Re-examining the transition into the N = 20 island of inversion: Structure of 30 Mg

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Physics Letters B

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Re-examining the transition into the N = ^{20 island of inversion:}

Structure of ³⁰ Mg

B. Fernández-Domínguez

^a,b,c,∗

, B. Pietras

^a

, W.N. Catford

^d

, N.A. Orr

^b

, M. Petri

^a,e,f

, M. Chartier

^a

, S. Paschalis

^a,f

, N. Patterson

^d

, J.S. Thomas

^d

, M. Caamaño

^c

, T. Otsuka

^g

, A. Poves

^h

, N. Tsunoda

^g

, N.L. Achouri

^b

, J.-C. Angélique

^b

, N.I. Ashwood

ⁱ

, A. Banu

^j,1

, B. Bastin

^b

, R. Borcea

^l

, J. Brown

^f

, F. Delaunay

^b

, S. Franchoo

^m

, M. Freer

ⁱ

, L. Gaudefroy

ⁿ

, S. Heil

^e

, M. Labiche

^o

, B. Laurent

^b

, R.C. Lemmon

^o

, A.O. Macchiavelli

^k

, F. Negoita

^l

, E.S. Paul

^a

, C. Rodríguez-Tajes

ⁿ

, P. Roussel-Chomaz

ⁿ

, M. Staniou

^l

, M.J. Taylor

^f,2

, L. Trache

^j,l

, G.L. Wilson

^d

aDepartmentofPhysics,UniversityofLiverpool,Liverpool,L69 7ZE,UK

bLPC-Caen,IN2P3/CNRS,ENSICAEN,UNICAENetNormandieUniversité,14050Caen Cedex,France cUniversidadedeSantiagodeCompostela,15754SantiagodeCompostela,Spain

dDepartmentofPhysics,UniversityofSurrey,GuildfordGU2 5XH,UK

eInstitutfürKernphysik,TechnischeUniversitätDarmstadt,64289Darmstadt,Germany fDepartmentofPhysics,UniversityofYork,Heslington,YorkYO10 5DD,UK

gCNS,UniversityofTokyo,7-3-1 Hongo,Bunkyo-ku,Tokyo,Japan

hDepartamentodeFisicaTeóricaandIFT-UAM/CSIC,UniversidadAutónomadeMadrid,E-28049Madrid,Spain iSchoolofPhysicsandAstronomy,UniversityofBirmingham,Birmingham,B15 2TT,UK

jCyclotronInstitute,TexasA&MUniversity,CollegeStation,TX-77843,USA

kNuclearScienceDivision,LawrenceBerkeleyNationalLaboratory,Berkeley,CA 94720,USA lIFIN-HHBucharest-Magurele,RO-077125,Romania

mIPN-Orsay,91406Orsay,France

nGANIL,CEA/DRF–CNRS/IN2P3,BP55027,14076CaenCedex 05,France

oNuclearStructureGroup,CCLRCDaresburyLaboratory,Daresbury,WarringtonWA4 4AD,UK

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

Articlehistory:

Received14December2017

Receivedinrevisedform1February2018 Accepted1February2018

Availableonline6February2018 Editor:D.F.Geesaman

Intermediateenergysingle-neutronremovalfrom³¹Mghasbeenemployedtoinvestigatethetransition intotheN=^{20 islandofinversion.Levelsupto5 MeVexcitationenergyin30Mgwerepopulatedand} spin-parityassignmentswereinferredfromthecorrespondinglongitudinalmomentumdistributionsand

γ-raydecayscheme. Comparisonwith eikonal-modelcalculationsalsopermittedspectroscopic factors to be deduced. Surprisingly, the 0⁺₂ level in ³⁰Mg was found tohave astrengthmuch weaker than expectedinthe conventionalpicture ofapredominantly2p−2h intruderconfiguration having alarge overlapwiththedeformed³¹Mggroundstate.Inaddition,negativeparitylevelswereidentifiedforthe first timein³⁰Mg, one ofwhichislocated atlow excitationenergy. Theresults are discussedinthe light ofshell-model calculationsemployingtwo newly developedapproaches with markedlydifferent descriptionsof thestructure of³⁰Mg. It isconcluded thatthe cross-shelleffects inthe regionofthe islandofinversionatZ=^{12 are} considerablymorecomplexthanpreviouslythoughtand thatnp−^nh configurationsplayamajorroleinthestructureof³⁰Mg.

©^{2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

*

Correspondingauthor.

E-mailaddress:[email protected](B. Fernández-Domínguez).

1 Presentaddress:DepartmentofPhysicsandAstronomy,JamesMadisonUniver- sity,Harrisonburg,VA22807,USA.

2 Presentaddress:Divisionofcancersciences,UniversityofManchester,Manch- ester,M139PL,UK.

The“islandofinversion”(IoI)inwhichtheneutron-richN≈²⁰ isotopes of Ne, Na and Mg exhibit ground states dominated by cross-shell intruder configurations, has attracted much attention since thefirstobservations[1,2].Inparticular,thisregionhasbe- comethetestinggroundforourunderstandingofmanyofthecon- ceptsofshellevolutionawayfromβ-stabilityandhassparkedthe https://doi.org/10.1016/j.physletb.2018.02.002

0370-2693/©^{2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

intruder-dominateddeformed0₂ isomericstateat1.788 MeV[19, 20] and withnegativeparitylevels expectedtoappear, according toshell model calculations, ata relatively highexcitation energy (>3.5 MeV[21]).

Very recently, calculations employing a new type of interac- tion – EEdf1 – have reproduced many of the properties of the neutron-richisotopesofNe,MgandSi[22].Significantly,theinter- actionwasderived forthesd+^{p f shellsfrom}fundamentalprin- ciplesandexplicitly includingthree-body forces.Intriguingly, the EEdf1 calculationspredict that multiple particle–hole excitations playamuchbiggerrolethansuggestedbytheearliercalculations.

Forexample, in the Mgisotopic chain the admixture of neutron 2p−^{2h and 4p}−4h configurations increases suddenly at N=¹⁸ [22]. Indeed, the ground state structure of ³⁰Mg is predicted to be very strongly influenced by the intruder f p-shell configura- tions, with∼^{75% ofthe groundstate} wavefunction beingofthis nature [22].

Inorder to test thesetwo very differentpictures of the tran- sitioninto the IoI the structuraloverlaps between the ³¹Mg and 30Mgstatesareofcriticalimportance.Todate,however,thereare onlyindirectestimates,basedonprotonresonantelasticscattering on ³⁰Mg [23]. In the present work, intermediate energy single- neutronremovalfrom³¹Mgisinvestigated.Inadditionto provid- ingameasureoftheoverlapsbetweenthe³¹Mggroundstateand thelevelspopulatedin³⁰Mg,the spinsandparitiesofpreviously knownandnewlyobservedstatesarededuced.

The experiment was performed at the GANIL facility where a high intensity ³⁶S primary beam (77.5 MeV/nucleon) was em- ployed,inconjunctionwiththeSISSIdevice[24].A beamanalysis spectrometerdelivered asecondary beamof³¹Mg(55.1 MeV/nu- cleon)witharateof∼^{55 pps. Thesecondarybeambombardeda} carbontarget (thickness171 mg/cm²)andthebeam-likeresidues wereanalysedaccordingtomomentumusingtheSPEGspectrom- eter[25] andidentified inmassandcharge usingstandard E-E- TOFtechniques.

The

γ

-rays emitted by the beam-like residues were detected usingan array of 8 EXOGAM Ge clover detectors [26] that were arrangedsymmetricallyintwo rings,eachof4detectors,atpolar angles of45^◦ and135^◦ withrespect to the beamaxis. The full- energypeakefficiencyforthearray,afterimplementingadd-back, wasmeasuredtobe 3.3±⁰.1%at1.3 MeVandtheenergyresolu- tion,afterDopplercorrection,was 2.7%.A morecompleteaccount oftheexperimentaldetailsmaybefoundinRef. [27].

The inclusive cross section for single-neutron removal from 31Mg was determined to be 90±12 mb where the error arises principallyfromtheuncertaintyintheintegratedsecondarybeam intensity.The

γ

-rayspectrum,foreventsobservedincoincidence with³⁰Mgresidues,isshowninFig.1,afterDopplerandadd-back

Fig. 1. (Coloronline.) Dopplercorrectedandadd-backreconstructedγ-rayenergy spectrum(Eγ >500 keV)incoincidencewith³⁰Mg.Theoverallfit(redline)in- cludesGeant4generatedlineshapesforeachtransition(blackhistograms)andan exponentialbackground(bluedashedline).Theinsetsshowthedetailsofthere- gionsfrom850to1100 keVand1575to2175 keV.

Fig. 2. (Color online.) Spectrum for the forward angle EXOGAM detectors for Eγ < 500 keV.Thegreyhistogram isthe simulatedlineshapefor the0⁺₂ →²⁺1 decay–Eγ=³⁰⁰±^{5 keV.Theredshadingreflectsthe}uncertaintyinthehalf-life –3.9±⁰.5 ns [19].

correctionswere applied.Nineknown transitions[28,21,29] were observed.TheenergiesandintensitiesarelistedinTable1andthe deduceddecayschemeshowninFig.3.A furtherweak,previously unreported transition, which is not in coincidence (within the statistics)withanyother

γ

-rayline,wasidentifiedat1660(2) keV.

The

γ

-ray energyspectrumwas fitted withlineshapes generated for each transition using Geant4 [30], plus a smooth continuum background.

Below 500 keV, no

γ

-ray lines were observed other than an asymmetric peak at ∼^{300 keV} corresponding to the known 306 keVtransitionfromtheisomeric0⁺₂ 1789 keVleveltothe2⁺₁ state (half-life3.9(5) ns[19]).Thelineshape fortheisomeric de- cay was simulated (Fig. 2) using Geant4andtaking intoaccount the half-life and the ³⁰Mg post-target velocity (β=⁰.303). The analysis employed only the data acquired with the forward four detectorsasthecorresponding lineshapeexhibitedparticularsen- sitivitytothelifetime.

The³⁰Mgleveland

γ

-decayschemeinFig.3isinaccordwith previous studies [28,21,29], withthe exception oftwo previously reported transitionsat 990 keVand 1060 keV[21] forwhich no

Fig. 3. Levelschemeof³⁰Mgobtainedinthepresentwork.Thewidthsofthearrows reflecttheabsoluteintensitiesofthetransitions.Thespin-parityassignmentsabove 2 MeVarethosededucedhere(seetextandTable1).

evidencewas found inthepresentwork (insets Fig.1) orindeed inpreviousstudies[28,29].The

γ

-rayintensitiesweredetermined byusingthelineshapes fromthesimulationsandthencorrecting thecountsinthefullenergypeakfortheefficiencyoftheGearray.

Thebranchingratioforthedirectpopulationofeachlevelviathe neutron-removalfrom³¹Mgwasobtainedbygatingongamma-ray energyandwithfeedingcorrectionstakenintoaccount.Forthe0⁺₂ isomeric state, thedirect feedingwas deduced fromthe gamma- ray decay via the E2 radiative transitionsince the ratio E0/E2is verysmall(∼¹.4×^{10−2),giventhepartiallifetimeoftheE0de-} cay(

τ

(E0)=396 ns [20]).Theexclusivecrosssectionforeachstate istheproductofthedirectbranchingratioandtheinclusivecross section.TheresultsareincludedinTable1.

Thecrosssection,

σ

₋1n,toremove neutrons(nj)froma pro- jectile of mass A populating final states J π may be expressed theoreticallyas[31],

σ

₋1n

= 

nj



A

A

−

¹



N

C²S

(

J^π

,

n



j

) σ

sp

(

n



j

,

S^eff_n

),

(1)

where

σ

sp isthesingle-particlecrosssection, [^A/(A−¹)]^{N isthe} center-of-mass correction (N=²ⁿ+ ^{) [32], and S}n^eff= ^Sn+^Ex istheeffectiveseparationenergy(S_n(³¹Mg)=².310±⁰.005 MeV [33])withEx theexcitationenergyofthestateintheA-1system.

Thesingle-particlecrosssectionsandmomentumdistributions were computedusing the eikonal formalism [34–36]. The poten- tialsfortheneutron–target andcore–targetinteractionswere de- rivedusingtheJeukenne,LejeuneandMahaux(JLM)[37] nucleon–

nucleon effective interaction. The wavefunction of the removed neutron was calculated in a Woods–Saxon potential where the depth was adjusted to reproduce S_n^eff. The Woods–Saxon radius wasconstrainedusingSkyrmeHartree–Fockcalculations(Sk20in- teraction)andthediffusenesssetto0.7 fm.The¹²Ctargetnucleus was taken to have a Gaussian matter density witha root-mean- squareradiusof2.32 fm.

Compilations of the results of intermediate-energy single- nucleon removal suggest that there is a systematic variation in theratioofthe experimentalandtheoretical crosssections–the so-called quenching factor, R_s [38] – depending on the relative bindingenergiesoftheneutronandproton[39].Astheexactori- ginsofthisquenchingremaintobe properlyelucidated andmay well involve a combination of the structure inputs and reaction

Fig. 4. (Coloronline.) Exclusivemomentumdistributionsderivedforstatesin³⁰Mg, labelledbytheexcitationenergyinkeV,comparedtoeikonal-modelpredictions;

fitswereformomentaabove8750MeV/c(seetext).

theory,no attemptismadeheretorenormalisethe experimental spectroscopicfactors.Inadditionitmaybe noted,thatthe S^eff_n of the levels populated herecorrespond to R_s≈^{0.85–0.90, andany} correction, ifvalid, wouldbe smallerthan thepresentuncertain- ties.

The exclusive longitudinal momentum distributions extracted for the ground and excited states are presented in Fig. 4. The ground state distributionwas obtained fromthe inclusiveresults bysubtracting,withappropriate weighting,themomentumdistri- butions for the observed excited states. The theoretical momen- tumdistributionsderivedfromtheeikonalmodelcalculations[34]

werefoldedwiththeexperimentalresolution(FWHM=^{75 MeV/c)} andarecomparedtotheexperimental resultsinFig.4wherethe overallnormalisationhasbeenadjustedtoprovidethebestpossi- ble description.³ (Table 1). In orderto avoidanybias fromdissi- pativeprocessesinthereaction[40] whicharenotincorporatedin theeikonalmodelling,thetheoreticallineshapeswerecomparedto thedataonlyformomentagreaterthan8750 MeV/c,sincethein-

3 Webelievethatthisispreferabletothecommonlyadoptedprocedurewhereby thetheoreticallineshapesarenormalisedtothepeakoftheexperimentaldistribu- tion.

(2) (1.6)

– 1660(2) 2.4(2) 2.4(2) 2.2(3) –^c – – – –

a Afteraccountingforthecentre-of-masscorrection.Asystematicuncertaintyof∼^{10%relatedtothereactionmodellingisnotincludedinthequotederror[39,40].}

b Upperlimitsfromobservedyields(seetext).

c Thecorrespondingmomentumdistributionscouldnotbeextracted.

clusivemomentumdistribution,aswellasthatforthegroundand 2⁺₁ states,show evidenceoftailsatmomentabelowthisvalue.In thecasesofthelevelswithunknown spin-parities(i.e.,abovethe 0⁺₂ state),thelineshapesforthetwovaluesthatcomeclosestto reproducingthedataareshown.

Themostlikelyvaluesfortheremovedneutronwerededuced forall excepttwo levels (3.534and4.252 MeV)according tothe smallest

χ

²/

ν

values(Table 1). The absolutevalues of

χ

²/

ν

re- flect, in addition to statistical variations, contributions from any imperfections in the

γ

-ray gating and background substraction, anduncertainties in the theoretical lineshapes⁴ asevidenced by thecomparativelypoor

χ

²/

ν

forthe2⁺₁ level.

Removing a neutron from the 1s1/2 orbital in ³¹Mg leads to 0⁺ (and potentially 1⁺) states in ³⁰Mg. In the case of the 0⁺ groundstate, the deduced spectroscopic factor of 0.42±⁰.08 is muchlargerthantheindirectestimateofImaiet al.[23],namely C²S=⁰.07±⁰.03(stat)±⁰.07(sys), and both of the shell model predictions discussed below (C²S=⁰.11−⁰.13). Given that the crosssection to the groundstate is derived assuming that all of theyieldtoboundexcited levelshasbeenidentified (Sn(³⁰Mg)= 6.35±⁰.01 MeV [33]),both thecrosssection andthe associated spectroscopicfactor(Table1) shouldbe consideredasupperlim- its.Indeed,highenergy(andunobserved)

γ

-rays,wouldarisefrom any1⁺ levels populated by 1s1/2 and/or 0d3/2 neutron removal;

thesearepredictedtolie near5 MeV(Fig. 5) andcandidates are suggestedinβ-decaymeasurements[29].

In the case of the 0⁺₂ level, the spectroscopic factor of 0.20±⁰.04 deduced hereis,intermsofthe conventionalpicture ofanintruder-dominated2p−2h configuration,surprisinglylow.

Removinga neutronfromthe0d3/2 orbital in³¹Mgcanpopu- late 1⁺ or2⁺ states in³⁰Mg. The 2⁺₁ stateis populatedstrongly here,however,theassociatedspectroscopicfactor(0.44±^13)must be interpreted with caution as the deformed character of ³⁰Mg [45] willpermit dynamicalexcitations(and de-excitations)to oc- cur during the neutron removal. CCDC-type calculations suggest that such effects willresult ina net increase in theyield to the

4 Thesemayarisefromeffectsnotincorporatedinthemodelemployedhere[41, 42],thechoiceofthemodelorformalism(see,forexample,refs. [43,44])andun- certaintiesintheparametersofthemodelitself.

2⁺₁ state and thespectroscopic factordeduced hereshould,thus, beconsideredanupperlimit [46].

Thenext higheststatecharacterisedby =^{2 neutronremoval} isfoundat3.457 MeV.Afusion–evaporationstudy[21] suggested a 4⁺ assignment which would, fora single-step process, require neutronremovalfromthe1g9/2 orbital.Thisisincompatiblewith anyreasonablestructurefor³¹Mgandwiththeobservedmomen- tumdistribution.Giventhatany1⁺ levelsareexpected(Fig.5)at highenergy,a 2⁺₂ assignmentismadehere, inlinewiththe³⁰Na β-decaystudy[29]. The large spectroscopicfactor of0.48±⁰.07 suggestsanintruderdominatedstructure.

Negative parity states will be populated via removal of an f p-shellneutronfrom³¹Mg. Significantly,thelevel at2.467 MeV has a momentum distribution characteristic of =¹(1p3/2) re- moval, forwhich spin-parities of 1⁻ and 2⁻ are possible. Given that the

γ

-decay proceeds to the 2⁺₁ level, a 2⁻ assignment is clearly favoured⁵ since a 1⁻ assignment would favour direct E1 decaytothegroundstate. Thepresenceofanegativeparitystate atsuch alowenergyissurprisinginviewoftheshellmodelpre- dictions(Fig. 5)andincomparisonwiththe correspondinglevels in^26,28Mg(Ex=⁶.19 and5.17 MeV).

The momentum distribution for the 3.534 MeV level is com- patiblewith=^{2 or 1,andthuswith}spin-parityassignments of (1,2)⁺ or(1,2)⁻ for0d3/2 or1p3/2 neutronremovalrespectively.

Given,however,thatthe

γ

-decayproceedsonlyviadirectdecayto thegroundstateaspinof1isclearlyfavoured.Furthermoreanas- signmentof1⁻isstronglysuggestedsinceitwouldbethepartner ofthenearby2⁻ stateproducedby1p3/2 removal.

Thelevelsat3.298and4.252 MeVbothexhibitmomentumdis- tributions consistentwith=^{3 neutronremoval,although inthe} caseofthelater=^{2 removalisalsopossible.The} =^{3 (0 f}7/2) removalsuggestsspin-paritiesof3⁻or4⁻.Significantly,thelower ofthetwostatesdecaystothe2⁺₁ statewiththeassociatedtransi- tionbeingE1orE3forthe3⁻or4⁻assignmentsrespectively.The lattertransitionwould,however,veryprobablybeisomericwitha lifetimeapproaching1 μs,indicatingthatthelowerlevelis3⁻.For thehigherlyinglevel=^{2 neutronremovalsuggests}spin-parities

5 WhereasthiscontradictsRef. [19],thefeedingin³⁰Naβ-decayappearstobe forbidden[21,29],thusimplyingnegativeparity.

Fig. 5. (Coloronline.) Levelschemefor³⁰MgobtainedinthepresentworkcomparedtoshellmodelcalculationsusingtheEEdf1[22] andSDPF-U-MIX[15] interactions.

Spectroscopicfactors(seetextandTable1)andproposedspin-parityassignmentsareshownontheleftandrightsideoftheenergylevels,respectively.Theenergiesofthe experimentallyobservedstatesarelistedinTable1andFig.3.Theorbitalangularmomentum()fortheremovedneutronisalsoindicated:=^{0 (red),1 (green),2 (blue),} 3 (brown),undetermined(black)–seeTable1.

of(1, 2,3)⁺.Such assignments would be expectedto be charac- terised byM1decays[47] tothelowlying0⁺and2⁺statesrather thantheobserveddecaytothe3.298 MeV3⁻level.Assuchitmay bereasonablyconcludedthatthe4.252 MeVlevelispopulatedas the4⁻ spin-couplingpartnerofthe3⁻ state.

Turningnowtotheinterpretationoftheresultspresentedhere, Fig.5providesacomparisonwithshellmodelcalculations⁶ using the recently developedEEdf1 [22] and SDPF-U-MIX [15] interac- tions. The former was derived from chiral effective field theory nucleon–nucleoninteractions, whilst the latterisan extension of theSDPF-U interaction [9] whichallows forthe mixingofdiffer- entnp−nh configurations.Itshouldbenotedthatwhilethe³¹Mg ground state is essentially of intruder character in both calcula- tions, the details differ markedly: 90% of the SDPF-U-MIX wave functionis2p−^{2h,whilst,inthecaseofEEdf1,66%is2p}−^{2h and} 29%4p−^4h.

The difference between the two shell model calculations is mostapparentinthecharacterofthe³⁰Mgstates:theEEdf1pre- dicts the 0⁺₁, 0⁺₂, 2⁺₁ and 2⁺₂ levels to be overwhelmingly dom- inated (^{70%) by intruder} configurations while the SDPF-U-MIX suggestsa moreconventional situationwithonly the0⁺₂ and2⁺₂ stateshavingintrudercharacter (Fig.6).Incontrast,forthenega- tiveparity f p shellstates,thetwo calculationsagree(Fig. 5)that theyshouldlieatrelativelyhighexcitationenergy(^{3.5 MeV).}

Focusing onthenewresults,thespectroscopicfactorsmeasure thestructuraloverlapoftheIoInucleus³¹Mgwithkeylow-lying levelsin³⁰Mg.AsshowninFig.5,thespectroscopicfactordeduced herefor the 0⁺₂ state is in very good agreement withthe EEdf1 basedpredictionandatclearvariancewiththatoftheSDPF-U-MIX (beingafactor∼^{2weaker),suggestingtheincreasedimportanceof} 4p−4h configurations.

In order to explore further the influence of 4p−^{4h configu-} rations, calculations have been made using a three level mixing model(3LM) [48]. Inthisapproach, thestarting pointcomprised the unmixed np−^{nh (n}=⁰,2 and 4) 0⁺ levels derived fromthe SDPF-U-MIXinteraction.Themixingwasthenvarieduntiltheex- citationenergyofthe0⁺₂ stateequalledtheexperimentalvalue.As

6 TheEEdf1calculationswereperformedinthesdp f modelspaceforbothpro- tonsandneutrons,whilefortheSDPF-U-MIXtheprotonswereconfinedtothesd shell.

Fig. 6. (Coloronline.) Decompositionofthewavefunctionsin³⁰Mgforthe0⁺_1,2and 2⁺_1,2statesasderivedfromshell-modelcalculationsemployingtheEEdf1andSDPF- U-MIXinteractionsand,forthe0⁺_1,2levels,byathree-levelmixingmodel(3LM)– seetext.

maybe seenin Fig.6,the0⁺₂ level isstronglymixedwitha sig- nificant 4p−4h component (comparable tothe EEdf1 prediction).

The spectroscopic factors derived from the overlap of the SDPF- U-MIX ground state for ³¹Mg with the ³⁰Mg 0⁺₂ state from the 3LM(C²S=⁰.26)isinbetteragreementwiththeexperimentthan the SDPF-U-MIX prediction.In the case ofthe groundstate, the strength (C²S=⁰.22) istwice that ofthe SDPF-U-MIXprediction (Fig.5).Forcompleteness,itmaybenotedthatthe0⁺₃ levelinthe 3LM(C²S=⁰.15)ispredictedtolieataround3.8 MeV.

Turning to the negative parity states, the lowest in energy is the 2⁻, which is observed to lie well below those predicted by both theEEdf1andSDPF-U-MIXinteractions,withastrengthsig- nificantlyweakerthaneitherofthecalculations.Theproposed1⁻ spin-couplingpartnerofthe2⁻ isfoundtoliesome1 MeVhigher inexcitationenergywithaconsiderablestrength.Theshellmodel calculations are reasonable in termsof the excitation energybut underestimate the strength by a factor ∼^{2. Finally, the 3− and} 4⁻ levels are both reasonably well reproduced in terms of en- ergybythetwocalculations.However,whilethestrengthsofeach

shell-modelpredictionsusingtheEEdf1andtheSDPF-U-MIXinteractions.Theex- perimentalstrengths(pointswitherrorbars)for^30,32MgaretakenfromRef. [18].

arein very goodagreement withthe EEdf1 predictions, they are considerably over-predicted by the SDPF-U-MIX calculations. In- terestingly,theN=^{20 shell gap}incorporatedin theSDPF-U-MIX interactionisaround5.5 MeV,whilethatofEEdf1isonly2.8 MeV.

Finally,itisinstructivetomaptheevolutionofthestrengthof the f p-shellintruderstatesacrosstheboundaryoftheIoI.Thisis showninFig.7,wherethesummedstrengthofthenegativeparity levelsobserved inthe A-1nucleipopulatedinsingle-neutron re- movalfrom³⁰⁻³²Mgarecomparedtotheshell-modelcalculations using the EEdf1 and SDPF-U-MIX interactions. This comparison highlightstheenhanced role playedby thecross-shellexcitations in the EEdf1 calculation, which displays a smooth evolution of structure with neutron number, whereas the SDPF-U-MIX model showsa cleartransitionat³¹Mg. Theintegratedexperimentalin- truder strengths do not permit a definitive choice to be made betweenthetwodescriptionsof³⁰Mgbutdotendtosupportthe smoothevolutionpredictedbytheEEdf1model.

Inconclusion,thestructure of³⁰Mghasbeeninvestigated us- ing single-neutron removalfrom ³¹Mg. The results, mostnotably the relatively weak spectroscopic strength for the 0⁺₂ state and the identification of a low lying negative parity (2⁻) level, are at odds with the conventional picture of the transition into the IoI.Comparisons are madewiththeresults ofshellmodel calcu- lations employing two recently developed interactions with very differentdescriptionsoftheunderlyingstructureof^30,31Mg.These suggestthatthelowlyinglevelsin³⁰Mgaredominatedbynp−^nh configurations,includingsignificant 4p−4h contributions.As such the transition into the IoI at Z=^{12 appears to be} considerably morecomplexandlesswelldefinedthanpreviously thought.Ide- ally, improved measurements should be made (including high- energy

γ

-raydetection)soastoclarifythedirectpopulationofthe groundand2⁺₁ states.Inaddition,aninvestigationofthed(³⁰Mg,p) neutrontransferreactionwouldbevaluable.

Acknowledgements

Theauthorsacknowledgethesupportprovidedbythetechnical staffofLPCandGANIL, includingthat oftheir latecolleagues and

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