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

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Re-examining the transition into the N = 20 island of

inversion: Structure of

30

_Mg

B. Fernández-Domínguez, B. Pietras, W.N. Catford, N.A. Orr, M. Petri, M.

Chartier, S. Paschalis, N. Patterson, J.S. Thomas, M. Caamaño, et al.

To cite this version:

B. Fernández-Domínguez, B. Pietras, W.N. Catford, N.A. Orr, M. Petri, et al.. Re-examining the

transition into the N = 20 island of inversion: Structure of

30

_{Mg. Phys.Lett.B, 2018, 779, pp.124-129.}

�10.1016/j.physletb.2018.02.002�. �hal-01719652�

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

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

a_{DepartmentofPhysics,UniversityofLiverpool,Liverpool,L69 7ZE,UK}

b_{LPC-Caen,IN2P3/CNRS,ENSICAEN,UNICAENetNormandieUniversité,14050Caen Cedex,France} c_{UniversidadedeSantiagodeCompostela,15754SantiagodeCompostela,Spain}

d_{DepartmentofPhysics,UniversityofSurrey,GuildfordGU2 5XH,UK}

e_{InstitutfürKernphysik,TechnischeUniversitätDarmstadt,64289Darmstadt,Germany} f_{DepartmentofPhysics,UniversityofYork,Heslington,YorkYO10 5DD,UK}

g_{CNS,UniversityofTokyo,7-3-1 Hongo,Bunkyo-ku,Tokyo,Japan}

h_{DepartamentodeFisicaTeóricaandIFT-UAM/CSIC,UniversidadAutónomadeMadrid,E-28049Madrid,Spain} i_{SchoolofPhysicsandAstronomy,UniversityofBirmingham,Birmingham,B15 2TT,UK}

j_{CyclotronInstitute,TexasA&MUniversity,CollegeStation,TX-77843,USA}

k_{NuclearScienceDivision,LawrenceBerkeleyNationalLaboratory,Berkeley,CA 94720,USA} l_{IFIN-HHBucharest-Magurele,RO-077125,Romania}

m_{IPN-Orsay,91406Orsay,France}

n_{GANIL,CEA/DRF–CNRS/IN2P3,BP55027,14076CaenCedex 05,France}

o_{NuclearStructureGroup,CCLRCDaresburyLaboratory,Daresbury,WarringtonWA4 4AD,UK}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received14December2017

Receivedinrevisedform1February2018 Accepted1February2018

Availableonline6February2018 Editor:D.F.Geesaman

Intermediateenergysingle-neutronremovalfrom31_{Mghasbeenemployedtoinvestigatethetransition}

intotheN₌20 islandofinversion.Levelsupto5 MeVexcitationenergyin30_{Mgwerepopulatedand}

spin-parityassignmentswereinferredfromthecorrespondinglongitudinalmomentumdistributionsand

γ

-raydecayscheme. Comparisonwith eikonal-modelcalculationsalsopermittedspectroscopic factors to be deduced. Surprisingly, the 0+₂ level in 30_{Mg was found tohave astrengthmuch weaker than}

expectedinthe conventionalpicture ofapredominantly2p−2h intruderconfiguration having alarge overlapwiththedeformed31_{Mggroundstate.Inaddition,negativeparitylevelswereidentifiedforthe}

first timein30_{Mg, one ofwhichislocated atlow excitationenergy. Theresults are discussedinthe}

light ofshell-model calculationsemployingtwo newly developedapproaches with markedlydifferent descriptionsof thestructure of30_{Mg. It isconcluded thatthe cross-shelleffects inthe regionofthe}

islandofinversionatZ₌12 are considerablymorecomplexthanpreviouslythoughtand thatnp₋nh

configurationsplayamajorroleinthestructureof30_Mg.

©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

*

Correspondingauthor.

E-mailaddress:beatriz.fernandez.dominguez@usc.es(B. Fernández-Domínguez). 1 _{Presentaddress:DepartmentofPhysicsandAstronomy,JamesMadison} Univer-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,thisregionhas be-comethetestinggroundforourunderstandingofmanyofthe con-ceptsofshellevolutionawayfrom

β

-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_.

developmentofsophisticatedshell-modelinteractions. Theoretical approaches first employed mean field [3] and, later, shell-model calculations[4–9] to explain the enhanced binding energies and low2+excitationenergies,whereindeformationandadiminished N

=

20 shell gap [15] result in f p-shell intruder configurations dominatingthegroundstatewavefunctions.

In the case of the Mg isotopes, 30,31_{Mg were first suggested} to lie outside the IoI, based on their masses [10,11]. Subse-quent measurements, notably the measurements of the ground statespin-parity( J π

=

1

/

2+) andmagneticmoment[12,13] have combined with theoretical work (e.g., Refs. [14,15]) to produce a widely accepted picture in which 31Mg is the lightest magne-siumisotopewithin theIoI.Itsgroundstate ischaracterisedby a stronglyprolatedeformedintruderstructurewithanalmost pure neutron 2p

−

2h configuration[16,17]. In contrast, 30Mg is firmly placed outside the IoI and its structure interpreted as a spher-ical 0p

−

0h ground state [18] coexisting with a neutron 2p

−

2h intruder-dominateddeformed0+₂ 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,the inter-actionwasderived forthesd

+

p f shellsfromfundamental prin-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 31_{Mg and} 30_{Mgstatesareofcriticalimportance.Todate,however,thereare} onlyindirectestimates,basedonprotonresonantelasticscattering on 30_{Mg [23]. In the present work, intermediate energy} single-neutronremovalfrom31_{Mgisinvestigated.Inadditionto} provid-ingameasureoftheoverlapsbetweenthe31Mggroundstateand thelevelspopulatedin30_{Mg,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} wereanalysedaccordingtomomentumusingtheSPEG spectrom-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 MeVandtheenergy resolu-tion,afterDopplercorrection,was 2.7%.A morecompleteaccount oftheexperimentaldetailsmaybefoundinRef. [27].

The inclusive cross section for single-neutron removal from 31_{Mg was determined to be 90}

_±

_{12 mb where the error arises} principallyfromtheuncertaintyintheintegratedsecondarybeam intensity.The

γ

-rayspectrum,foreventsobservedincoincidence with30_{Mgresidues,isshowninFig.1,afterDopplerandadd-back}

Fig. 1. (Coloronline.) Dopplercorrectedandadd-backreconstructedγ-rayenergy spectrum(Eγ >500 keV)incoincidencewith30Mg.Theoverallfit(redline) in-cludesGeant4generatedlineshapesforeachtransition(blackhistograms)andan exponentialbackground(bluedashedline).Theinsetsshowthedetailsofthe re-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.Theredshadingreflectstheuncertaintyinthehalf-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 30_{Mg post-target velocity (}

_β

₌

₀

_.

_{303). The} analysis employed only the data acquired with the forward four detectorsasthecorresponding lineshapeexhibitedparticular sen-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. Levelschemeof30_{Mgobtainedinthepresentwork.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-removalfrom31_{Mgwasobtainedbygatingongamma-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),giventhepartiallifetimeoftheE0 de-cay(

τ

(

E0

)

=

396 ns [20]).Theexclusivecrosssectionforeachstate istheproductofthedirectbranchingratioandtheinclusivecross section.TheresultsareincludedinTable1.

Thecrosssection,

σ

₋1n,toremove neutrons(n



j)froma pro-jectile of mass A populating final states J π may be expressed theoreticallyas[31],

σ

₋1n

=



nj



A A

−

1



N C2S

(

Jπ

,

n



j

)

σ

sp

(

n



j

,

Seffn

),

(1)

where

σ

sp isthesingle-particlecrosssection,

[

A

/(

A

−

1

)

]

N isthe center-of-mass correction (N

=

2n

+ 

) [32], and S_neff

=

Sn

+

Ex istheeffectiveseparationenergy(Sn

(

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_neff. The Woods–Saxon radius wasconstrainedusingSkyrmeHartree–Fockcalculations(Sk20 in-teraction)andthediffusenesssetto0.7 fm.The12_{Ctargetnucleus} 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, Rs [38] – depending on the relative bindingenergiesoftheneutronandproton[39].Astheexact ori-ginsofthisquenchingremaintobe properlyelucidated andmay well involve a combination of the structure inputs and reaction

Fig. 4. (Coloronline.) Exclusivemomentumdistributionsderivedforstatesin30_Mg, labelledbytheexcitationenergyinkeV,comparedtoeikonal-modelpredictions; fitswereformomentaabove8750MeV/c(seetext).

theory,no attemptismadeheretorenormalisethe experimental spectroscopicfactors.Inadditionitmaybe noted,thatthe Seffn of the levels populated herecorrespond to Rs

≈

0.85–0.90, andany correction, ifvalid, wouldbe smallerthan thepresent uncertain-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,themomentum distri-butions for the observed excited states. The theoretical momen-tumdistributionsderivedfromtheeikonalmodelcalculations[34] werefoldedwiththeexperimentalresolution(FWHM

=

75 MeV/c) andarecomparedtotheexperimental resultsinFig.4wherethe overallnormalisationhasbeenadjustedtoprovidethebest possi-ble description.3 (Table 1). In orderto avoidanybias from dissi-pativeprocessesinthereaction[40] whicharenotincorporatedin theeikonalmodelling,thetheoreticallineshapeswerecomparedto thedataonlyformomentagreaterthan8750 MeV/c,sincethe

in-3 _{Webelievethatthisispreferabletothecommonlyadoptedprocedurewhereby} thetheoreticallineshapesarenormalisedtothepeakoftheexperimental distribu-tion.

Table 1

Resultsforsingle-neutronremovalfrom31_{Mg.Theobservedlevels(E}

x),transitionenergies(Eγ),intensities(Iγ),directfractionalpopulation(b)andcorrespondingcross sections(σ−1n)arelisted.Theorbitalangularmomentum()oftheremovedneutron,thecorrespondingchi-squaredperdegreeoffreedom(χ2/ν),inferredspin-parity ( Jπ),theoreticalsingle-particlecrosssection(σsp)andthededucedspectroscopicfactorC2Sexparealsoprovided.

Ex [MeV] Eγ [keV] Iγ (%) b (%) σ−1n [mb]  χ2_{/ν J}π _σsp [mb] C2_S expa 0.0 – – 28.3(39)b _25.5(48)b _{0 2.9 0}+ _{56.4 [0.42(8)]}b 1.482(2) 1482(2) 57.0(28) 12.2(33)b _11.0(33)b _{2 3.0 2}+ _{23.4 [0.44(13)]}b 1.782(5) 300(5) 8.6(13) 8.6(13) 7.7(15) 0 0.5 0+ 36.9 0.20(4) 2.467(3) 985(2) 8.4(5) 8.4(5) 7.6(11) 1 1.0 (2)− 32.8 0.21(3) (2) (1.6) 3.298(3) 1816(2) 13.0(8) 7.6(8) 6.8(11) 3 1.9 (3)− 17.6 0.35(6) (2) (2.8) 3.380(3) 1898(2) 4.2(4) 2.8(4) 2.5(5) –c _{– – – –} 3.457(3) 1975(2) 10.6(6) 10.6(6) 9.5(13) 2 0.8 (2)+ 18.7 0.48(7) (1) (2.2) 3.534(6) 3534(6) 12.3(9) 12.3(9) 11.1(16) 1 1.9 (1−) 28.9 0.35(5) (2) (2.0) 4.183(3) 799(2) 1.4(1) 1.4(1) 1.3(2) –c _{– – –} 4.252(3) 954(2) 5.4(3) 5.4(3) 4.9(7) 3 1.4 (4)− 16.6 0.27(4) (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),thelineshapesforthetwo



valuesthatcomeclosestto reproducingthedataareshown.

Themostlikely



valuesfortheremovedneutronwerededuced 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 30_{Mg. In the case of the 0}+ groundstate, the deduced spectroscopic factor of 0

.

42

±

0

.

08 is muchlargerthantheindirectestimateofImaiet al.[23],namely C2_S

₌

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 consideredasupper lim-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 suggestedin

β

-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 in31Mgcan popu-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 30_Mg [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])and un-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 anyreasonablestructurefor31Mgandwiththeobserved momen-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 alowenergyissurprisinginviewoftheshellmodel pre-dictions(Fig. 5)andincomparisonwiththe correspondinglevels in26,28_Mg(E

x

=

6

.

19 and5.17 MeV).

The momentum distribution for the 3.534 MeV level is com-patiblewith



=

2 or 1,andthuswithspin-parityassignments of (1,2)+ or(1,2)− for0d3/2 or1p3/2 neutronremovalrespectively. Given,however,thatthe

γ

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

Thelevelsat3.298and4.252 MeVbothexhibitmomentum dis-tributions consistentwith



=

3 neutronremoval,although inthe caseofthelater



=

2 removalisalsopossible.The



=

3 (0 f7/2) removalsuggestsspin-paritiesof3−or4−.Significantly,thelower ofthetwostatesdecaystothe2+₁ statewiththeassociated transi-tionbeingE1orE3forthe3−or4−assignmentsrespectively.The lattertransitionwould,however,veryprobablybeisomericwitha lifetimeapproaching1 μs,indicatingthatthelowerlevelis3−.For thehigherlyinglevel



=

2 neutronremovalsuggestsspin-parities

5 _{WhereasthiscontradictsRef. [19],thefeedingin}30_Na

β-decayappearstobe forbidden[21,29],thusimplyingnegativeparity.

Fig. 5. (Coloronline.) Levelschemefor30_{MgobtainedinthepresentworkcomparedtoshellmodelcalculationsusingtheEEdf1[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 mixingof

differ-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:theEEdf1 pre-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,forthe nega-tiveparity f p shellstates,thetwo calculationsagree(Fig. 5)that theyshouldlieatrelativelyhighexcitationenergy(



3.5 MeV).

Focusing onthenewresults,thespectroscopicfactorsmeasure thestructuraloverlapoftheIoInucleus31_{Mgwithkeylow-lying} levelsin30_{Mg.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.Themixingwasthenvarieduntilthe ex-citationenergyofthe0+₂ stateequalledtheexperimentalvalue.As

6 _{TheEEdf1calculationswereperformedinthesdp f modelspaceforboth} pro-tonsandneutrons,whilefortheSDPF-U-MIXtheprotonswereconfinedtothesd shell.

Fig. 6. (Coloronline.) Decompositionofthewavefunctionsin30_Mgforthe0+ 1,2and 2+1,2statesasderivedfromshell-modelcalculationsemployingtheEEdf1and SDPF-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(C2_S

₌

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(C2_S

₌

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,withastrength sig-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

Fig. 7. (Coloronline.) Comparisonoftheexperimentallydeducedsummedstrength forneutron f p-shelllevelspopulatedinone-neutronremovalfrom30−32_Mgwith shell-modelpredictionsusingtheEEdf1andtheSDPF-U-MIXinteractions.The ex-perimentalstrengths(pointswitherrorbars)for30,32_{MgaretakenfromRef. [18].}

arein very goodagreement withthe EEdf1 predictions, they are considerably over-predicted by the SDPF-U-MIX calculations. In-terestingly,theN

=

20 shell gapincorporatedin 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 cleartransitionat31_{Mg. Theintegratedexperimental} in-truder strengths do not permit a definitive choice to be made betweenthetwodescriptionsof30Mgbutdotendtosupportthe smoothevolutionpredictedbytheEEdf1model.

Inconclusion,thestructure of30Mghasbeeninvestigated us-ing single-neutron removalfrom 31_{Mg. 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 differentdescriptionsoftheunderlyingstructureof30,31_Mg.These suggestthatthelowlyinglevelsin30_{Mgaredominatedbynp}

₋

_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(30_Mg,p) neutrontransferreactionwouldbevaluable.

Acknowledgements

Theauthorsacknowledgethesupportprovidedbythetechnical staffofLPCandGANIL, includingthat oftheir latecolleagues and

friendsJ-M.GautierandJ-F.Libin.ThanksarealsoduetoJ. Pereira-Concaforfruitfuldiscussions.B.F.D.andM.C.Facknowledge finan-cialsupportfromtheRamónyCajal programmeRYC-2010-06484 and RYC-2012-11585 and from the Spanish MINECO grant No. FPA2015-71690-P. W.N. Catford acknowledges financial support fromtheSTFCgrantnumberST/L005743/1.Thisworkispartly sup-ported by MINECO(Spain) grant FPA2014-57196 andProgramme “Centrosde ExcelenciaSeveroOchoa”SEV-2012-0249.The partic-ipantsfromtheUniversitiesofBirmingham,Liverpool,Surreyand CCLRCDaresbury, GSI andIFIN-HH laboratoriesalso acknowledge partialsupportfromtheEuropeanCommunitywithintheFP6 con-tractEURONSRII3-CT-2004-06065.

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