In-beam γ -ray spectroscopy at the proton dripline: 40 Sc
A. Gade, D. Weisshaar, B. A. Brown, J. A. Tostevin, D. Bazin, K. Brown, R. J. Charity, P. J. Farris, A. M. Hill, J. Li, B. Longfellow, W. Reviol, D. Rhodes
IIn-beam γ -ray spectroscopy at the proton dripline: Sc A. Gade a,b , D. Weisshaar a , B. A. Brown a,b , J. A. Tostevin c , D. Bazin a,b , K. Brown a,d , R. J. Charity e , P. J. Farris a,b , A. M. Hill a,b , J.Li a , B. Longfellow a,b , W. Reviol f , D. Rhodes a,b a National Superconducting Cyclotron Laboratory, East Lansing, Michigan 48824, USA b Department of Physics & Astronomy, Michigan State University, East Lansing, Michigan 48824, USA c Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom d Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA e Departments of Chemistry, Washington University, St. Louis, Missouri 63130, USA f Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
Abstract
We report on the first in-beam γ -ray spectroscopy of the proton-dripline nucleus Sc using two-nucleon pickup onto anintermediate-energy rare-isotope beam of Ca. The Be( Ca, Sc + γ )X reaction at 60.9 MeV / nucleon mid-target energy selec-tively populates states in Sc for which the transferred proton and neutron couple to high orbital angular momentum. In turn, dueto angular-momentum selection rules in proton emission and the nuclear structure and energetics of Ca, such states in Sc thenexhibit γ -decay branches although they are well above the proton separation energy. This work uniquely complements results fromparticle spectroscopy following charge-exchange reactions on Ca as well as Ti EC / β + decay which both display very di ff erentselectivities. The population and γ -ray decay of the previously known first (5 − ) state at 892 keV and the observation of a newlevel at 2744 keV are discussed in comparison to the mirror nucleus and shell-model calculations. On the experimental side, thiswork shows that high-resolution in-beam γ -ray spectroscopy is possible with new generation Ge arrays for reactions induced byrare-isotope beams on the level of a few µ b of cross section. Keywords:
Since its discovery in 1955 [1], the neutron-deficient nucleus Sc has attracted attention for a variety of interests rangingfrom rp -process nucleosynthesis [2, 3] to the solar neutrino ab-sorption rate on Ar [4, 5]. In fact, Sc – five neutrons re-moved from stable Sc – is the last proton-bound scandiumisotope, with Sc shown to be unstable against proton emis-sion [6]. Sc is peculiarly located on the nuclear chart (Fig. 1):While it is the proton dripline nucleus of the scandium isotopicchain, it is easily produced from charge-exchange reactions onstable Ca (e.g., see [2, 7, 8]).Due to the low Sc proton separation energy of S p = . − ground state and the 34-keVfirst-excited (3 − ) state are nominally below the proton emis-sion threshold. The nuclear structure interest in this neighbor-ing isobar of Ca has been focused on the particle-hole natureof the states in Sc relative to the doubly-magic N = Z = Ca( p , γ ) Scproton capture rate drove the highest-resolution study of Scyet [2]. To obtain the Ti → Sc weak decay rate, which al-lows determination of the Ar neutrino absorption rate viaisospin symmetry [4], the β decay of Ti, populating high-lying, unbound low-spin states of Sc, was studied with pro-ton spectroscopy (e.g., see [5, 9]). The work reported herepresents the first in-beam γ -ray spectroscopy of this driplinenucleus, Be( Ca, Sc + γ )X, including observation of decaysfrom states above S p .The Ca secondary beam was produced by fragmentation Ti Ti Ti Sc Sc Ca Ca Ca Neutron number
N=20 Ca Sc Sc Ca Ti Ti Ti P r o t o n n u m b e r Ca Ca Ca V V V Sc Ca K K K K K K K K p unbound projectilereaction residuestable or T >1 10 yr . Figure 1: Part of the nuclear chart around Sc. In fact, Sc is the heavi-est dripline nucleus for which the directly neighboring isobar ( Ca) is actu-ally stable, allowing for extensive charge-exchange studies with stable beamsand targets. The only other such isobar pair in the sd shell or above is Na(dripline) - Ne (stable). Nevertheless, γ -ray spectroscopy of Sc had neverbeen performed. of a 140-MeV / nucleon stable Ca beam, accelerated by theCoupled Cyclotron Facility at NSCL [12], impinging on a799 mg / cm Be production target and separated using a 300mg / cm Al degrader in the A1900 fragment separator [13].The momentum acceptance of the separator was restricted to ∆ p / p = . Ca / s. About86% of the secondary beam composition was Ca, with the
Preprint submitted to Physics Letters B July 24, 2020 a r X i v : . [ nu c l - e x ] J u l ighter isotones comprising the less intense beam components.The secondary Be reaction target, of 188 mg / cm thickness,was located at the target position of the S800 spectrograph. Theprojectile-like reaction products were identified on an event-by-event basis in the S800 focal plane with the standard detectorsystems [14] (see Fig. 2). The Ca projectiles in the entrancechannel were selected through a software gate applied on thetime-of-flight di ff erence taken between two plastic scintillatorsbefore the target. Sc Ca Ca Ar S E n e r g y l o ss ( a r b . u n i t s ) <-- Time of flight (arb. units) Figure 2: Event-by-event particle identification, energy loss vs. time of flight,of the reaction residues produced in Ca + Be at 61 MeV / nucleon (mid-target). The energy loss was measured with the S800 ionization chamber andthe time of flight was taken between two plastic scintillators in the S800 anal-ysis beam line and at the back of the S800 focal plane. To show the reactionresidues together with a tail of the Ca projectiles entering the focal plane,a particle- γ coincidence trigger was required for the purpose of the figure. Anumber of (near) dripline reaction residues are marked (the data runs used forthe cross section determination are displayed). The high-resolution γ -ray spectrometer GRETINA [15, 16],an array of 36-fold segmented high-purity germanium detec-tors assembled into modules of four crystals each, was usedto measure the prompt γ rays emitted by the reaction residuesin flight. The 12 detector modules available were arranged intwo rings with four located at 58 ◦ and eight at 90 ◦ with respectto the beam axis. Online pulse-shape analysis provided the γ -ray interaction points for event-by-event Doppler reconstruc-tion of the γ rays emitted in-flight at about 30% of the speedof light [16]. The momentum vector of projectile-like reactionresidues as ray-traced through the S800 spectrograph was incor-porated into the emission-angle determination entering Dopplerreconstruction. Figure 3 displays the Doppler-reconstructed γ -ray spectrum obtained for Sc with nearest-neighbor addbackincluded [16].The inclusive cross section for the two-nucleon pickup from Ca to Sc was determined from the number of Sc detectedin the S800 focal plane relative to the number of Ca projec-tiles and the number density of the target. The rigidity of thespectrograph was chosen to center the two-neutron knockoutresidue Ca in the S800 focal plane and, therefore, Sc waso ff -center. Figure 4 shows the parallel momentum distributionof Sc within the acceptance of the spectrograph. Assumingthat the maximum of the distribution is at about 11.983 GeV / c Energy (keV) C oun t s / k e V Sc v/c=0.310 892(3) keV 1852(4) keV C oun t s / k e V Figure 3: Doppler-reconstructed γ -ray spectrum detected with GRETINA incoincidence with Sc reaction residues produced in the two-nucleon pickuponto Ca. The 892-keV γ -ray transition corresponds to the de-excitation ofthe known (5 − ) state reported at 893.5 keV [17] to the ground state. The second γ -ray cannot be attributed to an already known state in Sc. The inset showsthe γ -ray spectrum in coincidence to the 892-keV transition. Despite the verylow statistics, the spectrum is consistent with 1852 and 892 keV forming acascade. (see Fig. 4) and has a shape similar to what was observed in [18]for one-proton pickup from a Be target, a potential acceptanceloss of 20% is estimated . Including this uncertainty, the inclu-sive cross section amounts to σ inc = . + . µ b (with 3.75%statistical and 7% systematic uncertainty included in the sym-metric error bars and additional +
20% of uncertainty account-ing for a possible acceptance cut.). The systematic uncertaintyis attributed to the determination of a very low cross section inthe presence of background from pile-up.While, due to its unbound target final states, the present reac-tion mechanism is too complex to allow quantitative dynam-ical calculations, in common with other linear- and angular-momentum mismatched two-nucleon transfer reactions, suchas ( α, d ) and its inverse, see e.g. [21, 22], its strong selec-tivity of (stretched) transitions involving maximal orbital an-gular momentum transfer is a firm qualitative feature. Suchlarge (cid:96) -selectivity in one-neutron pickup at intermediate energyis shown in Fig. 2 of Ref. [23] and where, for a Be target, thereaction proceeds by the pickup of well-bound nucleons leavingthe target residue in the continuum [19]. Importantly, unlike the( α, d ) reaction, where the transfer vertex selects an np-pair withspin S =
1, here there is no such restriction, allowing, for exam-ple, for the direct population of the ( π f / , ν f / ) ( J = + ) final state.This di ff erence is illustrated by the Ar( α, d ) K reaction to themirror of Sc that was found to populate the ( π f / , ν f / ) ( J = + ) configuration but not the corresponding 6 + state [24] or by the Ca( α, d ) Sc reaction to the neighboring Sc isotope that pop-ulated the 7 + and 5 + states but not the 6 + [25].Turning to the γ -ray spectrum and the level structure of We note that the exact shape and centroid of the momentum distributionfrom this novel Be-induced reaction is not precisely known and future mea-surements of the shape and energetics may clarify the reaction mechanism andallow for a more precise estimate of the acceptance loss. This is not critical forthe results of the present work. p || − p (MeV/c) C o u n t s / b i n p =11.783 GeV/c Figure 4: Parallel momentum distribution of the Sc reaction residues relativeto the set value of the S800 spectrograph. The range shown corresponds tothe nominal acceptance of its focal plane. The magnetic rigidity was set tocenter Ca, placing the distribution of Sc slightly towards the edge of theacceptance with potential losses. The shape of the distribution is reminiscent ofthe observations for the corresponding fast-beam one-nucleon pickup reactionsexplored earlier [18, 19, 20]. Sc, the very favorable peak-to-background ratio manifestedin Fig. 3 enables the spectroscopy of rare isotopes produced atthe level of µ b. The γ ray observed at 892(3) keV (see Fig. 3)most certainly corresponds to the decay of the previously re-ported (5 − ) state at 893.5(20) keV to the 4 − ground state [17].Since this is the first γ -ray spectroscopy of Sc, we resort tothe mirror nucleus K and shell-model calculations for guid-ance on other potential decay branches from this state. Theshell model for Sc uses the sd p f - wb e ff ective shell-model in-teraction [26], a ( sd ) − ( f p ) + model space for the low-lyingnegative-parity states, and a ( sd ) − ( f p ) + model space for thepositive-parity states. In K, the 5 − → − transition to theground state dominates over the decay to the excited 3 − statewith a branching ratio of 100 vs. 0.15 (see Fig. 5), consistentwith the observation of only the 892 keV γ ray here. This isalso in agreement with the shell-model calculations that predictthe 5 − → − branch is even more suppressed.The population of the 5 − state in the reaction used herevery likely corresponds to the pickup of the proton into the f / orbital and the neutron into the partially filled d / or-bital, consistent with a resulting stretched configuration of( π f + / , ν d − / ) ( J = − ) . The selectivity of the reaction mechanismfavors population of high-orbital-angular-momentum statesand, thus, supports this picture. The proton decay of the state ispresumably hindered by the angular momentum barrier ( (cid:96) = Q p value for the p emission to the only energeti-cally allowed state in Ca, the 3 / + ground state (see Fig. 5).The 4 − and (3 − ) ground and first-excited state are proposed tohave the same π f / ν d / particle-hole configuration based on ( p , n ) reaction studies [7] but their population would not be ob-servable through prompt γ -ray spectroscopy (from the mirrornucleus, the 3 − state is expected to be a nanosecond isomer, alsowith the γ -ray energy below threshold in this work). The reac-tion mechanism also disfavors population of a 3 − configurationdue to the lower orbital angular momentum transfer relative tothe 5 − level. Ca+p Sc K - (2 - )(3 - )(5 - )(J + ) 4 - - - - + + + + g.s. E ne r g y ( k e V ) . . Sc SM - - + + - - Figure 5: Level schemes of the mirror pair Sc and K together with shellmodel for Sc (using the sdp f - wb Hamiltonian [26]) and the Ca + p systemrelevant to explore proton emission from the relevant excited states in Sc. Forall states of Sc discussed here, p emission can only reach the 3 / + groundstate of Ca due to the energetics of the two systems. Levels known in Scbut not observed here are indicated by a dashed line. Literature data takenfrom [17].
In the following, we explore the origin of the γ -ray transi-tion at 1852 keV. The next configuration that allows for highangular momentum can be realized by the pickup of the protonand neutron into the corresponding f / orbitals; our selectivityto high-angular-momentum configurations is again commensu-rate with the observation of a γ -ray decay. The highest J π statesof the resulting ( f / ) multiplet would be 6 + and 7 + . In K,the lowest-lying 7 + and 6 + states are reported at about 2.54 and2.88 MeV excitation energy, respectively, both with decays tothe 5 − state and to each other (Fig. 5). For Sc, if the 1852-keV γ ray, observed here for the first time, were to feed the(5 − ) state, this would place a new excited state at 2744(5) keVin the region where the high-spin positive-parity states are ex-pected. Also, the shell-model calculations performed using the sd p f - wb Hamiltonian [26] place these high-spin positive par-ity states in the same energy region (see Fig. 5). Turning to themirror first, the 7 + state in K is a nanosecond isomer due tothe high γ -ray multipolarities involved (see Fig. 5). In weakly-bound Sc, the 7 + state would be more than 2 MeV above theproton emission threshold, with the γ decay hindered. Both the6 + and 7 + states can decay by (cid:96) = Ca. For Q p = .
215 MeV, the single pro-ton decay width is 49 eV. The 6 + γ decay width is estimatedto be 0.0020 eV (uncertain by up to a factor of 10) and, there-fore, for the 6 + state to decay by γ -ray emission rather thanproton decay, the π g / spectroscopic factor has to be of order10 − , which is plausible but cannot be quantified with present3hell-model Hamiltonians. The γ width of the 7 + , however, issmaller than that of the 6 + by about a factor of 10 , indicat-ing that the 7 + level will likely decay by fast proton emission,given a g / spectroscopic factor of the order mentioned above,and would escape detection in the present experiment. Protonspectroscopy of these two states would indeed be interesting asthe γ - p competition provides information on the g / intrusioninto the model spaces in this region which is otherwise out ofreach.Connecting this back to the reaction mechanism of two-nucleon pickup onto Ca, the shell-model occupancies andtwo-nucleon amplitudes (TNAs) for Ca and Sc o ff er per-spective. In terms of the [( π d / ) , ( π f / ) , ( ν d / ) , ( ν f / )] orbitaloccupancies, the dominant configuration of the 6 + and 7 + statesin Sc is [4,1,2,1] (34% and 65%, respectively). The 0 + groundstate of Ca is dominated by [4,0,2,0] on the other hand. Thus,these two states under discussion are indeed populated by theaddition of a proton and neutron into the f / orbitals, favoredby the reaction mechanism used here.So, 6 + remains as the likely assignment of the new state ob-served in Sc but with the caveat that a strong 6 + → + γ branch would be expected based on the decay pattern of K.Using the branching ratio from K and the intensity of the1852-keV transition, about 185 counts would be expected atabout 200 keV for a 6 + → + transition based on the mirror.There is no evidence for such a strong transition anywhere inthe spectrum (see Fig. 3).The shell-model calculation, with a calculated 6 + -7 + energyspacing of only 127 keV for K and Sc, has the 6 + → − branch as the strongest transition with 6 + → + predicted tobe only 1.5% of that. Adjusting the shell-model calculationso that it modifies the 6 + -7 + energy gap to match the 336 keVobserved in K increases the 6 + → + branch to 21% rela-tive to the strongest decay (to the 5 − ). The calculation with the sd p f - wb Hamiltonian, which does not contain the Coulomb in-teraction, gives a similar result for K and Sc. The additionof the Coulomb interaction would change the mirror branch-ing ratios in two ways. First, the 6 + → − B ( E
1) value couldexhibit a mirror asymmetry. There are examples in this massregion where the mirror B ( E
1) values di ff er by up to factorsof ten [27]. Second, the 6 + -7 + spacing could change. For thedominant configurations of [4,1,2,1] for Sc and [2,1,4,1] for K the 6 + -7 + spacing is the same since the f / configurationis the same for both. The next most important configuration forthe 6 + states is [3,2,3,0] for Sc and [3,0,3,2] for K. Fromexperiment, the 6 + member of the proton ( f / ) configurationin Ti is lowered by 149 keV compared to the neutron ( f / ) configuration in Ca (see Fig. 1 in Ref. [28]). Such a shiftlowers the 6 + state in Sc by 76 keV compared to K and re-duces the branching to the 7 + to 11% relative to the 6 + → − branch. Assuming a 6 + → + branching of 21% relative to the6 + → − transition would lead to about 20 counts expected inthe low-energy region of the γ -ray spectrum (see Fig. 3). We donot see evidence in the spectrum but cannot exclude it either atthe present level of statistics. This makes the data compatiblewith a scenario close to the shell-model calculations but wouldrequire the aforementioned mirror asymmetry in the 6 + → − E ff erence in the branching ratioof the 6 + state between K and Sc.Assuming the placement of the γ -ray transitions in Sc asproposed in Fig. 5 and supported by the low-statistics coinci-dence of Fig. 3, 58(8)% of the cross section feeds the (5 − ) stateat 892 keV and 22% the ( J + ) level at 2744 keV. This leaves20(2)% of the inclusive cross section not resulting in prompt orsu ffi ciently strong γ rays. Consequently, this is the amount ofcross section that could be carried by the 4 − ground state andthe potential (3 − ) nanosecond isomer.In summary, we report the first γ -ray spectroscopy of the pro-ton dripline nucleus Sc, using a two-nucleon pickup reactiononto a fast rare-isotope beam of Ca. Two excited states wereobserved to be populated, the previously known (5 − ) state at892 keV and a new level proposed at 2744(5) keV. The natureof the states is discussed in comparison to the mirror nucleus K and aided by the strong high-angular-momentum selectiv-ity of the fast-beam pickup reaction. More broadly, this workdemonstrates that in-beam γ -ray spectroscopy is possible withhigh-resolution enabled by new-generation germanium detec-tion arrays on the level of a few µ b of cross section. This workalso marks the first exploration of such a fast-beam two-nucleonpickup reaction and consistency with the dominant role of mo-mentum matching is shown as might have been expected fromsimilar work on fast-beam one-nucleon pickup reactions.This work was supported by the U.S. National ScienceFoundation (NSF) under Grant No. PHY-1565546, by theDOE National Nuclear Security Administration through theNuclear Science and Security Consortium, under Award No.de-na0003180, and by the U.S. Department of Energy, O ffi ceof Science, O ffi ce of Nuclear Physics, under Grants No. de-sc0020451 (MSU) and DE-FG02-87ER-40316 (WashU) andunder Contract No. DE-AC02-06CH11357 (ANL). GRETINAwas funded by the DOE, O ffi ce of Science. Operation of thearray at NSCL was supported by the DOE under Grant No. de-sc0019034. J.A.T acknowledges support from the Science andTechnology Facilities Council (U.K.) Grant No. ST / L005743 / References [1] N. W. Glass, J. R. Richardson, Phys. Rev. 98 (1955) 1251.[2] V. Y. Hansper, A. E. Champagne, S. E. Hale, C. Iliadis, and D. C. Powell,Phys. Rev. C 61 (2000) 028801.[3] C. Iliadis, R. Longland, A.E. Champagne, A. Coc, and R. Fitzgerald,Nucl. Phys. A 841 (2010) 31.[4] W. E. Ormand, P. M. Pizzochero, P. F. Bortignon, and R. A. Broglia, Phys.Lett. B 345 (1995) 343.[5] M. Bhattacharya, A. Garca, N. I. Kaloskamis, E. G. Adelberger, H. E.Swanson, R. Anne, M. Lewitowicz, M. G. Saint-Laurent, W. Trinder,C. Donzaud, D. Guillemaud-Mueller, S. Leenhardt, A. C. Mueller, F.Pougheon, and O. Sorlin, Phys. Rev. C 58 (1998) 3677.[6] C. L. Woods, W. N. Catford, L. K. Fifield, N. A. Orr, Nucl. Phys. A 484(1988) 145.[7] T. Chittrakarn, B. D. Anderson, A. R. Baldwin, C. Lebo, R. Madey, J. W.Watson, and C. C. Foster, Phys. Rev. C 34 (1986) 80.[8] S. L. Tabor, G. Neuschaefer, J. A. Carr, F. Petrovich, C. C. Chang, A.Guterman, M. T. Collins, D. L. Friesel, C. Glover, S. Y. van der Werf,S.Raman, Nucl. Phys. A 422 (1984) 12.
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