Persistence of the {Z=28} shell gap in {A=75} isobars: Identification of a possible {(1/2^-)} μs isomer in {^{75}}Co and β decay to {^{75}}Ni
S. Escrig, A. I. Morales, S. Nishimura, M. Niikura, A. Poves, Z. Y. Xu, G. Lorusso, F. Browne, P. Doornenbal, G. Gey, H.-S. Jung, Z. Li, P.-A. Söderström, T. Sumikama, J. Taprogge, Zs. Vajta, H. Watanabe, J. Wu, A. Yagi, K. Yoshinaga, H. Baba, S. Franchoo, T. Isobe, P. R. John, I. Kojouharov, S. Kubono, N. Kurz, I. Matea, K. Matsui, D. Mengoni, P. Morfouace, D. R. Napoli, F. Naqvi, H. Nishibata, A. Odahara, E. Sahin, H. Sakurai, H. Schaffner, I. G. Stefan, D. Suzuki, R. Taniuchi, V. Werner, D. Sohler
aa r X i v : . [ nu c l - e x ] J a n Persistence of the Z = 28 shell gap in A = 75 isobars: Identification of a possible (1 / − ) µ s isomer in Co and β decay to Ni S. Escrig,
1, 2, ∗ A. I. Morales, † S. Nishimura, M. Niikura, A. Poves,
5, 6
Z. Y. Xu,
4, 3
G. Lorusso, F. Browne,
7, 3
P. Doornenbal, G. Gey,
8, 9, 3
H.-S. Jung, Z. Li, P.-A. Söderström, T. Sumikama, J. Taprogge,
5, 2, 3
Zs. Vajta,
13, 3
H. Watanabe, J. Wu,
11, 3
A. Yagi, K. Yoshinaga, H. Baba, S. Franchoo, T. Isobe, P. R. John,
18, 19
I. Kojouharov, S. Kubono, N. Kurz, I. Matea, K. Matsui, D. Mengoni, P. Morfouace, D. R. Napoli, F. Naqvi, H. Nishibata, A. Odahara, E. Şahin, H. Sakurai,
4, 3
H. Schaffner, I. G. Stefan, D. Suzuki,
17, 3
R. Taniuchi, V. Werner,
22, 19 and D. Sohler Instituto de Física Corpuscular, CSIC-Universitat de València, E-46071 València, Spain Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain RIKEN Nishina Center, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, 113-0033 Tokyo, Japan Departamento de Física Teórica, Universidad Autónoma de Madrid, E-28049 Madrid, Spain Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid, E-28049 Madrid, Spain School of Computing, Engineering and Mathematics,University of Brighton, Brighton BN2 4GJ, United Kingdom LPSC, Université Grenoble-Alpes, CNRS/IN2P3, F-38026 Grenoble Cedex, France ILL, F-38042 Grenoble Cedex, France Department of Physics, University of Notre Dame, Notre Dame, 46556 Indiana, USA Department of Physics, Peking University, 100871 Beijing, China Department of Physics, Tohoku University, 6-3 Aramaki-Aoba, Aoba, Sendai, 980-8578 Miyagi, Japan Institute for Nuclear Research (Atomki), P.O. Box 51, H-4001 Debrecen, Hungary IRCNPC, School of Physics and Nuclear Energy Engineering, Beihang University, 100191 Beijing, China Department of Physics, Osaka University, Machikaneyama 1-1, Toyonaka, 560-0043 Osaka, Japan Department of Physics, Tokyo University of Science, 2641 Yamazaki, Noda, 278-8510 Chiba, Japan Université Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France Dipartimento di Fisica e Astronomia, Universitá di Padova and INFN Sezione di Padova, I-35131 Padova, Italy Institut für Kernphysik, Technische Universität Darmstadt,Schlossgartenstr. 9, D-64289 Darmstadt, Germany GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy Wright Nuclear Structure Laboratory, Yale University, New Haven, 06511 Connecticut, USA Department of Physics, University of Oslo, NO-0316 Oslo, Norway (Dated: January 18, 2021)
Background:
The evolution of shell structure around doubly-magic exotic nuclei is of greatinterest in nuclear physics and astrophysics. In the ‘south-west’ region of Ni, the development ofdeformation might trigger a major shift in our understanding of explosive nucleosynthesis. To thisend, new spectroscopic information on key close-lying nuclei is very valuable.
Purpose:
We intend to measure the isomeric and β decay of Co, with one proton- and twoneutron-holes relative to Ni, to access new nuclear structure information in Co and its β -decaydaughters Ni and Ni.
Methods:
The nucleus Co is produced in relativistic in-flight fission reactions of
U at theRadioactive Ion Beam Factory (RIBF) in the RIKEN Nishina Center. Its isomeric and β decay arestudied exploiting the BigRIPS and EURICA setups. Results:
We obtain partial β -decay spectra for Ni and Ni, and report a new isomeric tran-sition in Co. The energy ( E γ = 1914(2) keV) and half-life ( t / = 13(6) µ s) of the delayed γ raylend support for the existence of a J π = (1 / − ) isomeric state at 1914(2) keV. A comparison withPFSDG-U shell-model calculations provides good account for the observed states in Ni, but thefirst calculated / − level in Co, a prolate K = 1 / state, is predicted about 1 MeV below theobserved (1 / − ) level. Conclusions:
The spherical-like structure of the lowest-lying excited states in Ni is proved.In the case of Co, the results suggest that the dominance of the spherical configurations over thedeformed ones might be stronger than expected below Ni. Further experimental efforts to discernthe nature of the J π = (1 / − ) isomer are necessary. ∗ [email protected] † Ana.Morales@ific.uv.es
I. INTRODUCTION
The neutron-rich region approaching Ni, with 28 pro-tons and 50 neutrons, is in the spotlight of the most im-portant radioactive-ion beam facilities as this nucleus isthe most exotic doubly-magic one ever synthesized in lab-oratory [1–3]. As more access to new structural featuresis obtained in nearby nuclei [4–14], Ni appears to be thelast spherical system prior to the hitherto unattainabledomain of the r -process reaction path [15]. Indeed, themost advanced theoretical calculations presently avail-able [15, 16] predict the coexistence of spherical andprolate deformed shapes in Ni, with a + deformedbandhead lying at about the same excitation energy ofthe first + state, or even below [15, 17]. Interestingly,first experimental fingerprints for the existence of the de-formed configuration have recently been provided by R.Taniuchi et al. [17], who have proposed a 2.91-MeV de-formed (2 + ) candidate just above the spherical (2 +1 ) stateat 2.60 MeV. Just by adding a few neutrons or removinga few protons to the doubly-magic system, the prolate-deformed configuration is expected to drop below thespherical one and become yrast. Such an inversion, with Ni as the doorway to the new ground-state deformationregion, might have a substantial effect on the theoreticalpredictions on the location of the neutron drip line, asdeformed systems are expected to be more tightly bound[18], hence making a difference to our understanding ofthe r -process nucleosynthesis pathways.The robustness of the Z = 28 closed shell and the coex-istence of deformed and spherical shapes in the neutron-rich νg / Ni isotopes have been a matter of debate ina number of recent experimental and theoretical works[11, 19–32]. Particularly important is the conservationof the seniority quantum number υ –the number of pro-tons or neutrons that are not coupled in pairs to J = 0 [33, 34]– as it is a good indicator of gap stability. In theNi nuclei filling the νg / shell, the seniority is still a goodquantum number for a sub-set of solvable eigenstates[35–40], although it is still unknown if the deformation-driving forces might induce mixing of seniorities in close-lying states with equal J [11, 41, 42].The increase in collectivity as protons are removedfrom the Z = 28 closed-shell regime has also been deeplyinvestigated [5, 6, 13, 26, 43–47], indicating the develop-ment of a new island of inversion around N = 40 thatextends beyond the harmonic-oscillator shell. Theoreti-cally, the shaping of deformation around N = 40 appearsto be driven not only by the variation in the number ofprotons and neutrons as one moves away from stability,but by many particle-hole excitations across energy gapseventually induced by the proton-neutron tensor compo-nent of the nuclear force [48–51], which causes a reduc-tion of the πf / − πf / spin-orbit splitting as neutronsoccupy the νg / orbital [16, 22, 52].The convergence of the N = 40 island of inversion witha newly predicted region of deformation around N = 50 has been theorized recently [15]. This phenomenon iscomparable to the merging of the N = 20 and N = 28 closed shells, with similar underlying mechanisms driv-ing the onset of deformation and the disappearance ofthe classical shell closures. Although the observation of adeformed candidate state in coexistence with the normalspherical shape in Ni supports this prediction, more experimental information on lighter Z ≤ nuclei to-wards N = 50 is needed to fully comprehend how theshell structure evolves in the neutron-rich region below Z = 28 , and if there is a new N = 50 island of inversionin coalescence with the one at N = 40 .With these goals in mind, the isomeric and β decay of Co, with one proton and two neutron holes relative tothe Ni doubly-magic core, were investigated followingthe in-flight fission of a relativistic
U beam on a thinnatural Be target at the Radioactive Isotope Beam Fac-tory (RIBF) at RIKEN, Japan. Despite being pinpointedas one of the A ∼ nuclei with a significant impact on r -process estimates [53], the only experimental informationreported hitherto in the literature for Co is limited tothe half-life t / and an upper limit for the β -delayed one-neutron emission probability P n [2, 32, 54]. Here we pro-vide an additional lower P n limit, of help to extend theexperimental databases used by nuclear astrophysicists.For Ni, four γ rays at 232 keV, 893 keV, 950(20) keV and1100(20) keV have recently been reported [30, 32]. Whilethe first two were observed following β decay of Co inan in-flight fragmentation experiment in NSCL [32], thelatter two were reported in an intermediate Coulomb ex-citation experiment carried out at RIKEN [30]. Of them,only the 232-keV and 950(20)-keV transitions have tenta-tively been placed in the level scheme of Ni, decayingdirectly to the ground state from levels with proposedspins and parities J π = (7 / + ) and (13 / + ) , respectively.In both cases the J π arises from the νg n / , υ = 3 seniorityconfiguration. In the present work, an extended experi-mental study with new γ -ray transitions in both Co and Ni is reported. The new spectroscopic information iscompared to state-of-the-art large-scale shell-model cal-culations using the PFSDG-U interaction in the pf − sdg valence space [15]. On the basis of the experimental andtheoretical results presented here, we argue new spin as-signments and discuss the evolution of the spherical anddeformed configurations in the ‘south-west’ quadrant of Ni.
II. EXPERIMENTAL DETAILS
The present data were obtained during the EURICAcampaign at the RIBF, operated jointly by the RIKENNishina Center and the Center for Nuclear Study of theUniversity of Tokyo. The primary beam of
U wasdelivered by the RIKEN accelerator complex, which con-sisted of a linear injector (RILAC2) and four ring cy-clotrons (RRC-fRC-IRC-SRC). The beam energy was 345MeV/nucleon, with an intensity of approximately × pps. The nucleus Co and other neutron-rich nuclidesclose to Ni were produced by in-flight fission [55] on a3-mm-thick foil of Be. The secondary beam species ofinterest were separated in both the first and second stagesof the BigRIPS magnetic spectrometer [56] using dipolemagnets. The selected fission fragments were identifiedthrough the standard ∆ E - Bρ - T OF method in the sec-ond stage of BigRIPS. Beam-line detectors, as fast plas- A / Q
26 27 28 29 30 31 32 Z C oun t s ID_WAS3ABi
FIG. 1. (Color online) Three-dimensional cluster plot of the nuclei implanted in WAS3ABi as a function of their charge Z andmass-to-charge ratio A/Q . The cluster corresponding to Co is indicated by the red arrow. tic scintillators, parallel-plate avalanche counters and amulti-sampling ionization chamber, allowed for an event-by-event particle identification of the atomic number ( Z )and the mass-to-charge ratio ( A/Q ) of the secondary-beam products.The radioactive ion beam was conducted through theZero-Degree Spectrometer (ZDS) [57] to the EURICA β -decay spectroscopy station, consisting of the active beamstopper WAS3ABi [58] and the γ -ray spectrometer EU-RICA [59]. Since the radioactive nuclei identified in Bi-gRIPS were very energetic, it was necessary to place ahomogeneous aluminium degrader of variable thicknessbefore WAS3ABi in order to adjust the range of the ionsof interest within the implantation device.The silicon array WAS3ABi was not only used to stopthe radioactive nuclei but also to detect electrons andother charged particles emitted in their decay. WAS3ABiconsisted of eight layers of 1-mm-thick double-sided sil-icon strips detectors (DSSSD) with an interspace of 0.5mm between them. Each DSSSD had an active area of × mm and was segmented into sixty vertical stripsand forty horizontal strips, providing a total of 2400 pix-els of 1-mm pitch each. The WAS3ABi DAQ Systemrecorded the pixel position, time and energy informationof the implanted fission products and the emitted β elec-trons. Standard analog electronics were used to read theenergy and time signals of each strip, optimized for theenergy range of β particles. Meanwhile, in-flight fissionfragments released around 1 GeV in the detector, over-flowing the energy signals of the implantation strip andthe neighbouring ones. The position of implantation wasthen defined by the X and Y strips with the fastest timesignal [60].The EURICA array was set up surrounding the activebeam stopper and was used to record the energy and timeof γ rays during a time window of up to 110 µ s after thedetection of an implantation or β electron. As a result,the setup was sensitive to isomeric lifetimes ranging fromseveral ns to several hundred µ s. EURICA was madeof 84 high-purity germanium (HPGe) crystals, arrangedin 12 clusters of 7 crystals packed closely at an averagedistance of 22 cm from WAS3ABi. An absolute detection efficiency of approximately 11% at 662 keV was achievedafter applying a standard add-back routine [25]. III. ANALYSIS PROCEDURE
In the off-line analysis, implantation-like events weredefined by an overflow energy signal in at least one Xand one Y strip of WASA3Bi. These were requested tobe in coincidence with a high-energy signal in the last fastplastic scintillator of ZDS and in anticoincidence with anysignal above threshold registered in a β detector placedbehind WAS3ABi [61]. In this way, secondary reactionproducts generated during the implantation process wererejected to a large extent. The DSSSD of implantationwas then identified as the last one in which an X and a Ystrip were overflowed. On the other hand, electron-likeevents were defined by non-overflow energy signals above β threshold ( ∼
50 keV) in anticoincidence with the lastplastic scintillator of ZDS. Since a β electron typicallyfired several strips before leaving WAS3ABi, the totalenergy released in each DSSSD was obtained from thesum of the energies of adjacent strips within a 8- µ s timegate. The (x,y) position of the β -like particles was thencomputed as the energy-weighted average of the x and ystrips.Once defined, implantations and β particles were cor-related in position and time. In the present analysis,the spatial correlations were restricted to the DSSSDof implantation, and the maximum transverse distancewas fixed to ρ = p ( x − X ) + ( y − Y ) = √ pixels.The time window was set to t = 135 ms, correspond-ing to about five half-life periods of Co [2]. Additionalprompt-time correlations with γ rays were defined to ex-plore the structure of implanted and descendant nuclei.These were set according to the expected nuclear half-lives, and had maximal time windows of 800 ns for non-isomeric β -delayed transitions and ∼ µ s for isomerictransitions. For the study of coincident γ rays, a 400-ns time window was set. Background contributions fromrandomly correlated events were evaluated by applyingthe so-called backward-time technique [62], which ex-ploits correlations between implantations and preceding β electrons using the same conditions as for the normalcorrelations. IV. RESULTS
The distribution of implantations as a function of Z and A/Q is shown in the three-dimensional plot of Fig. 1,where the red arrow pointing to the Co nuclei illustratesthe good quality of the particle identification. In total, ∼ . × ions of Co were implanted in WAS3ABi.
IV.1. Isomeric spectroscopy
The two-dimensional energy-time matrix of the γ raysdetected within approximately µ s after the detectionof Co implantation events is shown in the left panel ofFig. 2. A newly identified isomeric γ transition can beseen at about 1900 keV. Matrix projections on the Y (en-ergy) and X (time) axis are shown in the right top andbottom panels of the figure, respectively. The resultingenergy for the isomeric transition is E γ = 1914(2) keV.Due to the scarce statistics, the half-life has been ob-tained from an unbinned maximum likelihood fit to asingle exponential time distribution function describingthe decay time behaviour of the γ events registered afterthe so-called prompt flash (which is visible at Time ∼ ).No background contributions have been considered in thefitting procedure due to the absence of random γ eventsin the region of interest of the energy-time matrix. Theresulting half-life is t / ( Co ∗ ) = 13(6) µ s. The reporteduncertainty is only statistical and has been evaluated us-ing the RooFit package [63] with the MINOS method fordetermination of error parameters [64]. IV.2. β -decay spectroscopy The singles β -delayed γ -ray energy spectrum result-ing from the analysis procedure described in Sec. III isshown in Fig. 3. There, the most intense transitions at-tributed to the β ( Ni) and β n ( Ni) descendants arelabelled in bold and italics, respectively. As an example,the coincidence spectra gated on the 232-, 1045- and 738-keV γ transitions are shown in the three panels of Fig.4. While the first two are attributed to Ni, the thirdone is assigned to the β n daughter Ni. In all cases,the background contributions have been evaluated andsubtracted as described in Ref. [65].The full list of γ -ray transitions, absolute γ intensities,and γ - γ coincidence relations observed following β de-cay of Co is provided in Tables I and II. While Table Ishows transitions placed in the level scheme of any of thedescendant nuclei ( Ni, Ni or Cu), Table II showsthe list of γ rays attributed to Ni that have not beenplaced in the level scheme due to the absence of coinci-dent transitions. It is to note here the large intensity of the γ rays at 1061.8(11) keV and 2458.8(15) keV.The partial level schemes corresponding to the internaland β decay of Co are shown in Fig. 5. The orderingof the transitions following β decay is proposed accord-ing to γ -ray intensity balances, γ - γ prompt coincidencerelations, and γ -ray energy sum matchings according tothe information displayed in Table I. Apparent β feedingsand/or log f t values are indicated at the left of the levelschemes. These can be considered as upper and lowerlimits, respectively, due to the large Pandemonium effect[66] expected in odd-mass nuclei with large Q β values,as is the case of Co, with Q β = 14380(580) keV [67].In the figure, arrow widths are proportional to transitionintensities, and tentative spins and parities are shown inparentheses on the left of each level.In the β -decay daughter Ni, the levels at 1864.4(8)keV, 972.7(10) keV and 231.8(9) keV are establishedbased on the observation of three independent γ -ray cas-cades to the ground state, namely the 891-973-, 891-741-232- and 1632-232-keV γ cascades, and the directground-state transition at 1865 keV. The location of thelevel at 1044.6(12) keV is based on two arguments: first,the 1045-keV transition is the most intense one in theset of coincident γ rays formed by the 1045-, 417-, 867-,and 1596-keV peaks (see Table I); and second, its energycould match with the tentative direct ground-state tran-sition at 1100(20) keV reported by Ref. [30]. The place-ment of the states at 1461.1(17) keV, 1911.1(16) keV, and3057(4) keV, built up on top of the 1044.6(12)-keV level,is proposed according to the coincidence relationships in-dicated in Table I. Meanwhile, the observed states at1024.6(12), 1762.9(16), 2104.2(16), 2380(3) and 2606(3)keV in the β n daughter Ni were previously reported inthe direct decay of Co to Ni [11] and identified asfollowing the (8 +1 ) → (6 +1 ) → (4 +1 ) → (2 +1 ) → + and (4 +2 ) → (2 +1 ) → + γ cascades connecting states of se-niorities υ = 2 and υ = 4 . A lower limit for the β -delayedone-neutron emission probability of Co has been de-duced from the absolute intensity of the (2 +1 ) → + tran-sition at 1025 keV, resulting in P n ≥ . This value isin good agreement with the upper limit reported in theliterature, P n ≤ [54], and points to a rather lowground-state feeding in the β n decay Co → Ni.
V. DISCUSSIONV.1. β decay of Co to Ni The ground state of the odd-even parent nucleus Cois proposed to have a tentative J π = (7 / − ) based onthe lowest-lying πf − / proton-hole configuration. This as-signment is in accordance with the tentative J π = (7 / − ) attributed to the ground states of the lighter odd-evenisotopes Co and Co [13, 21]. Meanwhile, the maincontribution to the ground-state wave function in thedaughter nucleus Ni is expected from the unpaired neu-tron in the νg / shell, resulting in J π = (9 / + ) . Theassignment is supported by the systematics of lighter C oun t s / k e V Energy [keV]
Time [ (cid:1) s] E v e n t s / . (cid:0) s t ( Co*) = 13(6) (cid:2) s Time [ (cid:3) s] E n e r gy [ k e V ] FIG. 2. (Color online) Left: Energy-time matrix showing the γ rays detected after implantation of Co. The γ -ray energyis plotted against the ion- γ time difference. Top right: Projection of the matrix on the energy axis for a time window of ∼ µ s. Bottom right: Projection of the matrix on the time axis, gated on the 1914-keV transition. The fit to a single exponentialfunction is shown in red. The resulting half-life is indicated. See text for details.TABLE I. List of γ transitions observed in the β decay of Co and placed in the level scheme of any of the descendant nuclei.The nuclei to which the transitions are assigned, the γ -ray energies, the excitation energies of initial and final states, and theabsolute γ -ray intensities are given. As well, the β ( γγ ) coincidence relations are indicated for each transition. An asteriskhighlights those cases where the coincidence relation is established by only one observed count. For Cu, the excited statesare taken from Ref. [31].
Nucleus E γ (keV) E ix (keV) E fx (keV) I γ (%) Coincident γ rays Ni 231.8(9) 231.8(9) 0 41(4) 740.8, 891.4, 1632.2 Ni 416.6(13) 1461.1(17) 1044.6(12) 5.8(10) 1044.6, 1596 Ni 740.8(11) 972.7(10) 231.8(9) 7.1(13) 231.8, 891.4 Ni 866.5(12) 1911.1(16) 1044.6(12) 2.6(8) 1044.6 Ni 891.4(11) 1864.4(8) 972.7(10) 12.5(18) 231.8, 740.8, 972.9 Ni 972.9(12) 972.7(10) 0 7.0(13) 891.4 Ni 1044.6(12) 1044.6(12) 0 8.1(15) 416.6, 866.5, 1596* Ni 1596(3) 3057(4) 1461.1(17) 4.0(11) 416.6, 1044.6* Ni 1632.2(13) 1864.4(8) 231.8(9) 24(3) 231.8 Ni 1865.1(11) 1864.4(8) 0 1.6(7) – Ni 226.0(5) 2606(3) 2380(3) 1.5(5) 616.7, 738.3, 1024.6* Ni 616.7(14) 2380(3) 1762.9(16) 5.8(11) 226.0, 738.3, 1024.6 Ni 738.3(11) 1762.9(16) 1024.6(12) 7.9(13) 226.0, 616.7, 1024.6 Ni 1024.6(12) 1024.6(12) 0 17(3) 226.0*, 616.7, 738.3, 1079.7 Ni 1079.7(11) 2104.2(16) 1024.6(12) 3.2(9) 1024.6 Cu 504.8(14) 1989 1483.5 2.3(7) – Cu 883.0(6) 949.7 66.2 1.8(7) – Cu 992.2(9) 992.2 0 3.4(9) – Cu 1483.0(15) 1483.5 0 2.4(8) –
FIG. 3. The β -delayed γ -ray energy spectrum following implantations of Co nuclei during a time interval of 135 ms. Thepanels present two different ranges of the Y axis to facilitate the observation of weak γ rays. The transitions assigned to the β ( Ni) and β n ( Ni) daughters are marked in bold and italics, respectively. Expanded inset spectra are shown for the γ raysmarked with a dagger.TABLE II. Transitions attributed to Ni that have not beenplaced in the level scheme. The γ -ray energies and the abso-lute γ -ray intensities are shown. Nucleus E γ (keV) I γ (%) Ni 491.3(10) 1.5(5) Ni 566.8(11) 1.5(5) Ni 686.1(6) 1.4(5) Ni 1061.8(11) 5.8(12) Ni 1145.8(10) 1.8(7) Ni 1175.9(13) 2.2(8) Ni 1313.1(8) 1.4(6) Ni 1559.2(8) 1.5(7) Ni 2219.0(10) 2.0(8) Ni 2355.7(13) 1.6(8) Ni 2458.8(15) 5.6(15) neutron-rich νg / even-odd Ni isotopes [21, 68] and therecent experimental studies of Ni [30, 32].The strong β feeding to the excited state at 1864.4(8)keV, I β = 38(7)% , and the corresponding log ft = 4.7(2),provide a robust proof for the occurrence of an allowedGamow-Teller (GT) decay from the πf − / ground stateof Co. As the most energetic single-particle GT transi-tion occurring in the region of Ni transforms a neutronin the νf / orbital into a proton in the πf / shell, theassociated wave function in the final 1864.4(8)-keV stateof Ni is expected to have a large νf − / contribution,resulting in a tentative spin and parity J π = (5 / − ) .Further support for the (5/2 − ) assignment to this level Energy [keV] C oun t s / k e V Gate 232 keV Gate 1045 keVGate 738 keV
741 891 16321596867417 617226 1025
FIG. 4. From top to bottom, β ( γγ ) coincidence spectra gatedon the 232-, 1045- and 738-keV γ transitions. comes from the systematic comparison with the β -decaylevel schemes of lighter even-odd Ni isotopes (see Refs.[21, 68]), which shows that the most probable β -decaytransition populates the yrast (5 / − ) level. For thefirst excited state at 231.8(9) keV in Ni, we propose J π = (7 / + ) despite an observed (apparent) feeding of I β < . Our assignment is in agreement with the workof S. Go et al. [32] and it is equally based on the similarity TABLE III. Possible spins and parities J π for the state at972.7(10) keV, multiplicities of the de-exciting transitions at740.8(11) keV and 972.9(12) keV, and corresponding fractionsof branching ratios R derived from single-particle estimates.See text for details. J π Mult Mult R (cid:20) BR γ BR γ (cid:21) [E x (973 keV)] [E γ (741 keV)] [E γ (973 keV)]5/2 + M1 E2 . × − + E2 E2 . + E2 M3 . × − with the excitation energies of the (7 / +1 ) states in Ni(281 keV) and Ni (239 keV) [21]. This spin and parityarises mainly from the coupling of the first (2 + ) state inthe Ni core to the unpaired ν g / neutron, and has asmain configuration νg n / . Apart from this level, addi-tional states with J π = 3 / + , / + , / + , / + and / + are expected to arise from the +1 ( Ni ) ⊗ νg / multiplet. Excepting the / +2 level, the rest of statesare expected to lie at excitation energies between 1 MeVand 1.5 MeV (see Refs. [21, 30] and discussion in Sec.V.3).The almost non-existing β feedings to the levels at972.7(10) keV and 1044.6(12) keV indicate that, morelikely, they are not fed by allowed GT transitions butthrough internal γ feeding, in accordance with the for-biddenness of a νg / → πf / single-particle β transi-tion. In the case of the 972.7(10)-keV level, the energymatches well with that of the reported (13 / + ) state at950(20) keV [30]. The observation of a prompt, strong γ ray at 891 keV connecting the (5 / − ) level with thisstate, though, rules out spin assignments higher than / .Hence, the only positive-parity states remaining at thisexcitation energy are J π = 3 / + and / + . In TableIII, the quotients R between the single-particle branch-ing ratios of the γ rays decaying from the 972.7(10)-keVlevel are shown for each possible J π and transition mul-tipolarities. The γ -ray energies are 740.8(11) keV and972.9(12) keV. A comparison with the experimental quo-tient of these two transitions, R = 1 . , provides sup-port for a J π = (5 / + ) assignment. Based on this, andgiven the previous spectroscopic information from rela-tivistic Coulomb excitation (see Fig. 2 of Ref. [30]), wepropose the 1044.6(12)-keV state to have J π = (11 / + ) or (13 / + ) .The strong 1061.8(11)-keV transition observed in thesingles γ spectrum of Fig. 3 could very likely de-excitethe remaining J π = (13 / + ) or (11 / + ) level to theground state, as its energy matches well with those ofthe calculated / + and / + levels (see Fig. 5). How-ever, as such high positive-parity spin states cannot bedirectly fed from β decay of the Co ground state and nocoincident γ rays have been observed for the 1061.8(11)-keV transition, it has not been placed in the level schemeshown in Fig. 5. V.2. Isomeric decay of Co The absence of transitions in coincidence with the de-layed 1914(2)-keV γ ray in Co (see Fig. 2) leads to twopossible scenarios. In the first one, the observed tran-sition directly connects an isomeric level at 1914(2) keVwith the J π = (7 / − ) ground state. In such a case, themeasured γ -ray lifetime, t γ / = 13(6) µ s, suggests an M3or E4 character. An E4 nature can be rejected on the ba-sis that the spin and parity of the initial level then wouldhave to be J π = 15 / − , and a faster decay path wouldbe opened through the / − state that is expected atabout 1 MeV from systematics of the lighter νg / odd-even Co isotopes [13] and the present PFSDG-U calcu-lations (see Fig. 5). For an M3 character, J π = 13 / − or / − are possible. Of these, J π = 13 / − would aswell find a faster decay path through the / − or / − levels. Hence, only a J π = 1 / − state could result in anisomeric decay to the J π = (7 / − ) ground state. Thisis the first option presented for the experimental levelscheme of Co in Fig. 5.In the second scenario, the delayed transition may re-main unobserved if it is of low energy and has a high con-version coefficient. With the current setup, this is morelikely to happen for E2 or M2 transitions with energiesbelow 50-60 keV [69, 70]. Then, the observed 1914(2)-keV γ ray would follow in the subsequent decay to theground state. Taking a look at the lowest-lying statesexpected by the PFSDG-U calculations, a possible decaysequence would be (1 / − ) → (5 / ± ) → (7 / − g.s. ) . Thisoption is also indicated in Fig. 5. In this latter case,given the large energy difference of the E2/M2 and M3transitions, one would expect to detect as well a com-peting M3 branch to the ground state. Therefore, thenon-observation of two close-lying γ rays in Fig. 2 lendssupport for the first interpretation, i.e., that the 1914(2)-keV transition more likely connects the first (1 / − ) levelwith the (7 / − ) ground state. V.3. Comparison with shell-model calculations
The theoretical level schemes shown in Fig. 5 for Coand Ni have been obtained with shell-model (SM) cal-culations using the PFSDG-U interaction in a valencespace consisting of the full pf shell for protons and thefull pf − sdg shell for neutrons [15]. In general, wefind a good agreement between the observed yrast lev-els in Ni and their calculated counterparts, with anaccuracy below 200 keV. Regarding the 972.7(10)-keVlevel, the calculations also support a (5 / +1 ) assignmentfrom comparison of the reduced transition strengths,with B ( E
2; 5 / +1 → / +1 ) ≈ e f m , B ( E
2; 5 / +1 → / +1 ) ≈ . e f m , and B ( M
1; 5 / +1 → / +1 ) ≈ , µ N . In the present calculations, the neutron and pro-ton effective charges used for the electric quadrupole op-erator E are ε n = 0 . and ε p = 1 . [15]. Withthem, the B ( E strengths predicted for the / + and / + levels are B ( E
2; 11 / +1 → / +1 ) ≈ e f m and FIG. 5. (Color online) Experimental isomeric and β -decay level schemes of Co extracted from the present work. The energiesof the levels are given in keV. The thickness of the arrows is proportional to the intensities of the transitions connecting thestates. Spins and parities, apparent β feedings and log ft values are indicated at the sides of the levels. Theoretical states,obtained with the PFSDG-U interaction [15], are indicated in red and blue. See text for details. B ( E
2; 13 / +1 → / +1 ) ≈ e f m , respectively. Thesetheoretical results are of the same order than the cal-culations named as SM1 and SM2 in Ref. [30], and aresimilarly systematically lower than the recently measured B ( E values in Ni [30]. The origin of the discrepan-cies might be due to the population of the (5 / + ) statein the intermediate Coulomb excitation experiment, asit lies close in energy to the (13 / + ) and (11 / + ) candi-dates proposed by Ref. [30]. In addition, we have computed theoretical B ( GT ) strengths for the Co → Ni decay with the PFSDG-USM calculations. The corresponding log f t values for thelowest allowed states are given in Fig. 5. These havebeen obtained assuming a standard quenching factor of0.7. It is to note that the valence space employed is onlysuited for levels of natural (positive) parity; hence, thenegative-parity states derived from the B ( GT ) compu-tation have been placed by assuming that the excitation FIG. 6. (Color online) Evolution of the experimental (black) and theoretical (red, blue and green) levels discussed here for theodd-mass Co isotopes occupying the νg / shell. The experimental states are taken from [13] and the present work and thetheoretical ones are calculated with the PFSDG-U interaction [15]. The left panel shows states with a spherical-like structureand the right one shows the lowest-lying levels of the K = 1 / deformed band. energy of the lowest-lying theoretical / − state lies atthe excitation energy of the experimental (5 / − ) level,1864 keV. This assumption is supported by the excellentagreement with the SM prediction discussed in Ref. [21],which places a / − level with a strong ∼ contribu-tion from the νf − / configuration at 1821 keV.The calculations clearly indicate an abundance of pop-ulation to the lowest-lying / − state, with B ( GT ) =0 . and log f t = 4 . , in good agreement with theexperimentally measured log f t = 4 . . The slightlyhigher experimental value might be ascribed to the non-observation of some internal γ de-excitation branchesfrom the (5 / − ) state, as the one connecting with themissing / − level. This state is expected to have νp − / as main configuration and is predicted about 700 keV be-low by the LNPS [71] and the calculations of Ref. [21].Unfortunately, it has not been identified in the presentwork, maybe due to the limited statistics available ormaybe because it lies at a higher excitation energy, asdiscussed for its lighter neighbour Ni [21].Theoretically, three negative-parity states are fed by β decay at excitation energies around that of the experi-mental 3057-keV level. Their energies and J π values are2.82 MeV and / − , 2.96 MeV and / − , and 3.15 MeVand / − . The most strongly populated one is the / − level, with B ( GT ) = 0 . and log f t = 5 . . This resultis close to the experimental log f t value of the 3057-keVstate, log f t = 5 . . However, as the location of thislevel is only tentative due to the scarcity of β ( γγ ) coinci-dences, no spin-parity assignment is proposed. Anotherargument is that, given the large Pandemonium effect in-fluencing our data, none of the other two spins and pari-ties can be discarded, even if the calculated log f t valuesincrease up to log f t = 6 . . In the case of Co, the PFSDG-U levels are an exten-sion of the SM calculations reported in Ref. [13] for Co, Co and Co using the LNPS [71] and PFSDG-U [15]interactions. Similar to its lighter neighbours, two welldefined structures associated to spherical (red and green)and deformed (blue) shapes are distinguished at low ex-citation energies in Fig. 6. The first is related to thecoupling of the πf − / proton hole to the first + state inthe Ni core, which produces a multiplet of states with J π = 3 / − − / − . The second is attributed to pro-ton and neutron excitations across the shell gaps Z = 28 and N = 50 , and results in the development of a de-formed K = 1 / band with intrinsic quadrupole moment Q ≈ efm . On average, the deformed states have1.5 protons and 1.5 neutrons above the closed shells, com-pared with 0.5 protons and 0.5 neutrons for the spherical-like states. According to the calculations, the E2 transi-tions within the deformed band are expected to be muchstronger than those between the spherical-like states andbetween the two structures.In the previous work of T. Lokotko et al. [13] on thelighter νg / odd-mass A Co isotopes, excited spherical (7 / − ) and (9 / − ) levels arising from the coupling of the πf − / hole to the (2 +1 ) state in their A +1 Ni cores wereidentified. These are shown in black on the left panelof Fig. 6, together with the / − and / − levels cal-culated with the PFSDG-U interaction, depicted in redfor the sake of clarity. At first sight, one can notice thatthe excitation energies of the (7 / − ) candidates are onaverage 200 keV higher than their theoretical counter-parts. If this systematic behaviour is extended to thelower-spin members of the multiplet in Co (shown ingreen in the figure), their excitation energies could verylikely be degenerated with or slightly above the observed0isomeric state. This shift would lend support to the in-terpretation of the isomer provided in Sec. V.2, whichsupports an M3 assignment for the 1914(2)-keV transi-tion, corresponding to a (1 / − ) → (7 / − ) ground-statedecay.Theoretically, the lowest-lying spherical-like state with J π = 1 / − arises from the particle-core coupling config-uration πf − / ⊗ +1 ( Ni ) . The question comes naturally:Is this state expected at about the excitation energy ofthe observed isomer? Considering that the experimental (4 +1 ) level in Ni lies at 1920 keV [4] and that the en-ergies of the members of the πf − / ⊗ +1 ( Ni ) multipletare expected to increase at decreasing spin [72, 73], onecan presume that the first spherical-like / − state liesabove. Moreover, if the observed (1 / − ) level is spheri-cal, there still remains the question of why the deformed / − state, predicted at a much lower excitation energy,has not been observed as well. At least in the presentdata set, there are no indications for the existence of alow-spin β -decaying isomer. Based on these arguments,we presume that the (1 / − ) isomeric level reported herefor Co is more likely the bandhead of the deformed K = 1 / configuration. As it is shown in the right panelof Fig. 6, the deformed band would then be shifted up by ∼ N = 50 in the odd-mass Co isotopes may be far moreabrupt than expected by the PFSDG-U calculations (seethe right panel of Fig. 6). This, in turn, points to astronger dominance of spherical-like shapes at low exci-tation energies in the region immediately beneath Ni,posing the question of how fast deformation develops inthe N = 50 shell below Ni. Further spectroscopic dataon this and more exotic N ≤ nuclei will be necessaryto provide answer to this question. VI. SUMMARY AND CONCLUSIONS
The isomeric and β decays of Co have been investi-gated at the RIBF facility at RIKEN (Japan) using theBigRIPS and EURICA setups. First spectroscopic infor- mation is provided for Co, for which a new isomerictransition at 1914(2) keV with a half-life of t / = 13(6) µ s is reported. For the β -decay daughter Ni, new lev-els extending beyond those recently reported in Refs.[30, 32] are provided. In the case of the β n daughter Ni, the population of the (8 +1 ) candidate points to asimilar feeding pattern as in the decay Co → Ni.The nature of the observed states in Co and Ni hasbeen discussed in terms of large-scale shell-model calcu-lations using the PFSDG-U interaction in the pf − sdg model space [15]. In general, a good agreement be-tween experimental and calculated results is found in Ni for excitation energies and log f t values. In thecase of Co, the observed isomeric state is proposedto have J π = (1 / − ) , although a comparison with thePFSDG-U predictions reveals a 1-MeV discrepancy withthe expected excitation energy of the prolate-deformed J π = 1 / − bandhead, leaving no clear interpretation forthe nature of the observed state. ACKNOWLEDGEMENTS
The excellent work of the RIKEN accelerator staff forproviding a stable and high-intensity beam of
U is ac-knowledged. This work was partially supported by KAK-ENHI (Grants No. 25247045, No. 23.01752 and No.25800130); U.S. DOE Grant No. DE-FG02-91ER-40609;Spanish Ministerio de Ciencia e Innovación ContractsNo. FPA2009-13377-C02 and No. FPA2011-29854-C04; Spanish Generalitat Valenciana Contract PROME-TEO/2019/007; Spanish Comunidad de Madrid via the“Atracción de Talento Investigador” Program No. 2019-T1/TIC-13194; European Regional Development FundContract No. GINOP-2.3.3-15-2016-00034; National Re-search, Development and Innovation Fund of Hungaryvia Project No. K128947; and the German BMBF GrantNo. 05P19RDFN1. The authors acknowledge the EU-ROBALL Owners Committee for the loan of germaniumdetectors and the PreSpec Collaboration for the readoutelectronics of the cluster detectors. Part of the WAS3ABiwas supported by the Rare Isotope Science Project whichis funded by the Ministry of Education, Science andTechnology (MEST) and National Research Foundation(NRF) of Korea. [1] P. T. 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