Fast-timing study of 81 Ga from the β decay of 81 Zn
V. Paziy, L.M. Fraile, H. Mach, B. Olaizola, G.S. Simpson, A. Aprahamian, C. Bernards, J.A. Briz, B. Bucher, C.J. Chiara, Z. Dlouhý, I. Gheorghe, D. Ghiţǎ, P. Hoff, J. Jolie, U. Köster, W. Kurcewicz, R. Licǎ, N. Mǎrginean, R. Mǎrginean, J.-M. Régis, M. Rudigier, T. Sava, M. Stǎnoiu, L. Stroe, W.B. Walters
FFast-timing study of Ga from the β decay of Zn V. Paziy, L.M. Fraile, ∗ H. Mach,
1, 2, † B. Olaizola, ‡ G.S. Simpson, A. Aprahamian, C. Bernards,
5, 6
J.A. Briz, B. Bucher, C. J. Chiara,
9, 10, § Z. Dlouhý, ¶ I. Gheorghe, D. Ghiţˇa, P. Hoff, J. Jolie, U. Köster, W. Kurcewicz, R. Licˇa, N. Mˇarginean, R. Mˇarginean, J.-M. Régis, M. Rudigier, ∗∗ T. Sava, M. Stˇanoiu, L. Stroe, and W.B. Walters Grupo de Física Nuclear & IPARCOS, Facultad de Ciencias Físicas,Universidad Complutense - CEI Moncloa, E-28040 Madrid, Spain National Centre for Nuclear Research, BP1, ul. Hoża 69, 00-681, Warsaw, Poland LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, F-38026 Grenoble Cedex, France Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA Institut für Kernphysik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06520, USA Instituto de Estructura de la Materia, CSIC, 28006 Madrid, Spain Idaho National Laboratory, Idaho Falls, Idaho 83415, USA Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA Nuclear Physics Institute of the AS CR, Z-25068, Řež, Czech Republic "Horia Hulubei"National Institute for Physics and Nuclear Engineering, R-77125 Bucharest-Magurele, Romania Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway Institut Laue-Langevin, 71 avenue des Martyrs, 38042 Grenoble Cedex 9, France Faculty of Physics, University of Warsaw, PL 02-093 Warsaw, Poland
The β − decay of Zn to the neutron magic N = 50 nucleus Ga, with only three valenceprotons with respect to Ni, was investigated. The study was performed at the ISOLDE facilityat CERN by means of γ spectroscopy. The Zn half-life was determined to be T / = 290(4) mswhile the β -delayed neutron emission probability was measured as P n = 23(4)% . The analysis ofthe β -gated γ -ray singles and γ - γ coincidences from the decay of Zn provides 47 new levels and70 new transitions in Ga. The β − n decay of Zn was observed and a new decay scheme intothe odd-odd Ga nucleus was established. The half-lives of the first and second excited states of Ga were measured via the fast-timing method using LaBr (Ce) detectors. The level scheme andtransition rates are compared to large-scale shell-model calculations. The low-lying structure of Ga is interpreted in terms of the coupling of the three valence protons outside the doubly-magic Ni core.
PACS numbers: 21.10.-k, 21.10.Tg, 23.20.Lv, 27.50.+eKeywords: Zn, Ga, Ga, β − decay, measured γ - γ coincidences, T / , deduced Ga B(XL), AdvancedTime Delayed βγγ (t) method, fast-timing, HPGe, LaBr (Ce) detectors I. INTRODUCTION
Modifications to the standard ordering of the single-particle energies have been observed in exotic nuclei witha large disparity in proton and neutron numbers. Theygive rise to the disappearance of the conventional magicnumbers and the appearance of new shell gaps. The un-derstanding of the underlying physics driving such mod-ifications is one of the main subjects of modern nuclear-structure studies. It is recognized that monopole shifts ∗ E-mail at: [email protected] † Deceased. See acknowledgments. ‡ Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver,British Columbia V6T 2A3, Canada § Present address: U.S. Army Research Laboratory, Adelphi,Maryland 20783, USA ¶ Deceased. ∗∗ Present address: Institut für Kernphysik, Technische UniversitätDarmstadt, D-64289, Darmstadt, Germany are responsible for the evolution of shell structure far offstability, but the effect of the different components of themonopole interaction is still the subject of investigation[1], since it is not simple to disentangle them from theexperimental information. This is mainly due to the factthat effective single-particle energies (ESPEs) cannot bedirectly measured, and that single-particle and collectiveeffects arising from residual interactions are intertwined.The central term of the monopole interaction seems tobe responsible for the evolution of ESPEs, while the ten-sor term plays a leading role in the splitting of spin-orbitpartners.The regions in the immediate vicinity of exotic doubly-magic nuclei are key for mapping the single-particle de-grees of freedom around closed cores. The evolutionof the proton-neutron interaction arising from the ten-sor force and the role of neutron excitations across neu-tron shell gaps can be studied in these nuclei. Relevantingredients to theoretical models can also be obtained.Two unexplored areas in the table of nuclides still re- a r X i v : . [ nu c l - e x ] J un main: around the doubly-magic Ni and in the vicinityof
Sn.Although Ni, with 28 protons and 50 neutrons ( Z =28 , N = 50 ), is located 14 neutrons off the stability line,it is expected to be a doubly-magic nucleus due to the ro-bust shell gaps arising from the spin-orbit splitting bothfor protons ( πf / − πf / ) and neutrons ( νg / − νg / ).Evidence for strong Z = 28 and N = 50 shell closures in Ni has been recently obtained [2]. In this work the roleof collective effects in such an exotic nucleus, which weresubject of debate, has also been highlighted. It is there-fore of the greatest interest to understand its structureand that of nuclei around the Z = 28 , N = 50 doubleshell closure.The first evidence for the existence of Ni came from[3]. Afterwards its half-life was reported [4] to be T / =100 +100 − ms and more recently T / = 122 ± ms [5].The latter value does point towards the magic charac-ter of Ni. Theoretical calculations predicted the firstexcited state energy above 2 MeV [6, 7], which wouldalso be consistent with a doubly-magic character. Onlyrecently in-beam γ -ray spectroscopy of the elusive Niwas performed [2]. The experimental results togetherwith theoretical calculations [2] confirm the magic natureof Ni, but suggest competing spherical and deformedconfigurations in the region, and predict the breakdownof the Z = 28 shell closure towards heavier nickel iso-topes. In this context, mapping the Z = 28 isotopes andthe N = 50 isotones is of great interest. Monopole driftshave been observed in neighboring Z = 29 Cu isotopesleading to the modification of ground-state configurations[8, 9], which may also point to a weakening of the Z = 28 gap.The strength of the N = 50 neutron shell gap and theproton structure close to Ni can be obtained from the N = 50 isotones, and in particular from the odd-protonneighbors Cu and Ga. The nucleus Cu was notreachable until very recently, when the first spectroscopicstudy was reported [10] and its mass was precisely mea-sured [11]. From these studies the magicity of Ni andthe persistence of the Z = 28 gap is confirmed. In thisway Cu can be described as a valence proton coupledto the Ni core. A spin-parity of 5/2 − is suggested forits ground state (g.s), while the 3/2 − first-excited state isproposed at a high energy of 656 keV [10]. The loweringof the 5/2 − state and eventual inversion with the 3/2 − is shown for the Cu isotopic chain by recent Monte Carloshell-model (MCSM) calculations [9]. The Cu resultsare consistent with the description of Zn, two protonsabove Ni, in terms of two-proton configurations on topof the Ni core [12], which also confirm the persistenceof the N = 50 shell closure.The next odd N = 50 isotope, Ga, is the sub-ject of this paper. With three protons outside Ni,it provides important information about proton single-particle configurations and on the strength of the N = 50 shell closure when the number of protons increase. Inour study we have produced Zn isotopes at ISOLDE, CERN to populate Ga in β − decay. We have used γ -rayspectroscopy to greatly extend the known level scheme,and the Advanced Time Delayed ("fast-timing") βγγ (t)method [13, 14] to measure excited level lifetimes, anddeduce transition probabilities, which provide more strin-gent tests of the theoretical models and will help interpretthe structure of Ga.
II. PREVIOUS KNOWLEDGE OF Ga The first studies of the decay of Zn were performedin 1991 at the ISOLDE, CERN facility by Kratz et al. [15]. The half-life and the β -delayed neutron emissionprobability were investigated, the reported values being T / = 290(50) ms and P n = 7 . . Later, two γ transitions of 351 and 452 keV were identified as belong-ing to the decay of Zn to Ga by Verney et al. [16]at PARRNe, and by Köster et al. [17] at ISOLDE. Inthe latter measurement, due to the notable Ga activitypresent in the decay of Zn, a lower limit of 10% forthe P n value was suggested. Theoretical calculations [18]predicted P n = 13% . Measurements performed at theNSCL and published in 2010 by Hosmer et al. [4] pro-posed a considerably longer half-life of +93 − ms and ahigher P n = 30(13)% value for Zn.The β − decay of Zn was studied again at the PAR-RNe mass separator in [19]. The statistics obtainedin this experiment allowed for the 351.1-keV transitionto be attributed to Ga due to the new Zn half-lifevalue of ms. The existence of the second ex-cited state at 802.8 keV was confirmed by the observationof a 451.7-keV γ ray in coincidence with the 351.1-keVline. The first excited state was defined by the 351.1-keV transition based on γ -intensity considerations. Athird, weak transition was detected at 1621.6 keV anda tentative state of the same energy was added to thelevel scheme. Spin assignments for the ground, first-excited and second-excited states of Ga were tenta-tively proposed to be (5 / − ) , (3 / − ) , and (3 / − ) , re-spectively, based on shell-model calculations and pro-ton single-particle states. The authors suggested (1 / + ) spin-parity for the Zn ground state. Magnetic-momentmeasurements performed at ISOLDE [20] yielded a Gaground-state spin-parity value of 5/2 − , confirming theearlier tentative assignment.A study of the Ga structure was performed at LNLvia heavy-ion multi-nucleon transfer [21]. Several γ rays were attributed to Ga, and specifically a 1236-keV transition connecting a state of the same energy tothe g.s., which were assigned (9 / − ) and (5 / − ) spin-parities, respectively. A new measurement of the yrast states of Ga populated in fission [22] contradicts thisassignment, since none of the γ rays reported in [21]could be confirmed. Instead the (9 / − ) is observed at1340.7 keV. The 1398.5-keV and 1952.2-keV levels are as-signed (7 / − ) and (11 / − ) spin-parity, respectively [22].The two later states are also observed by in-beam spec-troscopy in knockout reactions at RIBF [23]. In spite ofthe large spin difference, the indirect population of thesehigher spin states in Ga from the β decay of ( / + ) Zn ground state should be possible.The most recent data of the β decay of Zn comes fromHRIBF at ORNL. The results were published in 2010 byPadgett et al. [24]. The decay scheme showed six newenergy levels and nine new γ transitions in addition tothe previously available ones. Transitions of 451, 916,1107, 1585 and 2358 keV were observed in coincidencewith the strongest 351-keV peak. Four other γ rays, onlyobserved in the singles γ spectrum, with energies of 1458,1936, 4294 and 4880 keV were placed directly feeding theground state. A new value of ms for the Znhalf-life was established and a β -delayed neutron branchof 12(4)% was determined using the 1083-keV transitionin Ge. In this work, a spin-parity assignment of (5 / + ) for the ground state of Zn, different from the earliervalue, was proposed, based on the J π = 5 / − Ga g.s.[20] and the β -feeding pattern. The first and the sec-ond excited states both received a tentative J π = (3 / − ) assignment.From the existing works, the structure of Ga is in-terpreted as arising from the coupling of valence protonsin the f p shell, leading to negative-parity states at lowexcitation energy. Positive-parity states, requiring theexcitation of a proton to the g / orbit across Z = 40 ,or particle-hole excitations of the Ni core, appear atenergies above 4 MeV. The high excitation energy pointstowards a robust N = 50 neutron shell closure, in agree-ment with the recently observed Cu structure [10].
III. EXPERIMENTAL SETUP AND DATAANALYSIS
The present experiment was performed at theISOLDE, CERN facility in the framework of a systematicfast-timing investigation of neutron-rich nuclei populatedfollowing the decay of Zn isotopes [25–27]. The selectiv-ity and efficiency for the production of Zn ion beams hadbeen previously optimized [28] in order to enhance thebeam purity for − Zn ions. Proton pulses with an av-erage charge of 5 µ C and 1.4-GeV energy, coming fromthe PS-Booster in intervals of multiples of 1.2 s, wereconverted into fast neutrons [29] that impinged onto ahot ∼ o C UC /graphite target, inducing fission re-actions. The thermally extracted products were guidedthrough a temperature-controlled quartz glass transferline [30] into a W ionizer where selective ionization wasperformed by the ISOLDE Resonance Ionization LaserIon Source (RILIS) [31]. The single-charged A = 81 ions were mass separated by the magnetic high resolu-tion mass separator (HRS), accelerated to 60 keV, anddirected to the experimental setup.The mass-separated Zn nuclei were continuously col-lected on an aluminum stopper foil, creating a saturatedsource. The estimated yield of Zn was 600 ions/ µ C. Time response (ps)
E ( k e V )
F E P C o m p t o n
FIG. 1. Relative Compton response (red) and full-energypeak (FEP) prompt curve (black) of one of the LaBr (Ce)crystals used in our experimental setup. The calibration isobtained with an A = 140 source. Since Rb atoms partially survived the quartz transferline selection and were surface ionized on the walls of theionizer, the long-lived T / = 4 . h contaminant Rbwas present in the beam, with about five times higherproduction than Zn, but much lower activity duringthe data taking. An electrostatic deflector (beam gate)blocking the delivery of ions to the experimental station,was used to avoid the accumulation of long-lived Rbactivity coming from the target long after most of the Zn had been released. For the mass 81 experiment, thebeam gate was closed 600 ms after the beam impingedon the target, and the collected species were allowed todecay out.The experimental setup included two HPGe detectors,two LaBr (Ce) detectors, and an NE111A plastic scin-tillator for β -particle detection, very close to the beamdeposition point. In particular, the 3-mm-thick plas-tic scintillator was located less than 1 mm away fromthe stopper foil in order to maximize the detection effi-ciency. This thin detector assures ultra-fast and uniformtime response independent of the incident β energy. Thegermanium detectors were used for the detection of γ radiation in the range of 30 to 7000 keV; their energyresolution was 2.0 keV at Co energies. Coincidenceswith the β detector were used for γ -ray background sup-pression, and γ - γ coincidences between the HPGe detec-tors to determine the decay scheme. For the lifetimemeasurements of the excited states in the tens of pi-coseconds to nanosecond range, fast-response inorganicLaBr (Ce) crystals with the shape of truncated cones [32]were mounted almost perpendicularly to the germaniumdetectors. These scintillator crystals have a fast-decaycomponent that makes it possible to achieve very goodtime resolution while maintaining acceptable energy res-olution [32, 33]. Each crystal was mounted onto a Pho-tonis XP20D0 fast-response 2-inch photomultiplier tube(PMT), optimized to give fast time response at the costof lower gain.The signals from all the detectors were processed by FIG. 2. The β -gated γ -ray singles spectrum obtained following the decay of Zn, after subtraction of the long-lived activity.The transitions in Ga are labeled by their energies. Some transitions from the β − n decay of Zn to Ga are marked withasterisks. a digital data acquisition (DAQ) system composed offour Pixie-4 Digital Gamma Finder cards, specially de-signed for γ -ray spectroscopy [34]. For the energy anal-ysis, the HPGe signals from the preamplifier were fedinto the DAQ, while the much faster scintillator signalstaken from the last PMT dynodes were shaped beforethey were sent to the digital system. The PMT anodesignals from the scintillator detectors were used for fasttiming. The signals were processed by analog ConstantFraction Discriminators (CFD), and then sent to Timeto Amplitude Converter (TAC) modules to measure thetime difference between the β start detector and the two γ scintillators, which acted as stop detectors. Addition-ally, two more TACs were included to record time differ-ences between the fast β and the slower HPGe detectors.Logic signals related to the beam parameters were alsorecorded including the time of proton impact on targetwhich triggers the production and release of Zn ions outof the target. These triggered beam pulses define thestarting time for the Zn accumulation and were usedto rule out the long half-life contaminants by setting timegates with this signal as a reference. The Pixie-4 systemis configured to write data in a triggerless mode. Coinci-dent events were constructed off-line in order to correlatethe time differences, the detector energies, and the otherrelevant running parameters.For the data analysis, a time gate starting 50 ms after the proton impact and ending 1200 ms after itwas adopted, which minimizes the presence of long-liveddaughter activity in the A = 81 data. Coincidence with β particles was imposed to suppress the background con-tributions. The energy spectra contain γ lines from the Zn decay chain and also a negligible fraction of con-taminant lines from the β + decay of Rb to Kr. Thestrongest line of this decay (446 keV) was around 4% asintense as the 351-keV transition of Ga. In addition,the subtraction of the long-lived activity (using a delayedtime window after proton impact) provides a clean energyspectrum containing γ rays from the β decay of Zn, in-cluding the β -delayed neutron emission branch. The γ rays from the decay can be assigned to de-excite energylevels in the Ga and Ga nuclei and their daughters.In the first ∼
50 ms after proton impact on the target,neutron-capture γ rays are observed in the HPGe spec-tra. This is due to neutrons that escape the converter inthe target area, thermalize and reach the measurementstation. These capture lines were used for high energycalibration of the HPGe detectors up to 7 MeV, togetherwith sources of Ba,
Cs,
Ba and
Eu for theenergy and efficiency calibrations.Excited-state lifetimes have been measured using theAdvanced Time-Delayed βγγ (t) fast-timing method [13,14, 35]. Coincidences between the fast-response plas-tic scintillator and the LaBr (Ce) crystals were used.The method consists of the use of triple βγγ coincidentevents. The β -HPGe-HPGe coincidences allow the decaybranches to be identified whereas the β -HPGe-LaBr (Ce)events make it possible to measure the lifetimes down tothe tens of picoseconds range. The decay path is selectedwith a gate on the HPGe detector, whereas the lifetime isobtained from the time difference between the β plasticscintillator and the LaBr (Ce) γ signal, which start andstop a time-to-amplitude converter (TAC), respectively.With a FWHM time resolution of the LaBr (Ce) detec-tors of 110 ps for the Co full energy peaks [32] and thevery fast time response of the β plastic scintillator be-low 50 ps, the β -LaBr (Ce) time distribution for prompttransitions, typically quasi-Gaussian, has a FWHM of120 ps. Half-lives longer than about 60 ps will appear asa slope on the delayed part of the time spectrum. Thelifetime can be extracted by the de-convolution of theslope of the time spectrum from the prompt time distri-bution. Shorter half-lives, down to tens of ps, are ob-tained by the centroid shift of the time distribution withrespect to the time distribution of a prompt transition ofthe same energy [13].The application of the centroid shift method requiresthe use of calibration curves for the time response as afunction of energy, both for the full-energy peaks (FEP)and Compton events. For the FEP prompt responsecurve we have used peaks from a Ba/
La calibra-tion source, primarily from excited states of
Ce withknown half-lives [36], including both the correction by theCompton curve and the level lifetime. Both curves areplotted in Fig. 1. The Compton response curve has beenconstructed with the time response of Compton eventsarising from the 1596-keV γ transition from Ce. Thetime response curves have a smooth behavior versus en-ergy, and they are very similar for γ -ray energies above400 keV. At lower energies the curves differ due to thephysics of the interaction [35], especially in the region ofbackscatter and X-ray events.Peak and background centroid corrections are madeseparately following their respective walk curves. Nor-mally the FEPs sit on background arising mainly fromCompton events coming from transitions with higherenergies. The time delay originating from the back-ground component is corrected according to the peak-to-background ratio with the help of the Compton correc-tion curve [35]. The resulting centroid of the FEP timedistribution is then compared with the baseline given bythe FEP correction curve. Any delay relative to the curveis then due to the lifetime carried by the transition giv-ing rise to the FEP and can be related to levels in thenuclide of interest. In addition, the timing analysis in-cludes standard corrections for the very small dependenceof the β time response with energy, and, if needed, forsmall electronics drifts during the measurement. T = 1 . 2 5 ( 3 ) s b ) T = 2 9 0 ( 4 ) m s a ) T = 1 . 7 0 ( 3 ) s c ) t ( s ) FIG. 3. Ground-state half-lives measured in this work.(a) Zn half-life obtained from three of the strongest Gatransitions at 351, 452 and 1341 keV. (b) Measurement of the Ga half-life by gating on the 216- and 828-keV transitionsin Ge. (c) Apparent Ga half-life (combined ground stateand 22-keV isomer).
IV. RESULTS
The significantly higher statistics obtained in our ex-periment compared to previous works is illustrated bythe spectrum shown in Fig. 2. Transitions up to 6.5 MeVin energy are observed, along with the strongest transi-tions at 351.1 and 451.6 keV. More than 20 γ decays withsizeable intensity are detected beyond 4 MeV.To obtain the Ga half-life, the 216- and 828-keV tran-sitions in Ge [38] were used. An exponential fit was em-ployed by limiting the lower time boundary to 2000 msafter proton impact, which corresponds to 6.9 half-livesof Zn, when less than 1% remains. The fitted slopeleads to T / = 1 . s for Ga as depicted in Fig. 3,consistent with the literature value of 1.217(5) s [37].Finally, gating on the 659-keV transition which de-excites the + Ge, we get the appar-ent Ga half-life, where a 22-keV − isomer has beenidentified above the − ground state [25]. The half-lives of these states were previously measured as 1.3(2)and 1.9(1) s, respectively, in the β -decay experiment de-scribed in [39]. According to the level scheme from Fig. 5of [39], the 659-keV state is β -fed directly from the low-spin isomer while the high-spin isomer populates it viathe 1083-keV γ ray that de-excites the 1743-keV level.Therefore, the time since proton impact spectrum gatedby the 659-keV will contain the contribution of half-livesfrom both isomers and the fitted value should lie between1.3 and 1.9 s. Using the same time fitting conditions asbefore we get T / = 1.70(3) s. As discussed in subsec-tion IV B below, this value is mainly due to the − isomerhalf-life, which is the state predominantly populated inthe β -n decay of Zn.Transitions arising from the β − decay of Zn havebeen identified from their time spectra after proton im-pact, which is consistent with the Zn half-life of 0.32(5)s adopted in [37]. In our experiment, the Zn half-life has been measured using the time spectrum gated di-rectly on three of the strongest Ga transitions of 351,452 and 1341 keV (see Fig. 3a). A simple exponential de-cay plus constant background function has been used inthe time range from 700 ms (with a slight delay after theend of implantation) to 2400 ms, restricting the time be-tween proton impact on target to two or more cycles (2.4s or longer). The weighted mean value obtained yields T / = 290(4) ms, in agreement with the recent literaturevalues [5, 24]. A. Zn β − decay to Ga The decay scheme of Ga has been extended usingcoincidences with previously known transitions employ-ing the γ - γ coincidence spectrum between both HPGedetectors. Figure 4 shows the energy spectra in coinci-dence with the 351- and 2358-keV transitions. Note that γ rays up to 5 MeV are registered in coincidence withthe strong 351-keV Ga transition. Table I summarizesthe information about the γ transitions associated withthe decay of Zn to Ga. The relative intensities ofthe γ -ray transitions were extracted using the full-energypeak areas from the β -gated γ -ray spectrum and werenormalized to the strongest transition at 351 keV. TABLE I: Gamma transitions in the decay of Zn to Ga. For those placed in the decay scheme, the initial and final levelenergies are given in the second and third columns. Relative intensities, normalized to 100 units for the 351-keV transition, areprovided. The strongest transitions observed in γ - γ coincidences are given in the last column. E γ (keV) E ilevel (keV) E flevel (keV) I relγ a Main γ - γ coincidences333.3 b b b b TABLE I –
Continued E γ (keV) E ilevel (keV) E flevel (keV) I relγ a Main γ - γ coincidences1506.4 a For absolute intensity per 100 parent decays, multiply by 0.374(22). b Weak transition, not observed in γ - γ coincidences. Tentatively placed in the level scheme. Based on the γ - γ coincidences, 70 transitions that were not previously observed in Ref. [24] have been placed in FIG. 4. γ - γ coincidence spectra gated by the strongest,351-keV transition (top) and the 2358-keV line (bottom). the level scheme, which is shown in Figs. 5 and 6. Weaktransitions that were not observed in coincidence withstrong Ga γ rays have not been included, since theycould also belong to the level scheme of Ga populatedin the β − n decay of Zn (see Sec. IV D). Such is thecase of 279-, 505-, 627-, 779-, 2627- and 2943-keV γ rays.Their combined intensities amount to 1.1% of the total γ intensity. However, some of the weak γ rays of 478,656, 894 and 1185 keV, fit the energy differences betweenalready established levels and were tentatively placed inthe level scheme. They are marked with broken lines.The high-energy γ rays not observed in coincidence withthose at 351 and 452 keV were placed as de-exciting astate with the same energy. We note that the availableenergy window for β − decay is Q β − = 11428(6) keV [40],compared to a value of Q β − n = 4953(6) keV [40] for β -delayed neutron emission. Therefore, γ rays with energiesabove 5 MeV that follow the Zn half-life must belongto Ga and not to Ga.In this way, 47 excited states of Ga in the energyrange up to the neutron separation energy of 6476(4) keV[40] have been observed, 40 of them for the first time. Weconfirm the existence of 351.1-, 802.5-, 1266.7-, 1458.3-, 1936.4-, 4294.9- and 4880.4-keV levels, already seen inthe latest β -decay study [24]. The states identified as (9 / − ) and (11 / − ) in fission γ -ray spectroscopy [22] arealso observed at 1341.0 and 1952.4 keV [26]. B. Beta-delayed neutron emission probability of Zn To obtain the β -delayed neutron emission probabilityof Zn we compared the number of decays arising fromthe direct Zn β -decay chain, using the absolute inten-sities of the two strongest lines in Ge, at 216 and 828keV [37], to the Zn β − n decay branch of the A = 80 chain, taking the absolute intensities per 100 parent de-cays of 666-, 1207-, and 1645-keV lines from the β de-cay of As to Se [41, 42]. We employ the literature value of 11.9(7)% for the Ga β − n branch [37] and ap-ply a small correction factor coming from the Ga β − ndecay probability of 0.86(7)%, also taken from the lit-erature [43]. Determining the areas of the above men-tioned transitions directly from the β -gated singles spec-trum and taking into account the absolute intensities weobtain P n =23(4)% for Zn.
C. Direct β feeding to the Ga ground state
For the absolute β feeding to be derived, it is necessaryto obtain the ground-state (g.s.) β feeding. Since there isno isomeric state reported for Ga, the total g.s. feeding,both γ and β , proceeds through the Ga ground-state β decay to states in Ge, and via the β -delayed neutronemission branch to states in Ge. A β -decaying isomerexists in Ge at 679 keV [38], for which no γ -ray branchwas observed. Therefore, these two states need to be con-sidered in the β decay of Ga, both for γ and β feeding.For the β -n branch from Ga we take an adopted P n value of 11.9(7)% from [37]. In addition, for the Zn the P n value of 23(4)% from our data is used, as describedin subsection IV B above.The γ -ray intensities in Ga and Ge are obtainedfrom our data without time conditions, thus containingthe short-lived and long-lived decay products from Znand its daughters, and normalized to the strongest 351-keV transition in Ga, Table I. The total γ intensityfeeding the ground state of Ga is measured to be I Gaγ,gs =203(4) . In the decay of Ga, the γ -ray intensity thatfeeds directly the 679-keV isomer state and the groundstate amounts to 101(3) and 95(3) in the same units,respectively, and thus the γ -ray feeding both states is196(4) units.To estimate the β -feeding intensity to the g.s. and679-keV isomer in Ge we make use of the spin assign-ments of 9/2 + and 1/2 + [38]. These levels are therefore β -fed from the Ga 5/2 − ground state via first-forbiddenunique β transitions with ∆ J = 2 , ∆ π = yes . It is thenreasonable to consider a lower limit of log U f t = 8.5 (seeFig. 1 of [44]) for both states. The β feeding calculatedwith these assumptions gives upper limits of 11.3% forthe 9/2 + g.s. and 6.6% for the 679-keV isomer repre-sented in absolute units (5.7(56)% and 3.3(33)% wereused for calculations).With these assumptions the value of the ground-state β feeding in Ga is extracted from the intensity balanceand is given with an upper limit of 2.4%. This leads tolog f t ≥ . , in good agreement with the systematics andselection rules for the first-forbidden non-unique β decaytransitions in the region.Using this value, the apparent β feeding of the remain-ing levels, I β ( E ) , is obtained by the intensity balance be-tween feeding and de-exciting γ rays. Internal conversionis neglected. High-energy transitions could have beenmissed or misplaced if coincidences are not observed,which means that the β feeding would be slightly modi- G a E ( k e V ) T / / - ( / - )( / - ) ( / + - / + ) ( / + , / + ) . I β - ( % ) L og ft % β - = ( ) T / = ( ) m s Q β - = ( ) k e V Z n . ( ) s ( ) p s ( ) p s ⩽ s ⩽ . ⩾ . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) FIG. 5. Level scheme of Ga up to 4.3 MeV in energy populated following the β decay of Zn. Dashed arrows indicatetentatively placed transitions. For the sake of clarity the decay scheme has been split in two sections. fied. We note the small energy gap between the highestlevel at 6434.6 keV and the neutron separation energy, S n = 6476(4) keV, which is still far from the available β -decay window, Q β − = 11428(6) keV [40]. With the Zn β -delayed neutron emission probability P n = 23(4)% and the ground-state feeding (taking I Gaβ,gs = . ), an ab-solute normalization factor of 0.374(22) is obtained forthe γ intensities in the decay of Zn to Ga from therelative ones tabulated in Table I.0 G a E ( k e V ) T / ( / + , / + ) . I β - ( % ) L og ft % β - = ( ) T / = ( ) m s Q β - = ( ) k e V Z n I n t e r m e d i a t ee n e r g i e s / - ( / - )( / - ) ( / + - / + )( / + - / + )( / + - / + )( / + - / + )( / + - / + )( / + - / + )( / + - / + )( / + - / + )( / + - / + ) . ( ) s ( ) p s ( ) p s ⩽ . ⩾ . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . . ( ) . ( ) . P n = ( ) % S n = e V ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) FIG. 6. Level scheme of Ga populated in the β decay of Zn, containing the high-lying states between 4.3 and 6.5 MeV inenergy. Dashed arrows indicate tentatively placed transitions. D. Zn β − n decay to Ga As discussed above, β -delayed neutron emission is en-ergetically allowed for the decay of Zn, with a Ganeutron separation energy S n = 6476(4) keV [40], wellwithin the Q β − window. The analysis of the β -gated γ spectrum has allowed 11 γ transitions to be assignedto Ga populated following the β − n decay of Zn. Thenuclide Ga was studied at ISOLDE during the same ex-perimental run, populated in the β − decay of Zn, andthe results of the analysis were published by Licˇa et al. [25]. The γ - γ coincidence analysis provides information1to place the observed Ga transitions de-exciting ninepreviously known low-energy levels. Our new scheme of Ga from β − n decay of Zn plotted in Fig. 7 is con-sistent with the structure from [25]. Table II containsthe detailed information about the γ transitions and fedenergy levels. We neglect any direct feeding of the − ground and the − first isomeric states in Ga from the( / + , / + ) ground state of Zn. The apparent β -nfeeding, I βn ( E ) , is obtained from the intensity balance.Internal conversion is included, specifically for the 75-keVtransition, by taking coefficients from [45] and assumingdipole transitions. It is worth noting that most of thepopulation from the β − n decay of Zn proceeds to the − state at 22 keV. The second isomer, with spin-parity + , is confirmed at 708 keV. We measured its half-lifeto be T / = 18 . ns using triple coincidences be-tween the β and two HPGe detectors. Our half-life forthe 708-keV state has slightly less precision but is in per-fect agreement with the value determined in [25]. TABLE II. Gamma transitions in Ga populated in the β − -ndecay of Zn. Intensities relative to the 74.9-keV transition,placements in the level scheme, and main γ - γ coincidences arelisted where available. E γ E ilevel E flevel I γ (keV) (keV) (keV) (%) γ - γ a a Weak transition, not observed in γ - γ coincidences.Tentatively placed in the level scheme. E. Half-lives of the excited states of Ga Two strong sequential transitions of 351 and 452 keVare observed in the level scheme of Ga (Fig. 5 andFig. 6). The first one de-excites the first excited stateof the same energy while the second one comes from the802-keV energy level. Selecting the 351-keV transition inthe HPGe detector and the 452-keV one in the LaBr (Ce)detectors, the β -LaBr (Ce) time difference distribution isdue to the lifetime of the 802-keV level plus the contribu-tions from the lifetimes of higher lying levels. By revers-ing the gates, selecting the 452-keV line now in the HPGeand the 351-keV one in the LaBr (Ce) detector, the ob-served time delayed spectrum arises from the lifetime ofboth the 802-keV and the 351-keV levels, plus the contri-butions from higher lying states. The difference betweenthe centroids of both time distributions, once corrected Ga E ( keV ) T / ( ) ns1.9 ( ) s1.3 ( ) s ( / + ,5 / + ) β - n (%) %β n - = ( ) T / = ( ) ms Q β n - = ( ) keV Zn - - ( ) ( ) ( ) ( ) ( + ) ( ) ( ) ( ) ( ) . ( ) . . ( ) . ( ) . ( ) . ( ) . ( ) . . ( ) . . ( ) . ( ) . ( ) . ( ) FIG. 7. Levels in Ga populated in the β − n decay of Znfrom our work. The half-lives of the 21.9-keV and groundstate were previously reported in [39]. for the different prompt positions at 351 and 452 keV(using the FEP response curve and their Compton back-ground contribution), yields the mean-life of the 351-keVlevel. Figure 8 shows two plots that illustrate the timedistributions under these conditions. The time differencebetween their centroids shown in the figure is not yet cor-rected by the effect of prompt position and the Comp-ton background response. After corrections, the centroidshift method gives the values of τ = 92(15) ps for the firstLaBr (Ce) detector and 80(13) ps for the second one. Wetake the average of both values and uncertainties, whichleads to a T / = 60(10) ps half-life.As a cross-check we have tried to de-convolute the slopein the time spectra in βγ (t) and βγγ (t) coincidences byselecting the 351-keV transition in the LaBr (Ce) detec-tors and fixing the prompt distribution to that given bythe 452-keV transition. Although the result is limitedby statistics, it is consistent with a slope that yields ahalf-life of the order of 50 ps.A similar procedure to that described above for the351-keV level is applied to measure the lifetime of the1936-keV state, using in this case the coincident 1585-and 2358-keV transitions. The results are at the limitof sensitivity and yield τ = 20(18) ps and τ = 6(16) psrespectively. We take the average value of τ = 13(17) psresulting in a one-sigma upper limit of T / ≤ ps forthis level.The half-life of the second excited state at 802 keV ismeasured by absolute comparison using parallel transi-tions [35]. The high-lying states in Ga are character-ized by short half-lives below ∼ γ transitions are in coincidence with the 351-keV γ ray(Fig. 5 and Fig. 6). By selecting those in the HPGedetectors and the 351-keV one in the LaBr (Ce) detec-tor, the β -LaBr (Ce) time difference will arise from the351-keV state lifetime. This can be compared with the2 TABLE III. Summary of half-lives of excited states in Ga, and experimental B ( M and B ( E reduced transition probabilitiesfor the de-exciting transitions, assuming pure multipolarities. They are compared to the theoretical values calculated with theJUN45 and jj44b effective interactions (see text for details). E level T / J π E γ B ( M W.u. B ( E W.u.(keV) (ps) (keV) EXP JUN45 jj44b EXP JUN45 jj44b
351 60(10) ( / − ) 351 8.5(14) × − × − × − / − ) 452 8(6) × − × − × − × − ≤ (478) ≥ × − ≥ . ≥ × − ≥ . ≥ × − ≥ . time distribution resulting from the selection of the 452-keV transition in the HPGe and the 351-keV one in theLaBr (Ce) detectors, which is due to both the 351-keVand 802-keV lifetimes. The difference between centroidpositions, once corrected by the calibrations, gives an av-erage of τ = 34(22) ps or T / = 23(16) ps for the 802-keVlevel half-life.The previously unknown half-lives obtained from thismeasurement are summarized in Tab. III. Using the life-times and γ -ray branching from our level scheme, thetransition probabilities for the de-exciting lines have beencalculated for the most probable multipolarities. Thetheoretical evaluation of conversion coefficients [45] forthese transitions show that all of them are well below 1%and thus were neglected. Pure transitions are assumedfor the experimental values.According to the measured B ( XL ) values, both the351- and 452-keV transitions are consistent with havinga predominant M character as in the case of the 345-keV transition in the N = 50 Br isotone [46] connectingthe well-established / − and / − states, as shown inFig. 9. Based on systematics, an M multipolarity is alsosuggested in [21] for the 307-keV transition connectingthe tentatively assigned (3 / − ) first excited state and (5 / − ) ground state in As, which was also measured in[47].
V. SHELL-MODEL CALCULATIONS
Large-scale shell-model calculations of nuclear states of Ga have been performed. Two state-of-the-art effectiveinteractions were implemented into the NuShellX@MSU[55] and ANTOINE [56] codes. The first interaction, la-belled JUN45, was developed by Honma et al. in 2009[57] and it was focused in the pf shell with a Ni core andcontains the p / , f / , p / and g / single-particleorbits. The interaction reproduces the experimental dataof low-lying states in the N = 49 isotones, Ge isotopesnear N = 40 , and N = Z nuclei with A = 64 ∼ ,but the valence space may not contain all the degrees offreedom necessary to account for all the features of thenuclear structure of the region [57].Another effective interaction, called jj44b, which madesuccessful predictions for nuclei near Ni, was created C oun t s / p s Time (ps)TAC1 Ga 452 keV Ga 351 keV C oun t s / p s Time (ps)TAC2 Ga 452 keV Ga 351 keV
FIG. 8. Time spectra obtained in triple βγγ (t) coincidenceswith the 351-keV γ transition selected in the HPGe detec-tors and the 452-keV in the LaBr (Ce) detector (dotted line)and with reversed γ gates (solid line). The left panel showsthe TAC spectra for the first LaBr (Ce) and the right panelthe spectra for the second LaBr (Ce). The time distributionsdo not include timing corrections of the prompt positions andCompton background contributions. Once corrected for these,the difference of the centroid positions of the time distribu-tions yields the mean-life of the 351-keV level. See text fordetails. in 2004 by Lisetskiy et al. [55]. It was constructed witha Ni core for the neutron space and a Ni core forthe proton space. The Hamiltonian was also based onthe Bonn-C
N N potential including four single-particleenergies and 65 T = 1 two-body matrix elements. The3 Cu
50 3181 Ga
50 3383 As
50 3585 Br
50 3787 Rb (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:144) (cid:45) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76)
712 3 (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:72) (cid:76) ps (cid:144) (cid:45) (cid:144) (cid:45) Ga
40 3173 Ga
42 3175 Ga
44 3177 Ga
46 3179 Ga
48 3181 Ga (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45)
487 1 (cid:144) (cid:45) (cid:144) (cid:45) (cid:60) (cid:144) (cid:45)
199 3 (cid:144) (cid:45) (cid:72) (cid:144) (cid:45) (cid:76) (cid:144) (cid:45)
229 3 (cid:144) (cid:72) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76)
128 3 (cid:144) (cid:45) (cid:72) (cid:144) (cid:45) (cid:76) (cid:144) (cid:45) (cid:72) (cid:144) (cid:45) (cid:76) FIG. 9. Top: level systematics of N = 40 − Ga isotopes. Bottom: N = 50 isotones. The low-lying levels of Ga isotopesare taken from references [48–51], except for Ga from this work, while the structure of the N = 50 isotones is based on[10, 52–54]. interaction was later updated [19] to better describe thestructure of Ga and it has been shown to reproducethe properties of the heavier isotopes of Ga [58]. Here weemploy the original jj44b interaction.The energy levels of Ga obtained with the JUN45and jj44b interactions are compared to our experimentalresults in Fig. 10. The calculations using the JUN45 in-teraction achieve a good agreement with the experimentfor the excitation energy of the low-lying states, but tendto overestimate the energy of the negative-parity levels inthe 1 − − + that will arisefrom the π ( g / ) configuration, at around 3 MeV. Thehigher-lying positive-parity states obtained from the cal-culations in this restricted model space must arise fromthe coupling of a π ( g / ) proton to a proton pair inthe negative-parity orbitals. These states cannot be re-lated to the experimentally observed ones, since the lat- ter should have a neutron intruder nature (1p-1h neu-tron configurations) in order to be connected to the Znground state via Gamow-Teller transitions.The occupation probabilities predicted with both in-teractions for the lowest-lying states are summarized inTable IV. Both sets of shell-model calculations are ableto properly reproduce the ground-state spin-parity to be5/2 − , in agreement with the experimental value [20]. Theproton occupation probability for the π ( f / ) configura-tion is 79% with JUN45 and 75% with jj44b. A spin-parity of 3/2 − is calculated for the first and the secondexcited states with both interactions, although their en-ergies differ considerably. According to the calculationsusing the jj44b interaction, the 351-keV level has a single-particle π ( p / ) character, with a large occupation valuefor the π ( f / ) ⊗ π ( p / ) configuration, whereas the 802-keV level has a preferred π ( f / ) configuration. Thecalculations for Ga using the PFSDG-U interaction [6]reported in [22] support this description.The calculated reduced transition probabilities for the γ rays de-exciting the lowest-lying excited states are4 Ga Exp IS441 JUN45 jj44b (cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76)(cid:72) (cid:144) (cid:43) ,5 (cid:144) (cid:43) ,7 (cid:144) (cid:43) (cid:76) (cid:144) (cid:45) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:144) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:72) (cid:45) (cid:76) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:45) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) (cid:144) (cid:43) E n e r gy (cid:72) k e V (cid:76) FIG. 10. Shell-model calculations with the JUN45 and jj44b interactions for Ga compared to the experimental data measuredin this work. The experimental spins were tentatively placed based on the β -feeding considerations. The positive-parity statesare marked in blue, except for the calculated 9/2 + state, which is highlighted in green. given in Table III and compared with the measured val-ues based on the experimental lifetimes and branchingratios. Only parity-conserving transitions of the lowestmultipolarities are considered due to the negative par-ity nature of the low-lying states. Here effective charges of e π = +1 . e and e ν = +1 . e were used, along witha quenched g factor of . g s,free . The harmonic oscilla-tor potential used was A − / MeV, as recommended in[59], which was found to better reproduce the transitionrates in this region.5
TABLE IV. Occupation probabilities for the proton configu-rations obtained with the JUN45 and jj44b interactions forthe first three states in Ga. E level J π JUN45 jj44b(keV) π ( f / ) π ( f / ) p / π ( f / ) π ( f / ) p / −
79% 4% 75% 2%351 (3/2 − ) 38% 51% 5% 78%802 (3/2 − ) 48% 41% 76% 5% VI. DISCUSSIONA. Ground-state feeding of Ga and ground-statespin-parity of Zn The structure of the nuclei immediately north of Niis defined by the ordering and occupation probabilities ofthe g / , d / , s / , g / , and d / neutron orbitals, andthe f / , p / , p / , and f / proton orbitals. For the Cu( Z = 29 ) isotopic chain, an inversion of the ordering ofthe p / and f / states above Cu has been observedas the neutron g / orbital is being filled. This has beeninterpreted as the effect of the monopole neutron-protontensor interaction [60].The Ga ground-state spin-parity has been estab-lished as 5/2 − from collinear laser spectroscopy per-formed at ISOLDE [20]. For the Zn g.s., positive-paritystates with a single-particle character, νs / or νd / ,have been proposed, leading to either 1/2 + spin-parityassignment, matching the extrapolation of the 1/2 stateenergies in the region [19], or 5/2 + , which is consistentwith the systematics of N = 51 isotones. Beta-decaytransitions from Zn to low-lying states in Ga are ex-pected to proceed via forbidden transitions, since theGamow-Teller operator will populate daughter states atmuch higher energy. Using the systematics for forbiddendecays [44] and based on the firm spin-parity assignment5/2 − for the ground state of Ga, two options are possi-ble: a first-forbidden decay from the 5/2 + to 5/2 − stateswith log f t > . or a first-forbidden unique decay from1/2 + to 5/2 − , more hindered and with log f t > . .In [24] Padgett et al. ruled out the previous suggestionof 1/2 + [19] for the ground state spin-parity of Zn. In-stead a 5/2 + assignment for the Zn ground state wasproposed [24] based on the apparent β -decay feeding tothe Ga 5/2 − ground state. Our experimental data yielda β ground-state feeding compatible with zero, with alog f t larger than 6.8. We note that high-energy transi-tions can still be missed in our detection set-up and that,on the contrary, some of the high-energy transitions thatare unambiguously identified as belonging in Ga havebeen tentatively placed in the level scheme as directlyfeeding the ground state based on the lack of observedcoincidences. Thus the experimental value needs to betaken with caution. Nonetheless, the observed negligibledirect β feeding to the ground state is in contrast to theprevious experiment [24]. This is because many weak γ transitions de-populating high-lying states in Ga have been added in our study, which has a dramatic effect onthe ground-state γ feeding intensity and decreases theapparent direct ground-state β branching from the pre-vious 52% to our ≤ β -feeding.From our measurement none of the possible spin-parityassignments of Zn can be ruled out, since a first for-bidden unique 1/2 + to 5/2 − transition, and thus a 1/2 +81 Zn ground-state spin-parity, is still possible.In any case, the role of first-forbidden transitions tolow-lying negative-parity states in Ga is not as rel-evant as previosuly proposed. A large fraction of thebeta-decay population may still proceed to higher-lyingpositive-parity states via allowed transitions. This is rat-ified by the sizeable β -delayed neutron emission proba-bility, which points to β feeding via GT transitions tohigh-energy levels above the neutron separation energyin Ga.
B. Low-lying structure of Ga In our experiment we have measured the first-excited351-keV state half-life to be T / = 60(10) ps. Assumingthat the transition connects states of negative parity, the B ( M rate for pure M multipolarity is . × − W.u., whereas the pure E rate would be a very col-lective 85(14) W.u. The reduced transition probabilitiesthus point to a retarded M transition which is consistentwith the results of the shell-model calculations (Table IIIand the systematics in [61]). This suggests a πp / dom-inant configuration for the 351-keV level (see Table IV).Owing to this fact, the 351-keV γ ray would be slightlyhindered due to the l -forbidden character of a πp / to πf / transition.A very similar structure is found in odd N = 50 nucleiwith Z > , as shown in Fig. 9, in particular for theneighboring isotone As. For the Z = 37 Rb isotone,the 3/2 − and 5/2 − levels are already reversed, the groundstate having a spin of 3/2 − . The 403-keV 5/2 − level hasa very similar half-life of T / = 80(5) ps [62] to the351-keV one in Ga, which gives a B ( M to withina factor of 2 for the 403-keV transition to the groundstate compared to the 351-keV transition in Ga. Thedominant πp / single-particle configuration of the 351-keV level is in accord with a narrow proton gap of theorder of 500 keV between the f / and p / orbitals, aspredicted for Cu by shell-model calculations [59, 63],but at odds with what was claimed in [64].For the second excited state at 802 keV, the calcula-tions, especially those with the JUN45 interaction (whichachieve a better agreement with the experimental exci-tation energies) show a strong admixture of the π ( f / ) cluster configuration and the π ( f / ) p / one. This givesrise to a 3/2 − spin-parity. Our measured half-life for thislevel is consistent with a 3/2 − assignment, and an M E component.Both of the 351- and 802-keV levels are fed frompositive-parity high-energy levels. These may be charac-terized by the occupation of πg / , πd / and πd / pro-ton single-particle states, or by the coupling of protonorbitals to neutron particle-hole states (thus requiringbreaking of neutron pairs across the N = 50 gap). Thede-excitations from these high-lying states, which likelyhave spins between / + and / + , to / − E high-energy transitionswith energies higher than 3.8 MeV. In view of the 3.5-MeV N = 50 energy gap measured for Ga by Hakala et al. [65] the 3859-keV transition which connects the β -fed 4209-keV level to the 351-keV state gives a roughestimate of the N = 50 energy gap from our data.Nine other excited states are experimentally found in Ga below 2 MeV. The calculations reproduce the leveldensity of these negative parity states. In a simplisticmodel where a quasiparticle is coupled to the Zn core,four states arising from the coupling of the π ( p / ) orbitto the 2 + core in Zn, would have spins of 1/2 − , 3/2 − ,5/2 − , and 7/2 − , whereas the π ( f / ) coupling to the 2 + level will give rise to the five states with spins rangingfrom 1/2 − to 9/2 − . An alternative description based on a π ( f / ) cluster configuration provides a similar picture.The π ( f / ) configuration yields 3/2 − , 5/2 − and 9/2 − spins, with the 9/2 − found at higher energies, and theircouplings to the 2 + of Ni in this case will provide theobserved levels. It is worth noting that both theoreticalcalculations reproduce rather well the excitation energyof the 9/2 − level at 1341.0 keV belonging to the π ( f / ) configuration. This is consistent with the calculationspresented in Ref. [22].A high density of levels in the region from 1 to 2 MeVcan be observed as well in the level scheme of As [52],with striking similarity to that of Ga. The level schemeof Br [46], populated by the β decay of Se has a verysimilar structure too. Out of these levels in Ga, the1936-keV state is strongly populated from the higher ly-ing 4295-keV positive-parity state. We have measured a21-ps upper half-life limit for the former, which does notallow us to unambiguously identify the multipolarity ofthe de-populating 1936- and 1585-keV transitions. How-ever, the decay pattern to the ground and first-excitedlevels, and the direct feeding from positive-parity states,makes a spin-parity assignment of 3/2 − or 5/2 − likelyfor this state. C. Positive-parity states
As mentioned above, the lowest positive-parity state isthe / + one predicted at energies close to 3.0 and 3.3MeV, depending on the interaction. This state has anexpected main πg / configuration and would not be di-rectly populated by the Zn β decay from a / + groundstate, and would have a limited feeding from a / + g.s.,yielding a high log f t value. Although the single-particle νg / orbit is shown to be at higher energy [21], any ad-mixture of a νg / component in the Zn g.s. wave func-tion would lead to an enhancement of allowed Gamow-Teller (GT) β transtions to the πg / orbit. In any case,indirect population of the / + state in Ga should bepossible. The systematics near A = 81 suggests a longhalf-life for this state due to the M behavior of the γ transition which would connect it to the / − groundstate. No such long lifetime, nor decay to lower energy / − , / − levels, could be observed in our measurement.The allowed GT β decay from the Zn ground-stateneutron ν ( d / ) or ν ( s / ) configuration populates high-energy states in the Ga daughter, since there are nolow-lying positive-parity states available. The positivestates would have to originate from the coupling of theodd proton orbitals ( p / , f / and p / ) to neutronparticle-hole states, therefore implying the breaking ofa neutron pair inside the N = 50 shell. These cross-shellstates arising from the excitation of the Ni core givean idea of the magnitude of the N = 50 shell gap, asdiscussed by Winger et al. [52] in the β decay of Ge to As, and Padgett and co-workers for Ga [24].The GT β decays to these core-excited states mustarise from the decay of neutrons in Zn in the f and p orbitals, which are strongly bound. Due to the reducedenergy window the β feeding would be reduced, but, inspite of the Fermi factor, these GT decays may still befavoured compared to the first-forbidden decays to low-lying negative-parity states. The large P n value mea-sured for Zn suggests a significant role of such allowed β transitions to high-lying states above the neutron sep-aration energy in Ga. Several levels with low apparentlog f t values can be identified in the 4 – 5 MeV energyrange. In our work we observe strong direct population tothe levels at 4209, 4295, 4369, 4880, 4921, 5178 and 5422keV, and to some others at higher energies. These statesare not included in our shell-model calculations due tothe restricted model spaces. Assuming a / + or / + g.s. for Zn, positive-parity assignments for these levelswith 1/2, 3/2, 5/2, and 7/2 spin values can be made. Anidentical situation can be observed in the N = 50 iso-tones As [52] and Br [46], populated following the β decay of Ge and Se, respectively.
VII. SUMMARY AND CONCLUSIONS
The high purity and intensity of the Zn beams deliv-ered by the ISOLDE facility at CERN have made it pos-sible to obtain about ten-fold higher statistics than pre-vious studies [24]. The level scheme of the semi-magic N = 50 nucleus Ga has been significantly expandedwith 47 new levels and 70 γ transitions in the energyrange up to 6.5 MeV. Most of these levels are very closeto the neutron separation energy. The 290(4)-ms half-lifeof Zn measured in this work is in good agreement withthe literature [5, 24].The direct β feeding to the Ga ground state mea-7sured in our experiment is negligible within the errorbars, and much lower than proposed previously; it is thuscompatible with both / + and / + assignments for the Zn ground state. We could not identify the / + stateseen in other N = 50 isotones and also predicted by ourshell-model calculations to lie at around 3 MeV. We havemeasured a β -delayed neutron emission probability valueof 23(4)% for the decay of Zn. This is more precise butalso consistent with 30(13)% measured by Hosmer et al. [4], but two-sigma away from the recent value reportedby Padgett and co-workers of 12(4)% [24].The level scheme of Ga populated following the β -delayed neutron emission from Zn was constructed forthe first time and it is in agreement with that describedin [25] from the β decay of Ga, including the low-lying22-keV isomer. Our measurements also confirm the exis-tence of the 708-keV isomer with an 18.3(13)-ns half-life.We have measured the half-life of the first excited statein Ga to be T / = 60(10) ps, which indicates an l -forbidden M transition of 351 keV to the 5/2 − groundstate. This in turn points to a transition between stateswith main πp / and πf / configurations. This is sup-ported by both the N = 50 systematics and by our shell-model calculations, where the dominant occupations forthe ground and first-excited states are found, and inagreement with earlier findings [19]. The calculated oc-cupation probability and our experimental results sug-gest a main π ( f / ) ⊗ π ( p / ) configuration for the firstexcited state of Ga. The calculated transition rate sup-ports this assignment too. For the second excited statea half-life of 23(16) ps is measured. This value provides B ( M
1) = 8(6) × − W.u. and B ( E
2) = 51(35)
W.u.(Table III) reduced probabilities which, together with theshell-model results, allows us to propose a π ( f / ) clus-ter configuration and a / − spin-parity assignment forthis state.A high density of negative-parity levels can be observed in the region from 1 to 2 MeV of the level scheme of Ga.This is consistent with π ( p / ) and π ( f / ) single-particlestates coupled to the 2 + core in Zn, and it is well re-produced by the shell-model calculations. These stateswill be of negative parity and should be populated byfirst-forbidden transitions if they are directly β fed. Thelevel scheme of the N = 50 isotone As [52] also shows adensity of levels around 1400 keV much like that of Ga.A similar structure is found in the N = 50 Br isotonepopulated by the β decay of Se [46]. The situationchanges beyond 5 MeV where we observe several stateswith sizeable apparent β feeding, which should arise fromallowed transitions from the Zn positive-parity groundstate. They can be interpreted as neutron particle-holeexcitations from the Ni core.
ACKNOWLEDGMENTS
The authors would like to express profound recogni-tion to the late Prof. Henryk Mach, who pioneered the βγγ (t) fast timing method and its application to exoticnuclei around Ni. Henryk was a true friend and an in-spirational character. His premature passing away is amajor loss for our community both from the human andscientific point of view.This work was supported by the Spanish MINECOthrough the FPA2015-65035-P and RTI2018-098868-B-I00 projects, by the US DoE Grant No. DE-FG02-94ER40834, by the German BMBF Grant05P19PKFNA, and Grupo de Física Nuclear (GFN) atUCM. The support by the European Union SeventhFramework through ENSAR (contract no. 262010) andISOLDE (CERN) Collaboration is acknowledged. V.P.acknowledges support by the Spanish FPI-BES-2011-045931 grant. Fast-timing electronics were provided bythe Fast Timing Collaboration and MASTICON. Figures5, 6 and 7 were created using the LevelScheme scientificfigure preparation system [66]. [1] T. Otsuka, T. Suzuki, M. Honma, Y. 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