. 2. Mass resolving power and resolvable mass differenceswith the PI-ICR technique (black line) as a function of accu-mulation time, t acc . For comparison, the achievable resolv-ing power with the Time-of-Flight Ion-Cyclotron-Resonance(TOF-ICR) technique (red line) is also shown. duce systematic uncertainties, the calibration was per-formed under the same experimental conditions as the Nb mass measurement, using the same accumulationtimes. A single contaminant species,
MoH , wasidentified in the Nb beam with an intensity roughly20 times weaker than the collected Nb ions. Accu-mulation times were chosen such that the contaminantmolecule and
Nb were completely resolved in the mea-sured spectra.Measurement of the
Nb cyclotron frequency wasachieved from several phase-accumulation times near190 ms. An example phase-measurement spectrum isprovided in Fig. 1. With the PI-ICR technique, an in-crease in the accumulation time results in a correspond-ing increase in mass resolving power of the measurement;this is presented in Fig. 2. As t acc increases, the spotsize FWHM also increases, which results in the drop-offfrom the extrapolation line. If a long-lived, excited statewere to occur in Nb within approximately 30 keV ofthe ground state, it could be partially obscured by thespot for t acc ≈ ≤ t acc ≤ / ≥
10 ms)excited states in
Nb. As the corresponding mass re-solving power surpasses the physical mass difference be-tween the ground state and any possible isomer, the twowould separate into resolved spots. The evolution of thespot FWHM with accumulation time was within the tol-erance that is expected due to Penning trap voltage in-stabilities, resulting in an exclusion limit of ≤ Nb was found to be − − I II III IV V
Time (s)
351 keV539 keV172 keV C oun t s T / ( s ) k e V k e V k e V Singh 2015Ha 2020This workMeasurement T = 1.097(21) T / ( s ) (a)(b) FIG. 3. (a) Illustration of the 14-s beam cycle used in the ex-periment. The data are gated on the 172-keV (2 +1 → +1 ), 351-keV (4 +1 → +1 ), and 539-keV (2 +2 → +1 ) transitions in Mo.Different stages of the time cycle are indicated at the topof the figure: (I) Room background; (II) Beam-on collection;(III) Beam-off collection; (IV) Mylar tape movement; and (V)Room background. Exponential functions fit to the ‘beam-off’ period are shown for each individual γ -ray transition. (b)The measured half-lives are provided along with the updatedevaluation of Ref. (Singh 2015: [20]) and recent measurementof Ref. (Ha 2020: [5]). The weighted mean (solid line) ± σ (dashed lines) of the three individual measurements from thiswork gives a value of T / = 1.097(21) s, which is consistentwith the work of Ha et al . [5] (1.10(5) s) but is ≈ % largerthan the adopted value (1.02(5) s). Ref. [19] which was adopted in the 2016 Atomic MassEvaluation [8]. In the previous work, the masses of sev-eral Nb isotopes, including
Nb, were measured withthe JYFLTRAP double Penning trap [19]. In that exper-iment, the expected isomer in
Nb was not observed,and there is no mention of a search for an isomer in
Nb. B. β -DECAY HALF-LIFE The most-recent NNDC evaluation of
Nb [20] re-ports a β -decay half-life of T / ) = 1.02(5) s. This isthe value reported in Ref. [21] from decay curves for the172- and 351-keV transition; other values ranging from Level (keV)20406080100 I (cid:96) ( % ) β - γ This work Ha 2020 De Frenne 2008 E Level (keV)002080100 1000 2000 3000 40004060 I β ( % ) FIG. 4. Accumulation of the apparent β -feeding strength of Nb as a function of excitation energy of the decay progeny,
Mo, from this work (red), Ha et al . (Ha 2020: [5]) (purple)and derived from γ -ray intensities given in the most-recentdata evaluation (De Frenne 2008: [16]) (black). A β -delayedneutron branch of 4.5(3) % for Nb is assumed [16]. β -decayhalf-life of Nb to be measured in this work with greaterprecision. Data were sorted into a two-dimensional ma-trix of HPGe γ -ray time relative to the beginning of thedata-collection cycle versus the measured energy of that γ ray. Exponential decay curves were obtained by ap-plying a cut on individual γ -ray energies and project-ing the data onto the timing axis. The decay half-lifewas obtained by fitting an exponential function with aconstant background to the beam-off portion of the cy-cle (indicated in Fig. 3). This process is presented forthree γ -ray transitions that depopulate low-lying excitedstates in Mo, namely the 172-keV (2 +1 → +1 ), 351-keV (4 +1 → +1 ), and 539-keV (2 +2 → +1 ) transitions. Aweighted mean of these values suggests that the β -decayhalf-life of Nb is T / = 1.097(21) s. The larger un-certainties of the data points for E γ = 351, 539 keV arereflective of lower statistics. This result is consistent withrecent measurement of Ha et al [5], which has a largeruncertainty (T / = 1.10(5) s). The improved precisionpoints to a discrepancy of ≈ % with the current adoptedvalue of 1.02(5) s [20]. C. APPARENT β -DECAY FEEDING Apparent β -decay feeding intensities have been ob-tained through a balance of the measured γ -ray in-tensities that feed and depopulate each level; the ex-panded level scheme is discussed in detail below. A β - delayed neutron-emission branch of 4.5(3) % for Nbis reported in the literature (see Refs. [22, 23], for ex-ample). Several Mo γ rays [24] were identified inthe coincidence data by setting gates at energies corre-sponding to transitions in this nucleus. For example,the strongest transition that depopulates the first ex-cited state at 95 keV is of mixed M E δ = -0.24(4) and total internal conversioncoefficient α = 0.355(22) [24]. A coincidence gate onthis γ ray revealed the two strongest transitions (whenfed from Nb β decay) at 138 keV and 254 keV. Forreference, I γ (254) ≈ % [ I γ (172)]. No γ rays from Mo → Tc β decay were observed.The total apparent β feeding to excited states in Mowas normalized to account for the adopted β -delayed neu-tron branch; accumulation as a function of level excita-tion energy is presented in Fig. 4 for this work, along withthat of Ref. [5] and Refs. [16, 21]. This highlights the all-too-common deficiencies of limited historical data avail-able in the literature, particularly concerning the decayproperties of neutron-rich isotopes in this region. Theadopted levels [16, 21] suggest that the average energyreleased from relaxation of the decay product, weightedby the quoted β -feeding intensities, is ≈
950 keV. In theproposed decay scheme of Ref. [5], this value increases byapproximately 30 % to ≈ β -decay Q value of9.931(10) MeV and lack of excited states observedabove 4 MeV implies that the Pandemonium effect [25]may be strong in this nucleus. Direct feeding of high-energy states embedded in a region of high level densitywould result in a cascade of low-energy, low-intensity γ rays that are below the threshold of sensitivity forthis measurement. As a result, the individual apparent β -feeding intensities are quoted as upper limits inTable I. Using the measured decay half-life, β -feedingintensities and adopted Q value, log- f t values have beencalculated using the NNDC LOGFT program [26]. Therange of extracted log- f t values, ≈ . − . , suggeststhat the observed excited states in Mo are most likelypopulated via a series of allowed or first-forbidden β decays.Since the adopted ground-state spin-parity assignmentof Nb is J π = 1 − [16], the β -feeding pattern should bedominated by allowed Gamow-Teller and Fermi decaysto J π = 0,1,2 − states in Mo, which must lie above thepairing gap in the even-even decay product. One wouldexpect these states to be connected to the lowest-lyinglevels via electric dipole decays; however, this is not thecase. Also, we do not report any excited 0 + states inthis work, while only a modest fraction of the observed β feeding proceeds to known 2 + levels. In fact, it wassurprising to find that at least half of the observed β feeding was to known states of spin J = 3 − . Thisdistribution of apparent β -feeding strength appears torule out a J π = 1 − assignment for the Nb groundstate, and is discussed in further detail below.
539 714724517 545 ,
550 590 , , , , , , ,
785 870 , , , , , , , , , , } }}} }} } Gate: 172 keV } C oun t s γ (keV) 15030060 FIG. 5. Background-subtracted, β -gated, γ - γ -coincidence matrix, gated on the well-known 172-keV (2 +1 → +1 ) transition in Mo, from (top) 0 keV to 1500 keV, and (bottom) 1500 keV to 3000 keV. The γ rays from transitions in Mo are labelledwith their energies. Note the change of y-axis scale at 750 keV in the top panel.
IV. OBSERVED γ DECAY OF MO Observed γ rays were assigned to Mo through in-spection of γ − γ coincidence relationships and β -decayhalf-life measurements. Placement of γ rays in the Modecay scheme was achieved through gating on knowntransitions that strongly depopulate low-lying excitedstates. Examples of background-subtracted projectionsof the γ - γ coincidence matrix used in this work, gatedon transitions that depopulate the established 172-keV( J π = 2 +1 ), 351-keV ( J π = 4 +1 ), 710-keV ( J π = 2 +2 ), 885-keV ( J π = 3 +1 ), and 1435-keV ( J π = 4 +2 ) levels are pre-sented in Figs. 5, 6, and 7, respectively. Where possible,the locations of excited states, and transitions that con-nect them, were confirmed by applying γ -ray coincidencegates to transitions lying higher in the level scheme. Thesame techniques were applied to confirm the identifica-tion of isobaric contamination in the data.Most relative γ -ray intensities, I γ , were determined bygating on a transition that depopulates the level to which the γ ray under inspection is directly feeding. Photopeakyields measured in the coincidence spectra were correctedfor their γ -ray detection efficiency, the gating transitiondetection efficiency and branching-ratio fraction, and, inthe case of the 172-keV gate, internal conversion. A the-oretical conversion coefficient of 0.171(2) was calculatedfor this transition using the BRICC code [27], assumingthat it is a pure E ≈ % forthe 351-keV (4 +1 → +1 ) transition. Different approacheswere taken for the three transitions that feed directly tothe ground state: I γ (172) was determined from the β -gated γ -ray singles data; I γ (710, 1150) were found bygating on transitions that feed into these excited states.The measured branching ratios of these two γ -ray tran-sitions were consistent with the corresponding I γ valuesmeasured from β -gated singles data. The I γ (172) valuesfrom this work are reported in Table I, with the 172-keV }}} Gate: 351 keV
172 363 ,
368 511545590 628652 784 ,
785 870 , E γ (keV)50 C oun t s FIG. 6. Background-subtracted, β -gated, γ - γ -coincidence matrix, gated on the well-known 351-keV (4 +1 → +1 ) transition in Mo, from (top) 0 keV to 1500 keV, and (bottom) 1500 keV to 3000 keV. The γ rays from transitions in Mo are labelledwith their energies. Note the change of y-axis scale at 250 keV in the top panel. transition normalised to 100 units.
A. EXCITED STATES OF Mo The work of Shizuma et al. in 1983 [21] was the firstto exploit β decay of Nb as a means to investigate thelevel structure of
Mo. For almost 40 years, this re-mained the only β -delayed γ -ray spectroscopy of Moreported in the literature. Structurally, much of what isknown on
Mo has come through high-fold, γ -ray spec-troscopy of prompt fission fragments with preferentialpopulation of high-spin states and extended rotationalbands [28–30]. At the time of writing, Ha et al. [5] exam-ined the role of triaxiality in − Mo via the β -decayof − Nb, extending the known level schemes of eachisotope.Shizuma et al [21] reported the location of the yrastJ π = 2 +1 , J π = 4 +1 and J π = 6 +1 states, and identifiedcandidates for the J π = 2 +2 , J π = 3 +1 and J π = 0 +2 lev- els, while the work of Ha et al [5] extended the levelscheme up to ≈ γ -ray transi-tions [5, 21], and further expand the level scheme up to ≈ γ -raytransitions. In this manuscript, transitions and levels re-ferred to as “new” are in relation to both Ref. [16] and therecent observations reported in Ref. [5]. The proposedexpansion of the level scheme is provided in Fig. 9. Four-teen of these excited states are associated with rotational-band structures identified in prompt spectroscopy of ac-tinide fission fragments [16]. A summary of the excitedstates observed in this work is provided in Table I, in-cluding level energies and spin-parity assignments, en-ergies and branching ratios of depopulating transitions,and apparent β -feeding intensities. Where possible, γ -decay branching ratios for transitions depopulating eachlevel have also been obtained by gating on a strong tran-sition that feeds the level under inspection. Transitionintensities reported in Ref. [5] are provided for reference (a)(b)(c)(d)Gate: 539 keVGate: 710 keVGate: 714 keVGate: 724 keV , C oun t s * * * * * *
613 878 * *** ** γ (keV) * FIG. 7. Background-subtracted, β -gated, γ - γ -coincidencematrix, gated on the established (a) 539-keV (2 +2 → +1 ), (b)710-keV (2 +2 → +1 ), (c) 714-keV (3 +1 → +1 ), and (d) 724-keV(4 +2 → +2 ) transitions in Mo, from 0 keV to 2500 keV. The γ rays from transitions in Mo are labelled with their en-ergies. A * indicates contamination from the energy gatesoverlapping nearby γ rays. where they are available.While the decay scheme has been extended extensivelyfrom Refs. [5, 21], the highest-lying level at ≈ ≈ β feeding occurs to a high-density re-gion of weakly populated states within this energy range.Such states are known to be beyond the sensitivity ofdiscrete-line spectroscopy, and so further measurementof this nucleus adopting a technique such as ‘total ab-sorption gamma-ray spectroscopy’ will be required. Forthis reason, limits are quoted for the apparent β -feedingintensities.In this study, we confirm the locations of most ex-cited states and transitions presented in Ref. [5]. Four γ rays were not observed: the 188-keV (2 +2 → +1 ), 175-keV(3 +1 → +2 ), 223-keV ( J π → − ), and 1624-keV (5 − → + )transitions. Examples of gated spectra in which the low-energy transitions would be expected are presented inFig. 8. The 1624-keV γ ray would be observed in the 351-keV gate of Fig. 6. With the proposed 188-keV, 223-keV,and 1624-keV transitions, we do not observe a significant
100 200 300 (a)(b)(c)Gate: 351 keVGate: 539 keVGate: 517 keV050100050100150 100050100150200 200 300
172 keV172 keV172 keV 188 keV175 keV223 keV E γ (keV) C oun t s FIG. 8. Background-subtracted projection of the β -gated, γ - γ -coincidence matrix, gated on the (a) 351-keV (4 + → + ), (b)539-keV (2 + → + ), and (c) 517-keV (J π → +(1) ) transitionsin Mo, from 100 keV to 300 keV. Expected locations ofthe unobserved γ rays from Ref. [5] are indicated by the redarrows and discussed in the text. rise above fluctuations in the background at these ener-gies. The 175-keV transition, if present, may be obscuredby the dominant 172-keV transition. Reference [5] lists a1930-keV (2815 → γ ray in coincidence with the 172-keV oneand therefore, suggest a different placement in the levelscheme with a new level at 2102 keV.We note two discrepancies with the low-lying statesobserved by Shizuma et al [21]: namely, the 957-keV( J π = (0 +2 )) level and the 1280-keV one of unknown spinand parity. Tentative placement of the 957-keV level wasbased on the observation of a 785-keV γ ray in coincidencewith the 172-keV transition. The non-observation of a957-keV γ ray connecting this level to the ground statewas suggested as evidence for this being the J π = 0 +2 level. Two γ rays with similar energies (784 keV and785 keV) depopulating the 2090-keV and 1307-keV lev-els, respectively, were identified in prompt-fission studies.Coincidence relationships observed in the current workare consistent with this decay pattern, and confirmed byRef. [5]. � + ���� + ������ + ������ + ������ � + ������ + ������ + ������� + ������ ( � - ) ������ ( � - ) ������ ( � - ) ������� + ������� + ������ ( � + ) ������ ( � + ) ������ ������������ ������������ ������������������ ������������������ ������������ ( � + ) ������������ ( � - ) ������������������ ( � - ) ������������������������������ ������������������������������ ������ ��������� ������������������������ ��� ���� ��� ���� ������� ���� ��� ���� ������ ��� ��� ��� ������� ��� ���� ��� Nb % β – = 100%0.0 ( ) J π ≥ 3 % β – n = 4.5(3)%Mo FIG. 9. Proposed level scheme of
Mo following the β decay of Nb. New excited states and γ -ray transitions are in red.Spins and parities, and the β -delayed neutron emission value are adopted from Ref. [16]. TABLE I: The γ -ray transitions and excited states in Mo observed in this work following the β decay of Nb. Initial-level(E i ), final-level (E f ) and γ -ray (E γ ) energies are given in keV; uncertainties are discussed in the text. Spins and paritiesare from Ref. [16] or proposed from the current work ( a ). Transition intensities (I γ ) are normalized to the 172-keV transition(100(2) units). Transition intensities (I litγ ) and β -feeding intensities (I litβ − ) presented in Ref. [5] are included here for comparison.Limitations of the apparent β -feeding intensities (I β − ) from this work are discussed in the text. For absolute intensity per 100parent decays multiply I γ by 0.71(8). E i J π i E γ E f J π f I γ I lit γ I β − I lit β − (keV) (keV) (keV) ( % ) ( % ) ( % ) ( % )0 0 + – – – – – 0 <8.4171.49(9) 2 + + + + + + + + + + + + + + + + + ) 628.0(4) 522.08(11) 4 + + + + + + + + + + + + ) 386.1(5) 1149.80(9) (2 + ) 1.4(4) 2.0(3) 1.0(2)1014.1(3) 522.08(11) 4 + + + + + + + + + + − ) 932.2(3) 885.07(12) 3 + + TABLE I – continued E i J π i E γ E f J π f I γ I lit γ I β − I lit β − (keV) (keV) (keV) ( % ) ( % ) ( % ) ( % )1882.15(21) 1359.7(5) 522.08(11) 4 + + + − ) 869.5(3) 1067.50(12) 4 + + + − ) 517.4(2) 1434.78(12) 4 + + a + − ) 783.5(2) 1306.60(19) 5 + + + + a + − ) 1113.6(7) 1033.08(23) 6 + a + + a + a + + ) 1781.2(3) 522.08(11) 4 + a + a + − ) a a a − ) 0.5(1)1363.9(3) 1434.78(12) 4 + + − ) 1.4(2) 2.0(3) 3.5(2)998.5(4) 1817.26(23) (3 − ) 1.4(3) 2.3(1)2898.3(5) 2013.2(4) 885.07(12) 3 + a + + + a + TABLE I – continued E i J π i E γ E f J π f I γ I lit γ I β − I lit β − (keV) (keV) (keV) ( % ) ( % ) ( % ) ( % )3814.8(6) (4,5) a + a + While the location of the J π = 0 +2 state is certainlynot at 957 keV, several candidates are described below.However, further experiments are necessary to confirmthe location and nature of these levels. Similarly, the1280-keV level was suggested on the basis of an 1108-keV γ -ray transition also found to be in coincidence with the172-keV one. Our analysis instead supports the place-ment of the 1108-keV transition as connecting the (3 − )state at 1817 keV to the 2 + state at 710 keV. The repo-sitioning of this γ -ray transition is also noted in Ref. [5],so there is no excited state at 1280 keV. Confirmation of known states
The 2 + g , 4 + g , and 6 + g members of the yrast rotationalband built on a prolate-deformed 0 + ground state ( g )have been identified. While the locations of the 8 + g and10 + g members are known [16], they are not fed by β -decay.The band built on the K π = 2 + ( γ band), 710-keV levelis observed up to the 5 + γ member at 1307 keV.Intra-band, ∆ J = 2 transitions (4 + γ → + γ and 5 + γ → + γ )were identified, however there was no evidence for ∆ J = 1transitions between the band levels. Known inter-band transitions between the γ and ground-state bandswere observed, with the exception of the spin-increasing5 + γ → + g one. Branching ratios measured in the currentwork indicate that the 2 + γ → + g decay path is slightlyenhanced with respect to the 2 + γ → + g transition.The strongest γ ray observed to feed the K π = 2 + bandhead is the 724-keV transition from the K = 4, 1435-keV level. Guessous et al identified this as a candidatedouble-phonon γ -vibrational state [31]. The known 5 + member of this band is also identified in the current work,although the 223-keV transition between these two lev-els was not observed. Three levels corresponding to a K π = 3 − , negative-parity band, suggested to arise froma ν [411] ⊗ ν [532] configuration [16], have been identi-fied in this work. The γ rays connecting each of thelevels in this sequence to the γ -vibrational band were ob-served. Two levels associated with a proposed K π = (2 + )band were also identified at 1150 keV and 1536 keV.Bandheads of the three other two-quasiparticle structureslisted in the adopted levels have been observed: the (5 − ),1952-keV level ( ν [413] ⊗ ν [532]); the (5 − ), 2147-keVstate ( π [413] ⊗ π [301]); and the (5 + ), 2302-keV level( π [420] ⊗ π [404]). A single γ ray was observed to de-populate each of these states; any other depopulating transitions that may occur fall below the level of sensi-tivity, I γ ≥ × I , of the present measurement. Identification of new states
Seventeen previously unobserved excited states havebeen added in this work: ten decay directly by singletransitions to levels within the yrast band, three are con-nected to the γ band, and four are connected to theproposed harmonic, two-phonon γ -vibrational state [31].While it is not possible to assign firm spins and paritiesto these new levels with the current data, it was possibleto place spin constraints on some from the observed de-cay pattern. Where available, these are described in thetext. Spin-parity assignments listed in Table I withoutparentheses are taken from the literature [16].Nine excited states are each observed to have a sin-gle γ -decay branch that connects it to one of the lev-els with a firm 4 + assignment. The weak apparent β -feeding intensities and lack of γ -decay branches to 2 + or3 + states suggest these are of moderate spin, and so a J = (4) or (5) assignment is suggested for these lev-els. The excited state at 2799 keV is unusual in that theapparent β -feeding intensity is larger than that of anyother state observed above 2-MeV excitation energy, andmultiple γ -decay pathways from the state were identified.Strong feeding to the 1435-keV, 4 + level and two J = 3 levels and relatively low log- f t value of 6.07(1) suggesta tentative J π = (4 − ) assignment is appropriate for thislevel. V. DISCUSSION AND CONCLUSIONS
The neutron-rich nuclei at A ≈
100 have proven to betechnically challenging from both experimental and the-oretical points of view. Ground-state charge-radii mea-surements point to a rapid spherical-to-prolate-deformedshape transition between N = 58 and N = 60 [32] sim-ilar to the well-established phenomenon observed be-tween stable N = 88 and N = 90 rare-earth nuclei[33]. This phenomenon appears to be strongest in zir-conium ( Z = 40) [34], persists in neighbouring strontium( Z = 38) [35] and weakens in molybdenum ( Z = 42) [36],an effect attributed to the triaxial nature of the latter iso-topes. This is supported by local trends in E (2 +1 ) and B ( E
2; 0 +2 → +1 ) values [37].3Coulomb-excitation measurements with radioactive-ion beams [38, 39] indicate that shape coexistence isprevalent in the region [40], whereby deformed J π = 0 +2 states at N <
60 migrate to become the ground statesat N ≥
60. Quantum phase transitions have been at-tributed as the driving force behind this rapid evolutionof the nuclear shape [41, 42]. Beyond N = 60, thereis increasing evidence that the deformation softens to-wards the neutron drip-line and that the triaxial degreeof freedom plays in an important role in the behaviour ofneutron-rich molybdenum isotopes [43–49].The picture becomes more complex in the adjacent,odd- Z niobium ( Z = 41) isotopes. In the case of Nb( N = 65), only a single investigation into the levelscheme exists in the literature from prompt-fission spec-troscopy [50]; direct observation of the β -decay prop-erties of this nuclide are similarly rare. Initial obser-vation of strong β -decay feeding to J = 4 , excitedstates in Mo prompted further investigation. Lighter-mass, odd-odd Nb isotopes exhibit an alternating patternof low-spin/high-spin β -decaying ground states and iso-mers. At Nb, the traditional N = 64 neutron sub-shellclosure is crossed, exposing a new valence space. Whileit is unlikely that the pattern of β -decaying isomers (seeabove) continues into Nb, it could explain the observedpattern in the γ -decay measurement.As discussed above, the new results indicate thatthe ground-state spin-parity assignment to Nb shouldbe revised. The adopted assignment, J π = (1 − ), ofRef. [16] is based upon potential-energy surface (PES)and projected shell-model (PSM) calculations presentedin Ref. [50]. They predict a triaxial π − [301] (cid:78) ν
52 + [413] ground state with ( β , γ ) = (0.35,15 ◦ ) deformation pa-rameters. At ( Z, N ) = (41,65),
Nb lies a long wayfrom the single stable isotope, Nb. Naively, one mightpredict the ground-state configuration to be dominatedby a two-quasiparticle coupling of the odd proton andneutron outside the Z = 40 and N = 64 sub-shell clo-sures, respectively. The works of Kurpeta et al. [51]and Urban et al. [52] provide the most-recent consider-ations of the neighbouring isotope, Nb, and its iso-bar,
Mo. They suggest (5/2 + ) and 1/2 + groundstates, respectively, for these nuclides from a combina-tion of β -decay feeding and assessment of systematictrends. A prolate π
52 + [422] (cid:78) ν
12 + [411] configurationwith ( β , γ ) = (0.32,0) was predicted for Nb in thePES calculations of Ref. [50], however the excitation en-ergy is 597 keV. With maximal spin coupling, as per theGallagher-Moszkowski coupling rule [53], a favoured 3 + assignment would be expected. A 3 + ground state couldexplain most of the β -decay feeding pattern observed inthis work; the feeding to 3 ± , and 4 ± states would thenbe accessible from allowed and first-forbidden β decays.The observed feeding to 5 ± states would favour a J π = (4 ± ) assignment. Maximal spin coupling of the π − [301] (cid:78) ν
52 + [413] configuration from Ref. [50] dis-cussed above would result in a J π = 4 − ground state; this assignment would violate the Gallagher-Moszkowskirule [53]. The requirement of such highly forbidden β decays to explain the observed feeding from a supposed1 − ground state cannot be ignored. In light of our decaystudy, non-observation of a β -decaying isomer from ourmass measurement, and the recent work of Ha et al [5],it is clear that the assumption of a J π = 1 − ground stateis incorrect and the spin assignments of all excited statesin Nb are in need of a full reappraisal.If the
Nb ground-state spin and parity were J = 3 + ,any β decay to the Mo ground state is ∆ J = 3 , ∆ π = 0 . This would be a unique, second-forbidden de-cay. In nature, 12 such cases are documented [54], withthe minimum log- f t being 13.9. With our new mass anddecay half-life measurements, this would correspond to abranch of < − % – far below the experimental sensi-tivity and sufficiently close to zero to not influence thecalculated distribution of strength or normalization. Ifthe spin and parity of Nb is J = 4 − , the ground-state β decay is unique, third forbidden. The only documentedexample of such a decay in the periodic table has a log- f t value of 21, implying that the branch is < − % .While the interpretation of Nb is uncertain, the pic-ture is much clearer for
Mo. Several theoretical studies[55–59] point to an emergence of triaxial softness in theneutron-rich molybdenum isotopes beyond N = 60 . Ineach case, triaxiality is essential to reproduce experimen-tal observations. This undoubtedly contributes to theevolution of collectivity across the isotopic chain.The distribution of excited states in Mo directlyfed by the β decay of Nb has been mapped up to ≈ β -feeding strength is observed between 1 MeV and2 MeV. An appreciable difference exists from the patternof feeding to low-lying states reported in Ref. [16]. Ref-erence [5] reports an upper limit of 8.4 % direct feedingto the ground state; a 4 − → + β transition most cer-tainly would not be observed with such a large intensity,or short decay half-life. While the possibility of a uniquefirst-forbidden decay (4 − → + ) cannot be excluded by thelog- f t values, the large intensity ( < . ) is unusual forsuch a decay mode. Large feeding intensities that resultfrom suggested unique first-forbidden β decay have alsobeen reported in neighbouring , Mo [5]. However,the apparent feeding intensities are also susceptible tostrong Pandemonium effects, discussed above.Several of the new excited states observed in this workmay be considered candidates for the elusive first-excited J π = 0 + state. If the Nb ground state has a J ≥ J π = 0 + statewould not be fed directly from β -decay. Shape co-existence appears to be well established in the regionand, therefore, one would expect to observe a low-lying J π = 0 + excited state in Mo; excited J π = 0 +2 statesin , Mo are reported at 893.4 keV and 1042.2 keV,respectively, in Ref. [5]. Of the 17 new levels in
Mo,seven are observed to decay via a single transition to the J π = 2 +1 state. The present data are sensitive to γ rays4with intensities of ≈ % relative to the 172-keV tran-sition. While the possibility of weak ground-state feed-ing or branches to other states below this level of sensi-tivity cannot be ruled out, determining the true natureand location of any J π = 0 + levels will require dedicatedexperimental searches. A search for mono-energetic E J π = 0 +2 level tothe ground state might be productive; this would be thepreferred decay mode if the co-existence is strong and the J π = 0 +2 state lies only tens of keV above the J π = 2 +1 level.In the A ≈
100 neutron-rich nuclei, despite very largedeformation, K -isomers have not been found, possiblydue to the fragility of the shell-stabilised shapes. In thisspecific case, the combination of a high Q -value for Nb β decay and soft shapes in the decay product leads tounusually large fragmentation, both in β -decay strengthand the subsequent γ -decay cascade. This, then, appearsto be a situation where ‘Pandemonium’ must occur, andso inferring the population of individual states from theobserved γ intensity balance becomes problematic. Infer-ring log- f t values, and thus spin assignments and struc-ture information, from these β -decay branches, as sug-gested by Ha et al [5], may be optimistic.In summary, ground-state and β -decay properties ofthe very-neutron-rich nuclide Nb have been studiedat the CARIBU facility at Argonne National Labora-tory. The ground-state mass of
Nb was measured tobe − β -decaying isomer above ≈ Nb. Detailed β -delayed γ -ray spectroscopy of theprogeny, Mo, was performed with the X-Array andSATURN low-energy decay-spectroscopy station. The β -decay half-life was found to be T / = 1.097(21) s. Thedecay scheme of Mo has been extended up to ≈ β -feeding inten- sity to J = 3-5 states in Mo, and non-observationof a β -decaying isomer, leads to the conclusion that theground-state spin-parity assignment for Nb, and thoseof excited states in this nuclide, should be reassessed.In future measurements with the X-Array, the additionof the MR-TOF separator to the CARIBU low-energybeam line and development of a new low-background,low-energy experimental hall will greatly improve thebeam purity and sensitivity of decay-spectroscopyexperiments. This work highlights the pressing needfor considerable theoretical effort to enable accurateinterpretation of spectroscopic data obtained for very-neutron-rich exotic niobium isotopes.
VI. ACKNOWLEDGEMENTS
The authors wish to acknowledge the excellent workof the Physics Support group of the ATLAS Facilityat Argonne National Laboratory. This material isbased upon work supported by the Australian Re-search Council Discovery Project 120104176 (ANU),the U.S. Department of Energy, Office of Science,Office of Nuclear Physics under Grants No. DE-FG02-94ER40848 (UML), No. DEFG02-97ER41041 (UNC),and No. DE-FG02-97ER41033 (TUNL), and Con-tract No. DE-AC02-06CH11357 (ANL), the NationalNuclear Security Administration, Office of DefenseNuclear Nonproliferation R&D (NA-22) and NSERC(Canada) under Contract No. SAPPJ-2015-00034.This research used resources of ANL’s ATLAS facil-ity, which is a DOE Office of Science User Facility.Fig. 9 in this article has been created using the Lev-elScheme scientific figure preparation system [M. A.Caprio, Comput. Phys. Commun. 171, 107 (2005), http://scidraw.nd.edu/levelscheme ]. [1] E. M. Burbidge, G. R. Burbidge, W. A. Fowler, andF. Hoyle, Reviews of Modern Physics , 547 (1957).[2] “Assessment of Fission Product Decay Data for DecayHeat Calculations, Nuclear Science, NEA/WPEC-25, In-ternational Evaluation Co-operation,” A report by theWorking Party on International Evaluation Co-operationof the NEA Nuclear Science Committee.[3] M. R. Mumpower, R. Surman, G. C. McLaughlin, andA. Aprahamian, Progress in Particle and Nuclear Physics , 86 (2016).[4] K. Langanke and G. Martínez-Pinedo, Rev. Mod. Phys. , 819 (2003).[5] J. Ha, T. Sumikama, F. Browne, N. Hinohara, A. M.Bruce, S. Choi, I. Nishizuka, S. Nishimura, P. Door-nenbal, G. Lorusso, P.-A. Söderström, H. Watanabe,R. Daido, Z. Patel, S. Rice, L. Sinclair, J. Wu, Z. Y.Xu, A. Yagi, H. Baba, N. Chiga, R. Carroll, F. Didier-jean, Y. Fang, N. Fukuda, G. Gey, E. Ideguchi, N. Inabe, T. Isobe, D. Kameda, I. Kojouharov, N. Kurz, T. Kubo,S. Lalkovski, Z. Li, R. Lozeva, H. Nishibata, A. Oda-hara, Z. Podolyák, P. H. Regan, O. J. Roberts, H. Saku-rai, H. Schaffner, G. S. Simpson, H. Suzuki, H. Takeda,M. Tanaka, J. Taprogge, V. Werner, and O. Wieland,Phys. Rev. C , 044311 (2020).[6] G. Savard, S. Baker, C. Davids, A. F. Levand, E. F.Moore, R. C. Pardo, R. Vondrasek, B. J. Zabransky, andG. Zinkann, Nuclear Instruments and Methods in PhysicsResearch Section B: Beam Interactions with Materialsand Atoms , 4086 (2008).[7] J. Van Schelt, D. Lascar, G. Savard, J. A. Clark, P. F.Bertone, S. Caldwell, A. Chaudhuri, A. F. Levand, G. Li,G. E. Morgan, R. Orford, R. E. Segel, K. S. Sharma, andM. G. Sternberg, Phys. Rev. Lett. , 061102 (2013).[8] M. Wang, G. Audi, F. G. Kondev, W. J. Huang, S. Naimi,and X. Xu, Chinese Physics C , 030003 (2017). [9] T. Y. Hirsh, N. Paul, M. Burkey, A. Aprahamian,F. Buchinger, S. Caldwell, J. A. Clark, A. F. Levand,L. L. Ying, S. T. Marley, G. E. Morgan, A. Nystrom,R. Orford, A. P. Galván, J. Rohrer, G. Savard, K. S.Sharma, and K. Siegl, Nuclear Instruments and Meth-ods in Physics Research Section B: Beam Interactionswith Materials and Atoms , 229 (2016), proceedingsof the XVIIth International Conference on Electromag-netic Isotope Separators and Related Topics (EMIS2015),Grand Rapids, MI, U.S.A., 11-15 May 2015.[10] N. E. Bradbury and R. A. Nielsen, Phys. Rev. , 388(1936).[11] S. Eliseev, K. Blaum, M. Block, C. Droese, M. Gon-charov, E. Minaya Ramirez, D. A. Nesterenko, Y. N.Novikov, and L. Schweikhard, Phys. Rev. Lett. ,082501 (2013).[12] R. Orford, N. Vassh, J. A. Clark, G. C. McLaughlin,M. R. Mumpower, G. Savard, R. Surman, A. Apra-hamian, F. Buchinger, M. T. Burkey, D. A. Gorelov,T. Y. Hirsh, J. W. Klimes, G. E. Morgan, A. Nystrom,and K. S. Sharma, Phys. Rev. Lett. , 262702 (2018).[13] R. Orford, J. A. Clark, G. Savard, A. Aprahamian,F. Buchinger, M. T. Burkey, D. A. Gorelov, J. W.Klimes, G. E. Morgan, A. Nystrom, W. S. Porter, D. Ray,and K. S. Sharma, Nuclear Instruments and Methods inPhysics Research Section B: Beam Interactions with Ma-terials and Atoms , 491 (2020).[14] A. J. Mitchell, P. F. Bertone, B. DiGiovine, C. J.Lister, M. P. Carpenter, P. Chowdhury, J. A. Clark,N. D’Olympia, A. Y. Deo, F. G. Kondev, E. A. Mc-Cutchan, J. Rohrer, G. Savard, D. Seweryniak, andS. Zhu, Nuclear Instruments and Methods in Physics Re-search Section A: Accelerators, Spectrometers, Detectorsand Associated Equipment , 232 (2014).[15] A. J. Mitchell, C. J. Lister, E. A. McCutchan, M. Al-bers, A. D. Ayangeakaa, P. F. Bertone, M. P. Carpen-ter, C. J. Chiara, P. Chowdhury, J. A. Clark, P. Copp,H. M. David, A. Y. Deo, B. DiGiovine, N. D’Olympia,R. Dungan, R. D. Harding, J. Harker, S. S. Hota, R. V. F.Janssens, F. G. Kondev, S. H. Liu, A. V. Ramayya,J. Rissanen, G. Savard, D. Seweryniak, R. Shearman,A. A. Sonzogni, S. L. Tabor, W. B. Walters, E. Wang,and S. Zhu, Physical Review C , 014306 (2016).[16] D. De Frenne and A. Negret, Nuclear Data Sheets ,943 (2008).[17] K. Siegl, K. Kolos, N. D. Scielzo, A. Aprahamian,G. Savard, M. T. Burkey, M. P. Carpenter, P. Chowd-hury, J. A. Clark, P. Copp, G. J. Lane, C. J. Lister, S. T.Marley, E. A. McCutchan, A. J. Mitchell, J. Rohrer,M. L. Smith, and S. Zhu, Phys. Rev. C , 054307(2018).[18] D. Radford, “ gf3 program,” https://radware.phy.ornl.gov/main.html , accessed: 2020-07-14.[19] U. Hager, A. Jokinen, V. V. Elomaa, T. Eronen,J. Hakala, A. Kankainen, S. Rahaman, J. Rissanen, I. D.Moore, S. Rinta-Antila, A. Saastamoinen, T. Sonoda,and J. Äystö, Nuclear Physics A , 20 (2007).[20] B. Singh, Evaluated Nuclear Structure Data Files (2015).[21] K. Shizuma, H. Lawin, and K. Sistemich, Zeitschrift fürPhysik A Atoms and Nuclei , 71 (1983).[22] M. B. Gómez-Hornillos, J. Rissanen, J. L. Taín, A. Al-gora, K. L. Kratz, G. Lhersonneau, B. Pfeiffer, J. Agra-munt, D. Cano-Ott, V. Gorlychev, R. Caballero-Folch,T. Martínez, L. Achouri, F. Calvino, G. Cortés, T. Ero- nen, A. García, M. Parlog, Z. Podolyak, C. Pretel, andE. Valencia, Hyperfine Interactions , 185 (2014).[23] J. Pereira, S. Hennrich, A. Aprahamian, O. Arndt, A. Be-cerril, T. Elliot, A. Estrade, D. Galaviz, R. Kessler, K.-L.Kratz, G. Lorusso, P. F. Mantica, M. Matos, P. Möller,F. Montes, B. Pfeiffer, H. Schatz, F. Schertz, L. Schnor-renberger, E. Smith, A. Stolz, M. Quinn, W. B. Walters,and A. Wöhr, Phys. Rev. C , 035806 (2009).[24] S. Lalkovski, J. Timar, and Z. Elekes, Nuclear DataSheets , 1 (2019).[25] J. C. Hardy, L. C. Carraz, B. Jonson, and P. G. Hansen,Physics Letters B , 307 (1977).[26] “National Nuclear Data Centre LOG-FT program,” , accessed: 2020-07-14.[27] T. Kibédi, T. W. Burrows, M. B. Trzhaskovskaya, P. M.Davidson, and C. W. Nestor Jr., Nuclear Instrumentsand Methods in Physics Research Section A: Acceler-ators, Spectrometers, Detectors and Associated Equip-ment , 202 (2008).[28] H. Hua, C. Y. Wu, D. Cline, A. B. Hayes, R. Teng, R. M.Clark, P. Fallon, A. Goergen, A. O. Macchiavelli, andK. Vetter, Physical Review C , 014317 (2004).[29] E. F. Jones, P. M. Gore, S. J. Zhu, J. H. Hamilton, A. V.Ramayya, J. K. Hwang, R. Q. Xu, L. M. Yang, K. Li,Z. Jiang, Z. Zhang, S. D. Xiao, X. Q. Zhang, W. C. Ma,J. D. Cole, M. W. Drigert, I. Y. Lee, J. O. Rasmussen,Y. X. Luo, and M. A. Stoyer, Physics of Atomic Nuclei , 1198 (2006).[30] X. Rui-Qing, Z. Sheng-Jiang, J. H. Hamilton, A. V. Ra-mayya, J. K. Hwang, X. Q. Zhang, L. Ke, Y. Li-Ming,Z. Ling-Yan, G. Cui-Yun, Z. Zheng, J. Zhuo, X. Shu-Dong, W. C. Ma, J. Kormicki, E. F. Jones, J. D. Cole,R. Aryaeinejad, M. W. Drigert, I. Y. Lee, J. O. Ras-mussen, M. A. Stoyer, G. M. Ter-Akopian, and A. V.Daniel, Chinese Physics Letters , 180 (2002).[31] A. Guessous, N. Schulz, W. R. Phillips, I. Ahmad,M. Bentaleb, J. L. Durell, M. A. Jones, M. Leddy,E. Lubkiewicz, L. R. Morss, R. Piepenbring, A. G. Smith,W. Urban, and B. J. Varley, Physical Review Letters ,2280 (1995).[32] R. Rodríguez-Guzmán, P. Sarriguren, L. M. Robledo,and S. Perez-Martin, Physics Letters B , 202 (2010).[33] R. F. Casten, Nature Physics , 811 (2006).[34] P. Campbell, H. L. Thayer, J. Billowes, P. Dendooven,K. T. Flanagan, D. H. Forest, J. A. R. Griffith,J. Huikari, A. Jokinen, R. Moore, A. Nieminen, G. Tun-gate, S. Zemlyanoi, and J. Äystö, Phys. Rev. Lett. ,082501 (2002).[35] F. Buchinger, E. B. Ramsay, E. Arnold, W. Neu, R. Neu-gart, K. Wendt, R. E. Silverans, P. Lievens, L. Ver-meeren, D. Berdichevsky, R. Fleming, D. W. L. Sprung,and G. Ulm, Phys. Rev. C , 2883 (1990).[36] F. C. Charlwood, K. Baczynska, J. Billowes, P. Camp-bell, B. Cheal, T. Eronen, D. H. Forest, A. Jokinen,T. Kessler, I. D. Moore, H. Penttilä, R. Powis, M. Rüf-fer, A. Saastamoinen, G. Tungate, and J. Äystö, PhysicsLetters B , 23 (2009).[37] B. Pritychenko, M. Birch, B. Singh, and M. Horoi,Atomic Data and Nuclear Data Tables , 1 (2016).[38] A. Görgen and W. Korten, Journal of Physics G: Nuclearand Particle Physics , 024002 (2016).[39] E. Clément, M. Zielińska, A. Görgen, W. Korten, S. Péru,J. Libert, H. Goutte, S. Hilaire, B. Bastin, C. Bauer,A. Blazhev, N. Bree, B. Bruyneel, P. A. Butler, J. But- terworth, P. Delahaye, A. Dijon, D. T. Doherty, A. Ek-ström, C. Fitzpatrick, C. Fransen, G. Georgiev, R. Gern-häuser, H. Hess, J. Iwanicki, D. G. Jenkins, A. C.Larsen, J. Ljungvall, R. Lutter, P. Marley, K. Moschner,P. J. Napiorkowski, J. Pakarinen, A. Petts, P. Reiter,T. Renstrøm, M. Seidlitz, B. Siebeck, S. Siem, C. Sotty,J. Srebrny, I. Stefanescu, G. M. Tveten, J. Van deWalle, M. Vermeulen, D. Voulot, N. Warr, F. Wenan-der, A. Wiens, H. De Witte, and K. Wrzosek-Lipska,Physical Review Letters , 022701 (2016).[40] K. Heyde and J. L. Wood, Rev. Mod. Phys. , 1467(2011).[41] T. Togashi, Y. Tsunoda, T. Otsuka, and N. Shimizu,Physical Review Letters , 172502 (2016).[42] C. Kremer, S. Aslanidou, S. Bassauer, M. Hilcker,A. Krugmann, P. von Neumann-Cosel, T. Otsuka,N. Pietralla, V. Y. Ponomarev, N. Shimizu, M. Singer,G. Steinhilber, T. Togashi, Y. Tsunoda, V. Werner, andM. Zweidinger, Physical Review Letters , 172503(2016).[43] W. Urban, T. Rząca-Urban, J. L. Durell, W. R. Phillips,A. G. Smith, B. J. Varley, I. Ahmad, and N. Schulz, TheEuropean Physical Journal A - Hadrons and Nuclei ,381 (2004).[44] A. G. Smith, D. Patel, G. S. Simpson, R. M. Wall, J. F.Smith, O. J. Onakanmi, I. Ahmad, J. P. Greene, M. P.Carpenter, T. Lauritsen, C. J. Lister, R. V. F. Janssens,F. G. Kondev, D. Seweryniak, B. J. P. Gall, O. Dorvaux,and B. Roux, Physics Letters B , 55 (2004).[45] D. Huai-Bo, Z. Sheng-Jiang, J. H. Hamilton, A. V. Ra-mayya, J. K. Hwang, Y. X. Luo, J. O. Rasmussen,I. Lee, C. Xing-Lai, W. Jian-Guo, and X. Qiang, ChinesePhysics Letters , 1517 (2007).[46] H. Watanabe, K. Yamaguchi, A. Odahara, T. Sumikama,S. Nishimura, K. Yoshinaga, Z. Li, Y. Miyashita, K. Sato,L. Prachniak, H. Baba, J. S. Berryman, N. Blasi,A. Bracco, F. Camera, J. Chiba, P. Doornenbal, S. Go,T. Hashimoto, S. Hayakawa, C. Hinke, N. Hinohara,E. Ideguchi, T. Isobe, Y. Ito, D. G. Jenkins, Y. Kawada,N. Kobayashi, Y. Kondo, R. Kracken, S. Kubono,G. Lorusso, T. Nakano, T. Nakatsukasa, M. Kurata-Nishimura, H. J. Ong, S. Ota, Z. Podolyak, H. Saku-rai, H. Scheit, K. Steiger, D. Steppenbeck, K. Sugi-moto, K. Tajiri, S. Takano, A. Takashima, T. Teranishi,Y. Wakabayashi, P. M. Walker, O. Wieland, and H. Ya-maguchi, Physics Letters B , 270 (2011).[47] A. G. Smith, J. L. Durell, W. R. Phillips, W. Urban,P. Sarriguren, and I. Ahmad, Phys. Rev. C , 014321(2012).[48] J. B. Snyder, W. Reviol, D. G. Sarantites, A. V. Afanas-jev, R. V. F. Janssens, H. Abusara, M. P. Carpenter,X. Chen, C. J. Chiara, J. P. Greene, T. Lauritsen, E. A.McCutchan, D. Seweryniak, and S. Zhu, Physics LettersB , 61 (2013).[49] D. Ralet, S. Pietri, T. Rodríguez, M. Alaqeel, T. Alexan-der, N. Alkhomashi, F. Ameil, T. Arici, A. Ataç, R. Avigo, T. Bäck, D. Bazzacco, B. Birkenbach,P. Boutachkov, B. Bruyneel, A. M. Bruce, F. Cam-era, B. Cederwall, S. Ceruti, E. Clément, M. L.Cortés, D. Curien, G. De Angelis, P. Désesquelles,M. Dewald, F. Didierjean, C. Domingo-Pardo, M. Don-cel, G. Duchêne, J. Eberth, A. Gadea, J. Gerl,F. Ghazi Moradi, H. Geissel, T. Goigoux, N. Goel, P. Gol-ubev, V. González, M. Górska, A. Gottardo, E. Gregor,G. Guastalla, A. Givechev, T. Habermann, M. Hackstein,L. Harkness-Brennan, G. Henning, H. Hess, T. Hüyük,J. Jolie, D. S. Judson, A. Jungclaus, R. Knoebel, I. Ko-jouharov, A. Korichi, W. Korten, N. Kurz, M. Labiche,N. Lalović, C. Louchart-Henning, D. Mengoni, E. Mer-chán, B. Million, A. I. Morales, D. Napoli, F. Naqvi,J. Nyberg, N. Pietralla, Z. Podolyák, A. Pullia, A. Proc-hazka, B. Quintana, G. Rainovski, M. Reese, F. Rec-chia, P. Reiter, D. Rudolph, M. D. Salsac, E. Sanchis,L. G. Sarmiento, H. Schaffner, C. Scheidenberger, L. Sen-gele, B. S. N. Singh, P. P. Singh, C. Stahl, O. Ste-zowski, P. Thoele, J. J. Valiente Dobon, H. Weick,A. Wendt, O. Wieland, J. S. Winfield, H. J. Woller-sheim, and M. Zielinska (for the PreSPEC and PreSPECand AGATA Collaborations), Phys. Rev. C , 034320(2017).[50] Y. X. Luo, J. O. Rasmussen, J. H. Hamilton, A. V. Ra-mayya, E. Wang, Y. X. Liu, C. F. Jiao, W. Y. Liang,F. R. Xu, Y. Sun, S. Frauendorf, J. K. Hwang, S. H. Liu,S. J. Zhu, N. T. Brewer, I. Y. Lee, G. M. Ter-Akopian,Y. Oganessian, R. Donangelo, and W. C. Ma, Phys. Rev.C , 044326 (2014).[51] J. Kurpeta, A. Płochocki, W. Urban, A. Abramuk,L. Canete, T. Eronen, A. Fijałkowska, S. Geldhof,K. Gotowicka, A. Jokinen, A. Kankainen, I. D. Moore,D. Nesterenko, H. Penttilä, I. Pohjalainen, M. Pomorski,M. Reponen, S. Rinta-Antila, A. de Roubin, T. Rząca-Urban, M. Vilén, and J. Wiśniewski, Phys. Rev. C ,034316 (2019).[52] W. Urban, T. Rząca-Urban, J. Wiśniewski, J. Kurpeta,A. Płochocki, J. P. Greene, A. G. Smith, and G. S.Simpson, Phys. Rev. C , 024318 (2020).[53] C. J. Gallagher and S. A. Moszkowski, Phys. Rev. ,1282 (1958).[54] B. Singh, J. Rodriguez, S. Wong, and J. Tuli, NuclearData Sheets , 487 (1998).[55] J. Skalski, S. Mizutori, and W. Nazarewicz, NuclearPhysics A , 282 (1997).[56] C. L. Zhang, G. H. Bhat, W. Nazarewicz, J. A. Sheikh,and Y. Shi, Phys. Rev. C , 034307 (2015).[57] J. Xiang, J. M. Yao, Y. Fu, Z. H. Wang, Z. P. Li, andW. H. Long, Phys. Rev. C , 054324 (2016).[58] H. Abusara, S. Ahmad, and S. Othman, Phys. Rev. C , 054302 (2017).[59] K. Nomura, R. Rodríguez-Guzmán, and L. M. Robledo,Phys. Rev. C94