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Exploring theLow-Z Shore ofthe IslandofInversionatN = 19 G. Christian,1,2,∗ N. Frank,3 S. Ash,3 T. Baumann,2 D. Bazin,2 J. Brown,4 P. A. DeYoung,5 J. E. Finck,6 A.Gade,1,2 G. F. Grinyer,2,† A. Grovom,7 J. D.Hinnefeld,8 E.M. Lunderberg,5B. Luther,9 M. Mosby,2,10 S. Mosby,1,2 T.Nagi,5 G. F. Peaslee,5 W. F. Rogers,7 J. K. Smith,1,2 J. Snyder,1,2 A. Spyrou,1,2 M. J. Strongman,1,2 M. Thoennessen,1,2 M. Warren,3 D. Weisshaar,2 andA.Wersal2 1DepartmentofPhysicsandAstronomy, MichiganStateUniversity, EastLansing, Michigan48824, USA 2NationalSuperconductingCyclotronLaboratory,MichiganStateUniversity,EastLansing,Michigan48824,USA 3Department of Physicsand Astronomy, Augustana College, RockIsland, Illinois61201, USA 4Department of Physics, Wabash College, Crawfordsville, Indiana 47933, USA 5Department of Physics, Hope College, Holland, Michigan 49423, USA 6Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA 7Department of Physics, Westmont College, Santa Barbara, California 93108, USA 2 8DepartmentofPhysicsandAstronomy,IndianaUniversityatSouthBend,SouthBend,Indiana46634, USA 1 9Department of Physics, Concordia College, Moorhead, Minnesota 56562, USA 0 10Department of Chemistry, Michigan StateUniversity, EastLansing, Michigan 48824, USA 2 (Dated:January6,2012) n Thetechniqueofinvariantmassspectroscopyhasbeenusedtomeasure,forthefirsttime,thegroundstate a J energyofneutron-unbound28F,determinedtobearesonanceinthe27F+ncontinuumat220(50)keV.Statesin 28Fwerepopulatedbythereactionsofa62MeV/u29Nebeamimpingingona288mg/cm2berylliumtarget.The 5 measured28FgroundstateenergyisingoodagreementwithUSDA/USDBshellmodelpredictions,indicating that pf shellintruderconfigurationsplayonlyasmallroleinthegroundstatestructureof28Fandestablishing ] x alow-ZboundaryoftheislandofinversionforN=19isotones. e - PACSnumbers:21.10.Dr,21.10.Pc l c u n Ahallmarkofthenuclearshellmodelisitsreproductionof tionsinnucleargroundstatesbecomeslessclear.Onthehigh- [ largeenergygapsatnucleonnumbers2,8,20,28,50,82,and N (eastern)side,therearestrongindicationsthatgroundstate 1 126. Althoughwellestablishedin stable nuclei, thesemagic intruderdominancepersistsinheavierisotopesofMg,Na,and v numbersbegintodisappearfornucleifar fromstability. For Ne. Forexample,recentmeasurementsof2pknockoutcross 7 example, it has been known for over 30 years that the large sectionsfrom38Sito36Mghaveindicateda0ℏw groundstate 6 shellgapatN=20diminishesforneutron-richnuclei[1–4]. occupationofonly38(8)%in36Mg[14],extendingtheregion 2 ThechangeinshellstructurearoundN=20isnowknownto ofinversiontoatleastN=24fortheMgisotopicchain. 1 bearesultofthetensorforce,whichisstronglyattractivefor 1. the spin flip pairs p d -n d and stronglyrepulsivefor the Untilnow,thelow-Z(southern)sideoftheislandhasbeen 0 5/2 3/2 almostcompletelyunexplored. Ameasurementofboundex- pairs p d -n f [5–7]. For nuclei in the region of N ∼20 2 5/2 7/2 cited states in 27F, which lies on the island’s western border 1 andZ.13,thereducedN=20gapallows pf shellintruder at N =18, has hinted at pf shell contributionsto its excited : configurations,in the form of multi-particle, multi-hole(np- v statestructure[15],butmassmeasurements[16]indicatethat nh ornℏw ) crossshellexcitations, to competewith standard i the 27F ground state is primarily sd shell. For the heavier X sd only configurationsif the gainin correlationenergyis on (N ≥19)fluorineisotopes, lyingwithin the island’swestern r the same order as the size of the shell gap [8–10]. This has a boundary,nodirectexperimentalinformationisavailable.All ledtotheestablishmentofthe“islandofinversion”—aregion thatisknownaredriplinesystematics,e.g.asoutlinedin[17]. ofnucleinearN =20forwhichtheintruderconfigurationis Thefluorineisotopicchainisalsotheonlyareainwhichthe dominantinthegroundstate. intruderstructureofZ<10, N≥19nucleicanbeexamined inanydetailsincetheneutrondriplineforalllighterelements The island of inversion was originally thought to only in- islocatedatN≤16[18–22]. ThismeansthattheN=19iso- clude those nucleiwith 10≤Z ≤12 and 20≤N ≤22 [11]. tonesofoxygenandbelowareunboundwithrespecttothree In more recent years, it has become clear that the island ex- or more neutrons, making their study extremely difficult, if tendsfurther,andmuchexperimentalefforthasbeenputforth notimpossible. to determine its boundaries [12]. On the low-N (western) and high-Z (northern)sides of the island—bothin the direc- Inthisletter,wereportonthefirstexperimentalinvestiga- tionofincreasingstability—itisgenerallyagreedthatground tionofthelow-ZborderoftheislandofinversionforN≥19 stateintrudercomponentsfadeawayforZ≥13andN≤18. nuclei. This is done via a measurement of the ground state Ground state observables for nuclei lying outside these lim- ofneutron-unbound28F,performedwiththetechniqueofin- itsarewelldescribedbysd shellmodelcalculations,suchas variantmassspectroscopy. Ourresults arethen comparedto those utilizing the USDA/USDB effective interactions [13]. bindingenergy(massdefect)predictionsoftheUSDA/USDB Heading away from stability, the role of intruder configura- shellmodel.Inparticular,investigationoftheN=19binding 2 energysystematicsprovidesstrongevidencethatonlytheiso- 140 n tonesatZ=10, 11, and12 arelocated withinthe island. In Bi addition to mappingthe island of inversion, the evolutionof /120 s intruderstructureinneutron-richfluorineisotopesisrelevant unt100 o to the abrupt shift in the neutron dripline observed between C 80 27F oxygen (ending at N =16) and fluorine (ending at N ≥22) [23]. 60 The experimentwas performed at the National Supercon- 40 ductingCyclotronLaboratory(NSCL)atMichiganStateUni- versity, using a primary beam of 48Ca20+ accelerated to 20 140MeV/uinthecoupledK500-K1200cyclotrons[24]. The 0 48Cabeamwasfragmentedina1316mg/cm2 berylliumpro- 40 42 44 46 48 50 52 duction target, and fragmentation products were selected in CorrectedToF(arb.units) theA1900fragmentseparator[25], withthethirdandfourth segmentssettoarigidityof3.47Tmandamomentumaccep- FIG.1. (Coloronline)CorrectedToFforfluorineisotopesproduced tanceof3.9%tooptimizethetransmissionof29Nefragments. from29Ne. Thesecondarybeamwaspassedthroughapairofplastictim- ingscintillators,thefirstlocatedattheA1900focalplaneand 0.2 s the second 44.3 cm upstream of a secondaryreaction target. nt E=0.1MeV u o Additionally, the beam was sent through a pair of position C sensitive Cathode Readout Drift Chambers (CRDCs) and a ed focusingquadrupoletriplet. Thedesired29Ne composedap- aliz E=0.2MeV m proximately2%ofthebeamandcouldbefullyseparatedfrom or 0.1 E=0.4MeV other componentsusing time of flight (ToF) and energyloss N measurements.Theincomingrateof29Nebeamparticleswas E=0.8MeV approximately70s−1,andthemedianenergyofthe29Newas E=1.5MeV 62MeV/u. The secondaryreaction targetwas berylliumwith a thick- 0 nessof288mg/cm2.Statesinneutron-unbound28Fwerepop- 0 0.5 1 1.5 2 2.5 3 ulatedbyone-protonknockoutanddecayedbyneutronemis- DecayEnergy(MeV) sion to 27F+n with a timescale on the order of 10−21 s. FIG.2. (Color online) Simulatedresolution and acceptance of the The decaysof the unboundstates potentiallyfeedboundex- experimentalsetup.Eachcoloredhistogramwasgeneratedbysimu- citedstatesin27F,necessitatingthemeasurementofneutrons, latinga28Fbreakupattheindicatedrelativeenergy,thenfoldingin charged fragments, and g -rays. The gammas were detected detectorresolutionandacceptancecuts. Theshadedcurvewasgen- usingtheCAESARCsI(Na)array[26],whichsurroundedthe eratedbysimulatinga28Fbreakupwiththerelativeenergyuniformly targetandprovidedanin-beamdetectionefficiencyof∼30% distributedfrom0–3MeVandfoldinginacceptanceandresolution. for1MeVgammas.Chargedfragmentsweredeflected43◦by Thecoloredhistogramsareallnormalizedtoatotalareaofunity,and theSweepermagnet[27]andpassedthroughapairofCRDCs, theshadedcurvewasarbitrarilyscaledtofitwithinthesamepanel. an ionization chamber, and thin (0.5 cm) and thick (15 cm) plastic scintillators. Neutrons were detected in the Modular themagnet,anddispersivepositionoftheincomingbeam. A Neutron Array (MoNA) [28], whose front face was located 658cm downstreamof the targetat0◦. MoNA was partially plot of the corrected ToF for fluorine elements is shown in Fig.1,with27Findicated. shadowedbytheentranceflangeoftheSweepervacuumbox, resultinginaneutronangularacceptanceofroughly±6.0◦in Thedecayenergy,Ed,ofthebreakupofunboundstateswas the dispersive (x) plane and ±2.5◦ in the non-dispersive(y) calculatedusinginvariantmassanalysis: plane. The charged particle measurements allowed for event-by- Ed =qm2f+m2n+2(cid:0)EfEn−pfpncosq (cid:1)−mf−mn, (1) eventisotopeselection. Elementswereselectedusingcutson both D E-ToF and D E-E, with D E taken from the ion cham- where m (m ), E (E ), and p (p ) refer to the mass, en- f n f n f n ber signaland E taken from the total chargecollectedin the ergy, and momentum of the charged fragment (neutron), re- thickscintillator.Foragivenelement,isotopeswereseparated spectively,andq istheopeninganglebetweenthetwodecay by correcting their ToF for the various paths taken through products. The neutron input to Eq. (1) was calculated from theSweeper. Thisamountstoremovingcorrelationsbetween ToF and position measurementsin MoNA using linear kine- ToF and a variety of other measured parameters, the most matics, while the charged fragment input was reconstructed importantbeingthe dispersivepositionandangleexitingthe frommeasurementsofthe post-Sweeperemittanceandthe x Sweeper(upto fourthorder),non-dispersivepositionexiting positionofthebeamontarget[29]. 3 of27F(around30CAESARcountswouldbeexpectedinthe eV caseof100%branchingtoanexitedstate). Statesin28Fwere 0k 30 populatedinadirectone-protonknockoutreactionfrom29Ne, 7 2 sonon-resonantcontributionstothedataarenotexpected.An / nts attempttofitthedatawithasingleBreitWignerresonanceis u 20 o shown as the shaded orange curve in the figure. In this fit, C thewidthwaslimitedtoG ≤1MeV,beyondwhichthefunc- 0 tion saturates and lineshapes become indistinguishable. The 10 optimal one-resonancefit parameters are E =590 keV and 0 G =1MeV.TheG valueistwoordersofmagnitudelarger 0 0 than the single particle prediction, already suggesting that a 0 0 0.5 1 1.5 2 2.5 3 single resonancecannotproperlydescribe the data. Further- DecayEnergy(MeV) more,avisualcomparisonofsimulationanddataindicatesa poorfit,withthesimulatedcurvebeingsignificantlynarrower thanthedatadespiteitsunphysicallylargeG value.Thebest- FIG.3. (Coloronline)Measureddecayenergyspectrum(including 0 smearingfromexperimental resolutionandacceptance) for27F+n fit of a single s-wave (as =−0.05 fm) is shown as the grey coincidences. The filled squares with error bars are the measured dot-dashedcurveandisclearlynotconsistentwiththedata. data, and the dashed red and dotted blue curves represent the 220 The poor fit of a single resonance suggests that multiple keV and 810 keV simulation results, respectively. The solidblack resonancesarepresentinthedata,andagoodagreementbe- curve is the sum of the two resonances, with the ratio of 220 keV tweensimulationanddataisachievedbymodellingwithtwo resonance tothetotalareabeing 28%. Thefilledorange curveisa independentBreitWignerresonances,withthewidthofeach simulationofasingleresonanceat590keV,andthegreydot-dashed curveisthebestfitofasingles-wave(as=−0.05fm). resonancefixedatitsapproximatesingle-particlevalue.Given thismodel,thebestfitisobtainedwiththelowerresonanceat 220(50) keV (G ≡10 keV) and the upper resonanceat 810 0 ResonantstatesweremodeledbyaBreit-Wignerlineshape keV (G 0 ≡100 keV), as shown in Fig. 3. The relative con- with energy dependentwidth, derived from R-Matrix theory tributionsofthelowerandupperresonancestothetotalarea [30].FreeparametersarethecentralresonanceenergyE ,the are28%and72%,respectively.Thestrongerpopulationofan 0 resonancewidthG ,andtherelativecontributiontotheoverall excited state is somewhat surprising; however, as discussed 0 decayspectrum. Theorbitalangularmomentumwasfixedat below, contributions from multiple unresolved excited state ℓ=2assumingtheemissionofa0d neutron.Thisassump- resonancesmaybepresentinthedata. Thusitisnotpossible 3/2 tionmaybeincorrectifintrudercomponentsaresignificantin todrawanydefiniteconclusionsfromtherelativeareasofthe 28F; however, separate analyses of the data using ℓ=1 and tworesonances. Toexaminethestatisticalsignificanceofthe ℓ=3 resonances give results that do not differ significantly two-resonanceversusone-resonancehypotheses,wecalculate from the ℓ=2 case. We also investigated the possibility of thelikelihoodratio(−2ln[L1/L2],whereL1andL2arethere- ℓ=0decaybymodellingthedataasans-wave[31]withthe spectivelikelihoodsof the one-resonanceandtwo-resonance scatteringlength,a ,freelyvarying. hypotheses)tobe22.6,providingamoderatelevelofsupport s Smearingfromexperimentalresolutionandacceptancewas forthetwo-resonancemodel. accountedforinaMonteCarlosimulationoftheexperimen- Asmentioned,itispossiblethatmorethantworesonances talsetup,includingallrelevantdetectorresolutionsandaccep- are present in the data, but the low statistics and limited ex- tancecuts.Thesimulationincludedarealisticincomingbeam perimentalresolutionpreventthe inclusionofadditionalres- profileandusedtheGoldhabermodel[32]todescribetheone- onancesinto the fitwith anysortof certaintyregardingtheir protonknockoutreactionpopulating28F. Ademonstrationof location. However,attemptstofitthedatawiththreeormore the simulated overall resolution and acceptance functions is resonances demonstrate that the location of the ground state shown in Fig. 2. To determine optimal fit parameters, large peakisinsensitiveto the presenceof multipleresonances. It MonteCarlodatasets(∼3millionevents)weregeneratedand should be noted that the placement of the ground state peak compared to the experimentaldata using an unbinned maxi- at220keVisprimarilydictatedbytheshapeofthespectrum mumlikelihoodtechnique[33]. below ∼300 keV and not by the dip at around 400 keV. In Themeasureddecayenergyof28Finto27F+n(withnoun- particular,modellingwith a strongresonanceatlower decay foldingofresolutionoracceptance)isshowninFig.3. Com- energies(.150keV)resultsinasharppeakthatisnotconsis- parisonwithFig.2revealsthatthemeasureddataarestrongly tentwiththegradualrisefromzeroseeninthedata.Likewise, distortedbyresolutionandacceptance.Inparticular,thewidth placingthelowestresonancetoohighresultsinamodelthat of the measured data is almost entirely due to experimental significantlyunder-predictsthenumberofeventsbelow∼300 resolution,andtheshapeofthedataabove∼0.8MeVisdom- keV. inated by the limited acceptance at higher relative energies. Combiningthepresentmeasurementofthe28Fneutronsep- No coincidentgammaeventswere recordedin CAESAR, so aration energy with the mass measurements of [16], which theobservedtransitionsareassumedtofeedthegroundstate placethe27Fatomicmassexcessat24630(190)keV,wede- 4 staffforprovidingahighqualitybeamthroughouttheexper- eV) 1.5 USDA imentand the NSCL design staff fortheireffortsin the con- M ( USDB structionofamagneticshieldforCAESAR.Additionally,we Eth 1 acknowledgethecontributionoftheentireMoNAcollabora- B tion,pastandpresent,andtheNSCLGammagroupfortheir − p 0.5 effortsinpreparingandrunningtheexperiment.Onthetheory x e E side,B.A.BrownandA.Signoracciprovidedassistanceand B 0 enlightening discussions regarding shell model calculations. ThisworkwassupportedbytheNationalScienceFoundation -0.5 undergrantsPHY-05-55488,PHY-05-55439,PHY-06-51627, PHY-06-06007,PHY-08-55456,andPHY-09-69173. -1 9 10 11 12 13 14 15 16 17 Z FIG.4.(Coloronline)Differencebetweenexperimentalandtheoret- ical(USDA,USDB)bindingenergiesforN=19isotones,9≤Z≤ ∗ [email protected]; Present address: TRIUMF, 4004 Wes- 17. The error bars onthe datapoints represent experimental errors brookMall,Vancouver,BritishColumbiaV6T2A3,Canada only. Thebluedotted,reddashed,andblackdash-dottedbandsrep- † Presentaddress:GANIL,CEA/DSM-CNRS/IN2P3,BvdHenri resenttherespective170and130keVRMSdeviationsofUSDAand Becquerel,14076Caen,France USDB interactions. Experimental values, save for Z=9 which is [1] C. Thibault, R. Klapisch, C. Rigaud, A. M. Poskanzer, fromthepresentwork,aretakenfrom[16]ifreportedthere; other- R.Prieels,L.Lessard, andW.Reisdorf,Phys.Rev.C12,644 wisetheyarefromthe2003AtomicMassEvaluation[34]. (1975). [2] G. Huber, F. Touchard, S. Bu¨ttgenbach, C. 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