Shell evolution of N = 40 isotones towards 60Ca: First spectroscopy of 62Ti

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Physics Letters B

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Shell evolution of N = 40 isotones towards ⁶⁰ Ca:

First spectroscopy of ⁶² Ti

M.L. Cortés

^a,b,∗

, W. Rodriguez

^c,a

, P. Doornenbal

^a

, A. Obertelli

^d,e

, J.D. Holt

^f

, S.M. Lenzi

^g

, J. Menéndez

^h

, F. Nowacki

ⁱ

, K. Ogata

^j,k

, A. Poves

^l

, T.R. Rodríguez

^l

, A. Schwenk

^e,m,n

, J. Simonis

^o

, S.R. Stroberg

^f,p

, K. Yoshida

^q

, L. Achouri

^r

, H. Baba

^a

, F. Browne

^a

, D. Calvet

^d

, F. Château

^d

, S. Chen

^s,a

, N. Chiga

^a

, A. Corsi

^d

, A. Delbart

^d

, J.-M. Gheller

^d

, A. Giganon

^d

, A. Gillibert

^d

, C. Hilaire

^d

, T. Isobe

^a

, T. Kobayashi

^t

, Y. Kubota

^a,h

, V. Lapoux

^d

, H.N. Liu

^d,e,u

, T. Motobayashi

^a

, I. Murray

^v,a

, H. Otsu

^a

, V. Panin

^a

, N. Paul

^d

, H. Sakurai

^a,w

, M. Sasano

^a

, D. Steppenbeck

^a

, L. Stuhl

^h

, Y.L. Sun

^d,e

, Y. Togano

^x

, T. Uesaka

^a

, K. Wimmer

^w

, K. Yoneda

^a

, O. Aktas

^u

, T. Aumann

^e,y

, L.X. Chung

^z

, F. Flavigny

^v

, S. Franchoo

^v

, I. Gašpari ´c

^aa,a

,

R.-B. Gerst

^ab

, J. Gibelin

^r

, K.I. Hahn

^ac

, D. Kim

^ac

, T. Koiwai

^w

, Y. Kondo

^ad

, P. Koseoglou

^e,y

, J. Lee

^ae

, C. Lehr

^e

, B.D. Linh

^z

, T. Lokotko

^ae

, M. MacCormick

^v

, K. Moschner

^ab

,

T. Nakamura

^ad

, S.Y. Park

^ac

, D. Rossi

^e

, E. Sahin

^af

, D. Sohler

^ag

, P.-A. Söderström

^e

, S. Takeuchi

^ad

, H. Toernqvist

^e,y

, V. Vaquero

^ah

, V. Wagner

^e

, S. Wang

^ai

, V. Werner

^e

, X. Xu

^ae

, H. Yamada

^ad

, D. Yan

^ai

, Z. Yang

^a

, M. Yasuda

^ad

, L. Zanetti

^e

aRIKENNishinaCenter,2-1Hirosawa,Wako,Saitama351-0198,Japan

bIstitutoNazionalediFisicaNucleare,LaboratoriNazionalidiLegnaro,I-35020Legnaro,Italy

cUniversidadNacionaldeColombia,SedeBogota,FacultaddeCiencias,DepartamentodeFísica,Bogotá,111321,Colombia dIRFU,CEA,UniversitéParis-Saclay,F-91191Gif-sur-Yvette,France

eInstitutfürKernphysik,TechnischeUniversitätDarmstadt,64289Darmstadt,Germany fTRIUMF,4004WesbrookMall,VancouverBCV6T2A3,Canada

gDipartimentodiFisicaeAstronomia,UniversitàdiPadovaandINFN,SezionediPadova,ViaF.Marzolo8,I-35131Padova,Italy hCenterforNuclearStudy,TheUniversityofTokyo,RIKENcampus,Wako,Saitama351-0198,Japan

iIPHC,CNRS/IN2P3,UniversitédeStrasbourg,F-67037Strasbourg,France

jResearchCenterforNuclearPhysics(RCNP),OsakaUniversity,Ibaraki567-0047,Japan kDepartmentofPhysics,OsakaCityUniversity,Osaka558-8585,Japan

lDepartamentodeFísicaTeóricaandIFT-UAM/CSIC,UniversidadAutónomadeMadrid,E-2804Madrid,Spain mExtreMeMatterInstituteEMMI,GSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany nMax-Planck-InstitutfürKernphysik,Saupfercheckweg1,69117HeidelbergGermany

oInstitutfürKernphysikandPRISMAClusterofExcellence,JohannesGutenberg-Universität,Mainz55099,Germany pDepartmentofPhysics,UniversityofWashington,SeattleWA,USA

qAdvancedScienceResearchCenter,JapanAtomicEnergyAgency,Tokai,Ibaraki319-1195,Japan rLPCCaen,ENSICAEN,UniversitédeCaen,CNRS/IN2P3,F-14050Caen,France

sStateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,PRChina tDepartmentofPhysics,TohokuUniversity,Sendai980-8578,Japan

uDepartmentofPhysics,RoyalInstituteofTechnology,SE-10691Stockholm,Sweden vIPNOrsay,CNRSandUniversitéParisSaclay,F-91406OrsayCedex,France

wDepartmentofPhysics,UniversityofTokyo,7-3-1Hongo,Bunkyo,Tokyo113-0033,Japan xDepartmentofPhysics,RikkyoUniversity,3-34-1Nishi-Ikebukuro,Toshima,Tokyo172-8501,Japan yGSIHelmholtzzentrum fürSchwerionenforschungGmbH,Planckstr.1,64291Darmstadt,Germany zInstituteforNuclearScience&Technology,VINATOM,P.O.Box5T-160,NghiaDo,Hanoi,VietNam aaRu ¯derBoškovi´cInstitute,Bijeniˇckacesta54,10000Zagreb,Croatia

abInstitutfürKernphysik,UniversitätzuKöln,D-50937Cologne,Germany

acDepartmentofScienceEducationandDepartmentofPhysics,EwhaWomansUniversity,Seoul03760,RepublicofKorea adDepartmentofPhysics,TokyoInstituteofTechnology,2-12-1O-Okayama,Meguro,Tokyo,152-8551,Japan

aeDepartmentofPhysics,TheUniversityofHongKong,Pokfulam,HongKong afDepartmentofPhysics,UniversityofOslo,N-0316Oslo,Norway

*

Correspondingauthorat:IstitutoNazionalediFisicaNucleare,LaboratoriNazionalidiLegnaro,I-35020Legnaro,Italy.

E-mailaddress:[email protected](M.L. Cortés).

https://doi.org/10.1016/j.physletb.2019.135071

0370-2693/©^{2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

agInstituteforNuclearResearchoftheHungarianAcademyofSciences(MTAAtomki),P.O.Box51,DebrecenH-4001,Hungary ahInstitutodeEstructuradelaMateria,CSIC,E-28006Madrid,Spain

aiInstituteofModernPhysics,ChineseAcademyofSciences,Lanzhou,PRChina

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received17September2019

Receivedinrevisedform29October2019 Accepted29October2019

Availableonline4November2019 Editor:D.F.Geesaman

Keywords:

Shellevolution Radioactivebeams Gamma-rayspectroscopy

ExcitedstatesintheN=^{40 isotone62Tiwerepopulatedviathe63V}(p,2p)⁶²Tireactionat∼200 MeV/nu- cleon attheRadioactiveIsotopeBeamFactoryandstudiedusingγ-rayspectroscopy.Theenergiesofthe 2⁺₁ →⁰⁺gs and 4⁺₁ →²⁺1 transitions,observedhere forthefirsttime, indicateadeformed ⁶²Tiground state. Theseenergiesare increased comparedtothe neighboring⁶⁴Crand ⁶⁶Feisotones, suggestinga small decreaseofquadrupole collectivity.The present measurement iswell reproducedby large-scale shell-model calculations based on effective interactions, while ab initio and beyond mean-field cal- culations do not yet reproduce our findings. The shell-model calculations for ⁶²Ti show a dominant configurationwithfourneutronsexcitedacrosstheN=^{40 gap.Likewise,theyindicatethatthe N}=⁴⁰ islandofinversionextendsdownto Z=^20,disfavoringapossibledoublymagiccharacteroftheelusive 60Ca.

©^{2019TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

Our understanding of atomic nuclei largely derives from the conceptofnuclearshellstructure.Withinthispicture,thearrange- mentofnucleonsinsidethenucleuscanbeexplainedbythefilling ofdiscreteenergylevels.Sizablegaps betweentheseorbitsdisfa- vorthepopulationofthehigher-energylevels,andareinterpreted asclosedshells,whichgiverisetomagicnumbers.Suchshellclo- surescan be evidencedby a relativelyhigh-lyingfirst excited 2⁺ state, a relatively smallelectric quadrupole transition probability tothe groundstate, B(E2)↓^{,anda steepdecrease ofthe separa-} tion energy. Experimentalevidence collected inthe last decades, particularlysincetheadventofradioactiveionbeams,hasshown that shellstructure undergoessignificant changesforisotopes far fromstability [1].Examples ofthese changes arethe appearance ofnew magicneutron numbers at N=³²,34 inthe Ca isotopes andneighboring isotopic chains [2–9], and at N=^{16 for O iso-} topes [10–12], as well asthe disappearance of the shell closure at N=^{8 [13–16], N}=20 [17,18] and N=28 [19,20] in various neutron-richisotopes.

GiventhatN=^40,whichcorrespondstothefillingoftheneu- tron p f shells, is a harmonicoscillator magicnumber, the study of the structure of N=40 isotones can provide insight into the mechanisms governing shell evolution. Indeed the characteristics ofthis isotonic chainvary with thenumber ofprotons. For ⁶⁸Ni ( Z=^{28), a high E}(2⁺₁) energyanda low B(E2)↓ ^{havebeen ob-} served [21]. However, due to the parity change between the p f shell andthe g9/2 orbit, the 2⁺₁ state involves atleast two neu- trons across N=^{40. Such a} neutron-dominatedexcitation could result in a large E(2⁺₁) energy and low B(E2)↓ ^{value without} a large shell gap [22]. For the neutron-rich Fe ( Z=^{26) and Cr} ( Z=^{24)isotopes,amonotonous decreaseofthe E}(2⁺₁)whenap- proaching N =^{40 and beyond has been} observed [23–26]. This decrease indicates a rapid development of collectivity when re- movingprotonsfromthe f7/2 shell.Incontrast,themeasurement ofthe E(2⁺₁)of^58,60Ti( Z=^{22)onlyshowedamoderatedecrease} towards N=40 [27,28].Thevery exotic⁶⁰Ca ( Z=^20),wherethe Caisotopic chainmeetsthe N=40 isotones, isa keynucleusfor shellevolution [29,30], butdifficulttoreach experimentally.Only recently its existence has been established [31], supporting the- oretical predictions for a bound ⁷⁰Ca. However, the heaviest Ca isotopewithknownspectroscopicinformationis⁵⁴Ca [4].

Theoreticalcalculationsintheshell-modelframework [32] con- cluded that the development of collectivity in N=^{40 nuclei is} duetoquadrupolecorrelationsthat giverise todeformedground states,dominatedbyintruderneutronorbitsbeyondthe p f shell.

Thisleadstoanislandofinversionbelow⁶⁸Ni,similartotheone formed around ³²Mg [32]. Thesecalculations predict an increase inthe E(2⁺₁) energyofthemoreexotic N=40 isotones⁶²Tiand 60Ca,whileconservingtheintrudercharacterinthegroundstate.

Ontheotherhand,symmetryconservingconfigurationmixingcal- culationswiththeGognyinteractionpredictaconservationofthe N=40 gap [33]. Theseresultsagree withcalculationsperformed usingthefive-dimensioncollectiveHamiltonian, whichsuggestan energy gap of about 4 MeVat N=^{40, predicting spherical 62Ti} and⁶⁰Ca [34,35].It is notedthat thebeyond-mean-field andthe shell modelcalculationsprovide similarresultsfor⁶⁴Cr and⁶⁶Fe, whiletheysubstantiallydivergefor⁶⁰Caand⁶²Ti.Therefore,spec- troscopy of ⁶²Ti offers a crucial test between the two different pictures. In addition,theproperties ofCa isotopes havebeenex- tensively studied with coupled-cluster theory [36] and valence- shellinteractions [3,37],inbothcasesusingtwo-nucleon(NN)and three-nucleon (3N) interactions fromchiral effective field theory.

Such calculationsagreewell withexperimental energylevelsand binding energies up to ⁵⁴Ca, andpredict the drip line to be lo- catedaround⁶⁰Ca.Thisisincontrasttodensityfunctionaltheories basedonthemeanfieldapproachwhichpredict,dependingonthe selected interaction, Ca isotopes tobe bound up to A=⁶⁸−^76.

Beyond N=^40, coupled-cluster theory suggests the existence of two-neutronhalosandEfimovstatesin⁶²Ca [38].

Clearly, spectroscopic information on exotic isotopes around 60Ca is necessary to deepen our understanding of the nuclear structure atN=^{40 andto benchmarkthe}theoretical predictions towardstheneutrondripline.Inthepresentwork,thefirstspec- troscopy of⁶²Ti is presented. This isotope representsthe closest nucleusto⁶⁰Caforwhichspectroscopicstudiescanbeperformed atexistingradioactivebeamfacilities.

The experiment was carried out at the Radioactive Isotope BeamFactory,operatedbytheRIKENNishinaCenterandtheCen- terforNuclear StudyoftheUniversity ofTokyo.A primarybeam of ⁷⁰Zn withan energyof 345 MeV/nucleon and an average in- tensityof240 pnAwas fragmentedona3-mmthick Betarget to produce a cocktail ofsecondary beams which included ⁶³V. The fragmentsofinterestwereselectedwiththe B

ρ

− ^E−^B

ρ

tech- nique using two wedge-shaped aluminium degraders situated at the dispersivefocal planesofBigRIPS [39].Event-by-eventidenti- ficationwas performedbyanenergylossmeasurementinanion- izationchamber,positionandanglemeasurementsinparallelplate avalanchecountersatdifferentfocalplanes,andthetime-of-flight measuredbetweentwoplasticscintillators.The⁶³Visotopes were

Fig. 1. Particleidentificationplot for theoutgoingfragments measuredwith the SAMURAIdipolemagnetandrelateddetectors.Incoming⁶³Visotopeswereselected withBigRIPS.⁶²Tiisotopesareindicatedbytheellipse.

deliveredto the focusarea infront of theSAMURAIdipole mag- net [40],withanaverageintensityof3 ppsandanaverageenergy of239 MeV/nucleon.AtthislocationtheMINOSdevice [41],com- posedofa151.3(13) mmlong liquidhydrogentarget surrounded byaTimeProjectionChamber(TPC),wasplaced.Theefficiencyof MINOStodetectatleastone protonwas measuredas93(4)%and the resolutionfor the vertexreconstruction was estimated to be better than 2 mm(

σ

) [42]. Following proton knockout reactions inthe liquidhydrogen target, the ⁶²Ti fragments hadan average energyof154 MeV/nucleon and wereidentifiedusingtheSAMU- RAIdipolemagnetandassociateddetectors [40].Fig.1showsthe particleidentificationobtainedwithSAMURAIwhenselecting⁶³V as incoming beam. A total of 1880 events corresponding to the 63V(p,2p)⁶²Tireactionwasreconstructed.Thetransmissionofthe unreacted ⁶³V beam along the beam line was measured to be 50.9(11)%andtheinclusive(p,2p) crosssection was determined tobe4.0(1) mb.

MINOSwas surrounded by the high-efficiency

γ

-ray detector array DALI2⁺,composed of 226NaI(Tl)detectors covering angles between∼^{15◦ and}∼^{118◦ with respectto the centerof thetar-} get [43,44].The array was energycalibratedusingstandard ⁶⁰Co, 88Y,¹³³Ba,and¹³⁷Cssources.Thefull-energy-peakefficiencyofthe arraywasdeterminedusingadetailedGEANT4 [45] simulationand wasfound tobe 30% at1 MeVwithanenergyresolution of11%

forasourcemovingat0.6c.

Dopplercorrected

γ

-rayspectrawereobtainedusingthereac- tion vertex and the velocity of the fragment reconstructed with MINOS. Peak-to-total ratio and detection efficiency improved by adding-up the energies of

γ

-rays deposited in detectors up to 10 cmapart.Toavoidthereconstructionofadd-backeventsfrom thelargeatomicbackground,

γ

-rayswithenergiesbelow100 keV were not taken into account in the analysis. The Doppler cor- rected spectrum obtained for the ⁶³V(p,2p)⁶²Ti reaction is dis- played in Fig. 2a). Two peaks are clearly visible and the

γ

−

γ

coincidenceanalysisdemonstrates theircoincidence (Fig. 2b).Us- ing a 2-dimensional

χ

² minimization, the energies of the tran- sitionswere deducedtobe 683(10) keVand823(20) keV.In this minimizationprocedure,thesimulatedresponseofDALI2⁺totran- sitions of differentenergies were fitted insteps of5 keV to the experimentaldataandthe

χ

² valuewasobtainedforeachcombi- nationofenergies. Thesimulationincludedtheexperimental res- olutionofeachcrystalanda doubleexponentialbackground was assumedforthefit.Theparametersoftheseexponentialfunctions werechosen basedonaconsistentanalysisofthespectraofpro- tonknockoutreactionsproducing⁵⁰Arand⁶⁰Ti.Theerrorsonthe

Fig. 2. a)Dopplercorrectedγ-rayspectrumof⁶²Tiobtainedfromprotonknockout from⁶³V.Thespectrumwasfittedbytheconvolutionofthesimulatedresponse ofDALI2⁺ totheobservedtransitionsandadoubleexponentialbackground.Two additionaltransitionsareincludedtoimprovethefit(seetextfordetails).b)Coin- cidencespectrumobtainedwhenapplyingthegateindicatedbythebluearea.

transitionenergiesincludethestatisticalerrorfromthefit,aswell asthe systematic errorarising fromthe calibration of the

γ

-ray detectorsandthepossiblelifetimeofthestates.Giventhatglobal systematicfits [46] suggestalifetimeofthe2⁺₁ statebelow30 ps, an uncertaintyof 15±^{15 pswas consideredforthedecayofthe} 2⁺₁,whilethe4⁺₁ wasconsidered shortlived.The besttotalfitas well astheindividual responsefunctionsofDALI2⁺ areshownin Fig. 2. The relative intensities ofthe peakssuggest the tentative assignmentofthe 683(10) keVandthe823(20) keVpeaksto the 2⁺₁ →⁰⁺gsand4⁺₁ →²⁺₁ transitions,respectively.

A structure in the

γ

-ray spectrum above theestimated back- groundwasobservedbetween1000and1500 keV.Twoadditional transitions at energies of 1222(37) keV and 1328(45) keV, were used to reproduce thisstructure. The significance levels of these peaksare 2

σ

and3

σ

,respectively. The inclusionof moretransi- tions didnot provide anyfurtherimprovementon the

χ

² of the fit.Astructure at320keVwas observedwitha significancelevel of1

σ

.Theexistence ofthispeak couldnot befirmlyestablished, therefore it was not considered, and its possible contribution to thepartialcrosssectionwas assumedtobewithintheerrorbars oftheanalysis.Thesepossibletransitionsindicatethepresenceof different states being populated in the reaction, but the limited resolutionofDALI2⁺ andthelow statisticsdidnotallowtoiden- tifythemnor toperform acoincidence analysis. Theexistence of such transitions, whichpotentially feed the2⁺₁ or4⁺₁ states,im- pliesafragmentedspectroscopicstrength.

Exclusive cross sectionsto populate the (2⁺₁) and (4⁺₁) states, from whichadditional feeding should be subtracted, were calcu- latedbasedon thefitted

γ

-rayintensities, thetotal transmission of the isotopes and the efficiency of MINOS. Cross sections of 1.5(3) mband0.8(1) mbwereobtainedforthe(2⁺₁)stateandthe (4⁺₁)state,respectively.Thecrosssectionsmeasuredforthepossi- bletransitionsat1222(37) keVand1328(45) keVweredetermined tobe0.2(1) mband0.3(1) mb,respectively.Asnofirmstatement can bemaderegarding thesetransitions,we limitthe interpreta- tion totheir possible directfeedingto the 2⁺₁ state. Forthis, the average value between100% feedingandno feeding was consid- ered andthe errorincreased to cover both possibilities, giving a exclusivecrosssectionof1.3(4) mbforthe(2⁺₁)state.

The evolution of measured E(2⁺₁) and E(4⁺₁) energies for the N=40 isotones between Ti and Ge [47] is presented in Fig. 3.

The E(2⁺₁) andE(4⁺₁) reportedinthisLetterfor⁶²Tihavea sim- ilar value than theones measured for⁶⁶Fe, higherthan those of

Fig. 3. SystematicsofE(2⁺₁)(filledsymbols)andE(4⁺₁)(opensymbols)foreven- evenN=40 isotones.Thecirclesrepresentthepresentmeasurement.Theblack, blue,andredlinesrepresentLSSM,SCCM,andVS-IMSRGcalculations,respectively (seetextfordetails).

64Cr.Itispointedout that⁶⁴Cr,witha E(2⁺₁)of420 keV,hasthe largestquadrupoledeformationobservedintheregion [26,48].Our resultsshowthefirstincreaseofE(2⁺₁)alongtheN=40 isotones towards⁶⁰Ca. Thisincrease establishesaparabolictrendandsug- gestsadecreaseinquadrupolecollectivity.This,inturn,could be interpreted asa signofa significant N=40 shellgap, and gives thepossibilityofadoublymagiccharacterfor⁶⁰Ca.

LargeScaleShellModel(LSSM)calculations,shownbytheblack linesinFig.3,werecarriedoutwiththeLNPSinteraction [32] us- ing a ⁴⁸Ca core anda valencespace which included the full p f shell for protons and the 0 f_5/2, 1p_3/2, 1p_1/2, 0g_9/2, and 1d_5/2 orbits for neutrons. This interaction has already successfully re- produced the E(2⁺₁) of the heavier N =40 isotones [32]. The LSSMcalculationsreproduceveryaccuratelythedataforboththe E(2⁺₁)and E(4⁺₁)ofthe N=40 isotonesincludingourvaluesfor 62Ti.Thisagreementstrengthensthetentativespinandparityas- signmentforthesestates.As shownin Ref. [32],the calculations predict a reduction of the 0 f5/2−^0g9/2 gap when going from 68Ni to ⁶⁰Ca, aswell asthe closeness ofthe quadrupole partner orbits0g9/2 and1d5/2.Duetothisproximity,quadrupolecorrela- tionsproducea gaininenergythat largelyovercomesthecostof exciting neutrons across the N=^{40 gap, thereby favoring many-} particle-many-holeconfigurations.Thissituationresemblesthebe- havior at N=^{20 and suggests an island ofinversion for N}=⁴⁰ isotones below⁶⁸Ni. For⁶²Ti,a gapofabout1 MeVispredicted, with a resulting wave function dominated by 4p-4h excitations (63%)andasignificant6p-6hcomponent(22%) [32].Furthermore, a ground-state deformation parameter β =⁰.28 for ⁶²Ti is ob- tained.Theagreementwiththemeasuredenergies ofthe N=⁴⁰ isotones, including ⁶²Ti, indicates that the island of inversion in thisregionextendsdownto⁶⁰Ca.Itisparticularlyremarkablethat although the E(2⁺₁) for⁶⁰Ca ispredicted to be 1.35 MeV, which representsanincreasewithrespecttotheneighboringisotones,a 4p-4hconfigurationdominance(59%)prevails [32].

Symmetryconservingconfigurationmixing(SCCM)calculations usingtheGognyD1Seffectiveinteraction [49,50] wereperformed for⁶²Ti,⁶⁴Cr,and⁶⁶Fe,andareindicatedbythebluelinesinFig.3.

Forthecalculations, each individual nuclear state wasdefined as thelinearcombinationofmultipleintrinsicmany-bodystateswith differentquadrupole(axialandtriaxial)shapes [51,33].Crankedor octupoledeformedstateswere not included,therefore,a system- aticstretchingofthelevelswithrespecttotheexperimentalvalues isexpected [52,53].TheE(2⁺₁)predictedfor⁶⁴Crand⁶⁶Felievery closetotheLSSMpredictions,andareinfairagreementwiththe experimental data. However, when going to ⁶²Ti, a more abrupt

increaseoftheE(2⁺₁)isobtained.FortheE(4⁺₁)energies,thecal- culationsoverestimate theexperimentalvaluesbyabout500 keV, although the minimum value for ⁶⁴Cr is maintained. It is noted that for ⁶⁴Cr and ⁶⁶Fe, where the deformation is well described bythemodel,theinclusionofcrankingwouldfurtherimprovethe agreementwiththeexperimentaldata.Withinthismodel,theen- ergygapatN=^{40 isconserved,leadingtoagroundstate of62Ti} highlymixedwiththesphericalconfiguration.Thisisalsothecase for ⁶⁰Ca, which is predicted asa doubly magic nucleus withan E(2⁺₁)of4.73 MeV [53].Itisnotedthat althoughthiscalculation yields asphericalgroundstate for⁶²Ti,the2⁺₁ and4⁺₁ statesbe- long to a deformedband starting at the0⁺₂ state. This band can correspond to the predictions ofthe LSSM calculationsandindi- cate that the SCCM calculations overestimate the N=^{40 gap in} thisregion.

Ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) [54–58] calculations were also performed for 62Ti,⁶⁴Cr,and⁶⁶Fe,asshownbythe redlines inFig.3.The chi- ral NN+^3N interaction labeled 1.8/2.0 (EM) in Refs. [59,60] was used, whichis based onthe NNpotential from Ref. [61] and3N forces fitted to light systems up to ⁴He only. With this NN+^3N interaction, ground-stateenergies upto Sn [58,59,62,63] aregen- erally well reproduced. As the VS-IMSRG captures 3N forces be- tween valence nucleons via an ensemble normalordering [57], a separate valence-space interaction is decoupled for each nucleus of interest. Here, the same model space as the LNPS Hamilto- nian isconsidered(addingthe 2s_1/2 neutronorbital for⁶²Ti).Us- ing the Magnusformulation of the IMSRG [64], operators at the two-body level are truncated in the so-calledIMSRG(2) approxi- mation. The VS-IMSRG interaction is diagonalized with the code ANTOINE [65],including,forthefirsttime intheVS-IMSRG,both intruder quadrupole partners, such as0g_9/2–1d_5/2 [66]. The VS- IMSRG overestimatesthe E(2⁺₁)and E(4⁺₁) excitation energies in 62Ti, ⁶⁴Cr, and ⁶⁶Fe, predicting all statesas spherical.Cross-shell excitations to the 0g9/2–1d5/2 orbits stay atthe 1p-1h level be- causeofthesubstantial N=^{40 shellgap,3.7 MeVin62Ti.Within} this model, a E(2⁺₁) of around 7 MeV is predicted for ⁶⁰Ca, an overestimationwhichisalsoobservedatothershellclosureswith the VS-IMSRG [59,63,67]. Thislimitation hasbeen related to the IMSRG(2) truncation [66], which may not fully capture correla- tions associatedwith cross-shellexcitations. Preliminary compar- isons withcoupled-clustertheory indicate thatkeepingoperators atthe three-body levelwill improvetheresults.Also, choosing a deformed reference state, instead of spherical as in the present work, may capture quadrupole correlations more efficiently [68, 69].

Single-particle theoreticalcrosssectionswerecomputedinthe DWIA framework [70]. The single-particle wave functions and the nuclear densitywere obtained by theBohr-Mottelson single- particle potential [71]. The optical potentials for the distorted waves in the initial and final channels were constructed by the microscopic foldingmodel [72] with theMelbourne G-matrix in- teraction [73] andwiththe calculated nuclear density. The spin- orbitpartofeach distortingpotential was disregarded.Asforthe transition interaction,the Franey-Loveeffective proton-protonin- teraction was adopted [74]. Cross sectionsat different beamen- ergies, from 240 MeV/nucleon at the entrance of the target to 154 MeV/nucleon at the exit, were calculated and weighted ac- cordingtotheenergylossinthetarget.Theoreticalcrosssections (

σ

theo) were obtainedby weighting the single particle cross sec- tionsbythecalculatedspectroscopicfactors.

The spinandparityofthe groundstate of⁶³Varenot known experimentally. The LSSM calculation suggestsit to be 3/2⁻, al- thoughstateswithspinandparityof5/2⁻and7/2⁻appearvery closeinenergy,suggestingthepresenceofisomericstates.Noex-

Table 1

Experimentallydeducedexcitationenergiesandcrosssectionsfor⁶²Tifollowingthe⁶³V(p,2p)⁶²Tireaction,andcomparisonwiththeoreticalcrosssectionsobtainedwith theLSSMcalculation.Thespectroscopicfactorsandcorrespondingcrosssectionsareshownforthethreepossiblevaluesofthespinandparityofthegroundstateof⁶³V.

Theexperimentalground-statecrosssectionwascalculatedbysubtractingthecrosssectionsofthemeasuredtransitionsfromtheinclusivecrosssection.

E (keV)

σexp (mb)

E (keV)

J^π lj σs.p

(mb)

J^π=3/2⁻ J^π=5/2⁻ J^π=7/2⁻

C²S σtheo(mb) C²S σtheo(mb) C²S σtheo(mb)

0 1.4(4) 0 0⁺₁ p3/2 1.56 0.03 0.05 – 0.04 – 0.58

f7/2 1.46 – 0.03 0.4

683(10) 1.3(4) 720 2⁺₁ p3/2 1.54 0.06 0.61 0.01 0.97 0.02 0.07

f7/2 1.44 0.36 0.66 0.03

1506(22) 0.8(1) 1570 4⁺₁ p3/2 1.50 – 1.30 0.04 0.38 0.04 0.44

f7/2 1.41 0.92 0.23 0.27

Fig. 4. Partialprotonremovalcrosssectionsforthe⁶³V(p,2p)⁶²Tireaction.Panel a)showstheexperimentalresults.Panelsb)tod)show LSSMcalculations using theLNPSinteractionassumingthegroundstateof⁶³Vas3/2⁻,5/2⁻ and7/2⁻, respectively.

perimentalevidence ofsuch stateshas beenreported so farand available data are consistent with a 3/2⁻ assignment [75]. Re- sultsofthecalculationsforthethreecasesareshowninTable1, anddisplayed inFig. 4, togetherwiththeexperimental results.It canbe seen that neither the absolutevalue orthe generaltrend shownbythe dataare reproduced bythe calculationin anysce- nario.Thecalculationforthegroundstateof J π=³/2⁻resembles bettertheexperimentaldataintermsofthenumberofstatesthat arepopulated, whilefor thecases of J π=⁵/2⁻ and J π=⁷/2⁻ a considerablepopulation of the6⁺₁ state would be expected. In particularforthecaseof J π=⁷/2⁻ apopulationofthe6⁺₁ state higherthan the one ofthe 2⁺₁ state wouldbe expected, at odds withtheexperimental result.Itisnotedthat thecalculatedspec- troscopic factors add up to less than half of the total strength

in thethree cases.Therefore, populationof higherlying states is expectedbythecalculations.Suchascenariowouldleadtounob- served transitionsfeedingthe4⁺₁ orthe2⁺₁ statesdirectly, which canaccount fortheexcessofthemeasured crosssectionincom- parisonwiththecalculations.Althoughnotingoodagreement,the lowmeasured andcalculatedpartialcrosssections,aswellasthe apparent fragmentationof the spectroscopicstrength, are consis- tent withthecollectivenature ofthe⁶²Ti groundstatediscussed inthiswork. However,the largeerrorbars prevent afirmercon- clusion.

Insummary,firstspectroscopyof⁶²Tiwas obtainedbymeans ofthe⁶³V(p,2p)⁶²Tireactionat∼200 MeV/nucleon.Transitionsat 683(10) keVand823(20) keVwereassignedtothedecayofthe2⁺₁ and4⁺₁ statesat683(10) keVand1506(22) keV,respectively.Our resultshowsforthefirsttimeanincreaseoftheE(2⁺₁)forN=⁴⁰ isotonestowards ⁶⁰Ca.LSSMcalculationswereingoodagreement with the experimental findings. The calculationssuggest that al- thoughthecollectivitydecreasesapproaching⁶⁰Ca,withan ensu- ingincreaseofE(2⁺₁),quadrupolecorrelationcontributionsremain andleadtotheextensionofthe N=^{40 islandofinversiondown} to⁶⁰Ca.SCCMcalculationsoverestimate themeasured E(2⁺₁)and E(4⁺₁)of ⁶²Ti, predictinga doubly magiccharacter of⁶⁰Ca anda weaklydeformedgroundstate in⁶²Ti,atvariance withthe LSSM calculations.Forthesecalculationsthe N=40 sphericalgapistoo largetoproducetheinversionbetweenthequasi-sphericalandde- formed 0⁺ states. VS-IMSRG calculations, which provide a good description of excited states in Ca isotopes, largely overestimate the E(2⁺₁) andE(4⁺₁) energiesof⁶²Ti, evenaftertheinclusion of theneutron 0g_9/2,1d_5/2 and2s_1/2 orbitals.The spectroscopicin- formationpresentedinthisLetteroffersan importantbenchmark forour understanding of nuclearstructure approaching ⁶⁰Ca and thelocationoftheneutrondripline.

WethanktheRIKENNishinaCenteracceleratorstaffandtheBi- gRIPSteamforthestableoperationofthehigh-intensityZnbeam and for the preparation of the secondary beam setting. K.O. ac- knowledgesthesupportbyGrant-in-Aid forScientific Researchof theJapanSocietyforthePromotionofScience(JSPS)JP16K05352.

A.P. issupported inpartby theMinisteriode Ciencia,Innovación yUniversidades (Spain),SeveroOchoa ProgrammeSEV-2016-0597 and grant PGC-2018-94583. F.B. is supported by the RIKEN Spe- cial Postdoctoral ResearcherProgram.L.X.C.and B.D.L.would like tothanktheVietnamMinistryofScienceandTechnology(MOST) for its support through the Physics Development Program Grant No. ÐTÐLCN.25/18. I.G. has been supported by HIC forFAIR and Croatian Science Foundation under projects no. 1257 and 7194.

D. So. was supported by the the European Regional Develop- ment Fund contract No. GINOP-2.3.3-15-2016-00034 andthe Na- tionalResearch,DevelopmentandInnovationFundofHungaryvia Project No. K128947. V.V. acknowledges support from the Span- ish Ministerio de Economía y Competitividadunder ContractNo.

FPA2017-84756-C4-2-P.K.I.H.,D.K.andS.Y.P.acknowledgethesup- port from the National Research Foundation of Korea grant No.