Shell evolution approaching the N=20 island of inversion: Structure of 26Na

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Shell evolution approaching the N=20 island of

inversion: Structure of 26Na

G.L. Wilson, W.N. Catford, N.A. Orr, C.Aa. Diget, A. Matta, G. Hackman,

S.J. Williams, I.C. Celik, N.L. Achouri, H. Al Falou, et al.

To cite this version:

JID:PLB AID:32023 /SCO Doctopic: Experiments [m5Gv1.3; v1.180; Prn:2/06/2016; 15:15] P.1 (1-7)

Physics Letters B•••(••••)•••–•••

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb 1 66 2 67 3 68 4 69 5 70 6 71 7 72 8 73 9 74 10 75 11 76 12 77 13 78 14 79 15 80 16 81 17 82 18 83 19 84 20 85 21 86 22 87 23 88 24 89 25 90 26 91 27 92 28 93 29 94 30 95 31 96 32 97 33 98 34 99 35 100 36 101 37 102 38 103 39 104 40 105 41 106 42 107 43 108 44 109 45 110 46 111 47 112 48 113 49 114 50 115 51 116 52 117 53 118 54 119 55 120 56 121 57 122 58 123 59 124 60 125 61 126 62 127 63 128 64 129 65 130

Shell

evolution

approaching

the

N

=

20 island

of

inversion:

Structure

of

26

Na

G.L. Wilson

a

,

W.N. Catford

a

,

∗

,

N.A. Orr

b

,

C.Aa. Diget

c

,

A. Matta

a

,

G. Hackman

d

,

S.J. Williams

d

,

I.C. Celik

a

,

N.L. Achouri

b

,

H. Al Falou

d

,

R. Ashley

e

,

R.A.E. Austin

f

,

G.C. Ball

d

,

J.C. Blackmon

g

,

A.J. Boston

e

,

H.C. Boston

e

,

S.M. Brown

a

,

D.S. Cross

d

,

M. Djongolov

d

,

T.E. Drake

h

,

U. Hager

d

,

i

,

S.P. Fox

c

,

B.R. Fulton

c

,

N. Galinski

d

,

A.B. Garnsworthy

d

,

D. Jamieson

j

,

R. Kanungo

f

,

K. Leach

j

,

1

,

J.N. Orce

d

,

k

,

C.J. Pearson

d

,

M. Porter-Peden

i

,

F. Sarazin

i

,

E.C. Simpson

a

,

S. Sjue

d

,

D. Smalley

i

,

C. Sumithrarachchi

d

,

S. Triambak

d

,

l

,

C. Unsworth

e

,

d

,

R. Wadsworth

c

a_{DepartmentofPhysics,UniversityofSurrey,Guildford,SurreyGU27XH,UK}

b_{LPC,ENSICAEN,CNRS/IN2P3,UNICAEN,NormandieUniversité,14050CaenCedex,France} c_{DepartmentofPhysics,UniversityofYork,York,YO105DD,UK}

d_{TRIUMF,4004WesbrookMall,Vancouver,BC,V6T2A3,Canada} e_{DepartmentofPhysics,UniversityofLiverpool,Liverpool,L693BX,UK} f_{DepartmentofPhysics,StMary’sUniversity,Halifax,NS,B3H3C3,Canada} g_{DepartmentofPhysics,LouisianaStateUniversity,BatonRouge,LA70803,USA} h_{DepartmentofPhysics,UniversityofToronto,Toronto,Ontario,M5S1A7,Canada} i_{DepartmentofPhysics,ColoradoSchoolofMines,Golden,CO80401,USA} j_{DepartmentofPhysics,UniversityofGuelph,Guelph,ON,N1G2W1,Canada}

k_{DepartmentofPhysics,UniversityoftheWesternCape,P/BX17Bellville,7535,SouthAfrica} l_{TheiThembaLaboratoryforAcceleratorBasedSciences,SomersetWest7129,SouthAfrica}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received7August2015

Receivedinrevisedform20May2016 Accepted31May2016 Availableonlinexxxx Editor: D.F.Geesaman Keywords: 81V35 Nuclearstructure 26_Na γ-Raytransitions Transferreactions Shellmigration

The levels in 26_{Na with single particle character have been observed for the first time using the}

d(25Na, p

γ

)reactionat5 MeV/nucleon.Themeasuredexcitationenergiesandthededucedspectroscopic factorsareingoodoverallagreementwith(0+1)_¯h

ω

shellmodelcalculationsperformedinacomplete

spsdf p basisandincorporatingareductionintheN₌20 gap.Notably,the1p3/2neutronconfiguration

was found toplay anenhanced role inthe structure ofthe low-lying negativeparitystatesin 26_Na,

comparedtotheisotone28_{Al.Thus,theloweringofthe1p}

3/2orbitalrelativetothe0 f7/2occurring in

the neighbouring Z₌10 and 12 nuclei– 25,27_{Ne and}27,29_{Mg –is seenalsoto occurat Z=11 and}

furtherstrengthenstheconstraintsonthemodellingofthetransitionintotheislandofinversion.

©2016PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

The breakdownof the shell model magic number N

=

20 for neutrons,inthecaseofneutron-richisotopesnear31Naand32Mg

[1,2],hasledtotheconceptofan“islandofinversion”,where neu-tronspreferentially occupyorbitalsabovethenormal N

=

20 gap, leavingvacanciesbelowit[3,4].Themechanismisnowunderstood

*

Correspondingauthorat:DepartmentofPhysics,UniversityofSurrey,Guildford, SurreyGU27XH,UK.

E-mailaddress:[email protected](W.N. Catford).

1 _{NowatDepartmentofPhysics,Colorado SchoolofMines,Golden,CO80401,}

USA.

intermsoftheshellmodeltoinvolvespecificvalencenucleon in-teractions[3,5]aswellasamonopoleshiftintheeffectivesingle particle energies [6]. Ina wider picture, themonopole migration oflevels isunderstoodasarisingfromthetensorandthree-body componentsofthenucleon-nucleonforcebetweenvalence nucle-onsinpartiallyfilledorbitals[7,8].

The level schemesof nucleiwithodd N, such as N

=

15 and N

=

17 (Fig. 1,provideimportantinsightintotheevolutionofthe single particle structure approaching the island of inversion. Be-tween Z

=

8 and 14, the proton d5/2 orbital is filled, and this

http://dx.doi.org/10.1016/j.physletb.2016.05.093

JID:PLB AID:32023 /SCO Doctopic: Experiments [m5Gv1.3; v1.180; Prn:2/06/2016; 15:15] P.2 (1-7)

2 G.L. Wilson et al. / Physics Letters B•••(••••)•••–•••

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Fig. 1. (Colouronline.) EnergiesoflowestlevelsinisotonesN=15 (dashedline)andN=17 (fullline).EnergiesforN=13 areincludedforoxygen.ThepointsforZ=10–16 arederivedfromrefs.[9–13]andcompilations,whilstthoseforoxygenarefromrefs.[14,15].Theenergyreferenceischosentobethe7/2− level(seetext)andthe Z positionof26_{Naisindicated.}

affectsthe energies oftheneutron orbitals. The referenceenergy isthe7

/

2−level,asitisexpectedthattheenergyofthe f7/2

neu-tron orbital (a j> orbital, i.e. j

= 

+

1

/

2) will depend relatively weakly on the filling of the proton d5/2 orbital (also j> [7]). In thecaseof21,23_{Othe J π}

₌

₇

_/

₂− _{assignmentsaretentative[14,15]}

butthe smallwidth observedin 23_{O[15] supports the7}

_/

₂−

as-signment.Thesystematicsandalsotheshellmodel[15]suggesta neardegeneracybetweenthe3

/

2+and3

/

2−statesinoxygen.As maybe seen, 26_{Nafalls ina key region wherethe shellclosures}

at N

=

20 and 16 are weakening andstrengthening respectively. As such, compared to the isotone 28Al, the levels in 26Na corre-spondingto a neutroninthe 0d3/2 orbital wouldbe expectedto

liehigherinenergy,whereas stateswithaneutronoccupyingthe 1p3/2 orbitalmaybedegeneratewiththe0 f7/2 levelsorevenlie

belowthem.2 _{Inordertoexplorethisbehaviourthepresentstudy} hasbeenundertakentolocatethecorrespondinglevelsusing neu-trontransferonto25_{Na,producedasasecondarybeam.Aswillbe}

shown, the detectionof coincident gamma-rays hasdramatically enhancedtheexcitationenergyresolutionandprovidedvital com-plementaryinformationonthespinsandparitiesofthepopulated levels.

Previous studies have identified the ground state of 26Na as having J π

=

3+ [16,17]andthere arethree 1+ statesfed bythe beta-decay of 26Ne [18,19]. Apart from the low-lying quartet of states(3+

,

1+

,

2+

,

2+)below407keV[20],whichhavebeenvery recently probed via Coulomb excitation [21], the manyobserved states[20,22,23,19]haveastructurethatisalmostcompletely un-known.The(d, p)reactionemployedherewillselectivelypopulate the levels with a predominantly single-particle structure, which arethosemostusefulfortestingshellmodelpredictions.

The experiment was undertaken at the ISAC-II facilityat TRI-UMF. A pure beam of 5.0 MeV/nucleon 25Na ions of intensity 3

×

107 pps was employed to bombard a self-supporting (CD2)n

deuteratedpolythenefoilofthickness0.5mg/cm2.Thetargetwas mounted at the centre of the SHARC silicon strip detector array

[24] which was surrounded by 8 segmented germanium clover gamma-raydetectorsoftheTIGRESSarray [25].Fourcloverswere centred at90◦ inthe laboratory andfour at 135◦, givinga total

2 _{Amultipletoflevelsforeachneutronconfigurationisexpected,accordingto}

thecouplingoftheneutronwiththeunpairedprotoninthe0d5/2orbital.

absolute photopeak efficiency of some 3% at 1.33MeV. In order to identifyeventsinSHARC arisingfromfusion-evaporation reac-tions initiated onthecarboninthetarget (asource ofsignificant background), an Al foilfollowed by a thin plasticscintillator de-tector (the TRIFOIL [26]) were installed 400 mm downstream of the target.The Al thicknessof 30 μmwas chosen tostop fusion-evaporationresidues whilst transmittingthebeam andthe prod-uctsofdirect reactions[27].Further,the scintillatorfoilwas thin enough(10 μm)totransmittheradioactivebeam.

Events were recorded whenever a particle was registered in SHARC, including a logic signal to indicate whether the TRIFOIL hadfired during thesame beambunch.The TRIFOIL allowed the events corresponding to theproduction of26_{Na via the(d, p)}

re-action to be highlighted in the analysis inorder to optimise the software gating.In thefinal determination ofthe absolute differ-entialcrosssectionsofthe(d, p)reaction,theTRIFOILrequirement wasnotimposed,however,owingtoitsefficiencybeingdependent on theposition onthe foil,andhence onthe angleofthe recoil proton[28].Thecoincidentgamma-rayswererecordedinTIGRESS and their energies were corrected for Doppler shift (v

/

c

≈

0

.

1)

[28].

The excitation energy spectrum for states populated in 26_Na,

reconstructedfromtheobservedenergyandangleoftheprotons, isshowninFig. 2wherethe resolutionis350keV(FWHM).This figure illustrateshowcloselyspacedstatescould bedistinguished using the gamma-ray data. The FWHMresolution in gamma-ray energy at1.8 MeV, afterDoppler correction, was 18 keVat135◦ and23 keVat90◦.Thisresolution,ratherthanthatofthe proton-derived excitation energy spectrum, defined the precision with whichindividual statescould beselected.Ontheother hand,the proton-derived excitation energy was critical in determining the energy at which the 26_{Na was populated in the (d, p) reaction}

(i.e. prior to gamma-decay of the states). In addition, gating on this excitation energywas employed in the determinationof the gamma-raybranchingratios[28].

Elasticallyscattereddeuteronsfromthetargetwereprominent in the spectrum of particle energy versus angle and the cor-responding differential cross section was extracted [28]. Optical model parameters for d

+

26_{Mg at an almost identical centre of}

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G.L. Wilson et al. / Physics Letters B•••(••••)•••–••• 3

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Fig. 2. (Colouronline.) Excitationenergyspectrumforstatesin26_{Na,reconstructed}

fromthemeasuredenergyandangleoftheprotonsfromthed(25_{Na, p)reaction.}

Thespectrumforalleventsisshown(red),plustheresultsforcoincidenceswith theknowngamma-raysof233keV(blue)and407keV(blackhistogram)in26_Na.

Thedataareforprotonlaboratoryanglesbackwardof90◦.ATRIFOILrequirement hasbeenimposedinallcases(seetext).

The best-fitnormalisationthus gave theproduct of thedeuteron target thickness and the total integrated beam flux. The uncer-taintyassociatedwiththisfittingwas estimatedtobe 3%.An es-timateofsystematicuncertaintiesinthisanalysiswasobtainedby repeatingtheprocedurewithparameterstakenfromd

+

28Si scat-teringatthesameenergy[30].Thevariationwaslessthan2%.

Fig. 3 shows the Doppler corrected gamma-ray energy (Eγ ) plotted against the excitation energy in 26Na (Ex) as derived

fromtheprotonenergyandangle.Thesuperior resolutionofthe gamma-rayenergyisclearly apparent,andthestatesthatoverlap inExcanbedistinguishedusingthegamma-rayenergy.Anumber

oflevelswithground-stategamma-raybranches(Eγ

=

Ex)canbe

seen,including many ofthe more strongly populatedstates. The neutronseparationenergyisSn

=

5

.

57 MeV[31].Thegroundstate

branchgenerallyhasa lowerandbetter definedunderlying back-groundthananyother peakinFig. 3andhenceforthemostpart onlythesepeakswerechosen forinitialanalysis3 (Table 1).With suitablebackgroundsubtraction[28],theyieldofprotonscouldbe deducedfor individual states in26_{Naasa function of laboratory}

angle.These distributions were converted to absolutedifferential crosssectionsby takingintoaccountthegeometryofSHARC,the elasticscatteringnormalisation,themeasuredgamma-ray branch-ing ratios and the gamma-ray detection efficiency (corrected for Dopplerandrelativisticangularaberration effects).Theoverall sys-tematicerrorassociatedwiththeseeffectswastypically5–6%.

Differential cross sections for states populated in 26Na are showninFig. 4,plottedintermsofthelaboratoryscatteringangle. These are compared with reaction calculations performed using the code TWOFNR [33] employing the Adiabatic Distorted Wave Approximation(ADWA) of Johnson andSoper [34] withstandard input parameters [35] including theChapel-Hill (CH89) nucleon– nucleus optical potential [36]. This formalism benefits interalia fromhavingnorequirementforadeuteron-nucleusoptical poten-tial.Themagnetic substatepopulations fromTWOFNRwere used tocheckthat thegamma-raycoincidencerequirementdidnot al-tertheshapeofthedifferentialcrosssectionsbymorethanafew percentacross thefull rangeof protonangles[28].Spectroscopic factors,S,wereextractedbynormalisingthecalculateddifferential

3 _{Afullanalysisincludingcascadedecaysandthemoreweaklypopulatedstates}

willfollow.

Fig. 3. (Colouronline.) PlotoftheexcitationenergyExof26Nastatespopulatedvia

thed(25_{Na, p)reaction,asdeducedfromtheprotonenergyandangle,versusthe}

energyofanycoincidentgamma-ray(afterDopplercorrection),Eγ.Gamma-decays directlytothegroundstateliealongthediagonal Ex=Eγ,whilstcascadedecays resultineventslyingabovethediagonal.Dataareforlaboratoryprotonangles back-wardof90◦.ATRIFOILrequirementhasbeenimposed(seetext).

crosssectionstothedatausingthefullrangeofanglesshownin

Fig. 4.The transferred angularmomentum, L,that best describes the shape of the measured angular distribution for each state is listedinTable 1.

Statesforwhichmorethanonevalueispossibleforthe trans-ferred angularmomentum havebeen analysed by fittinga linear combinationofthecalculatedcross sectionsusing thetwo possi-ble valuesL1 andL2 (where L1

=

L). Itis importantto note that

thecontributionfromthelargerofL1 andL2 issuppressed(fora

similarspectroscopicfactor)duetopoorerkinematicmatching.As aresult, thespectroscopicfactordeducedforthehigherLisseen generallytoexhibitalargerstatisticaluncertainty.Asmaybeseen inTable 1,theadditionofL2tothefitdoesnotsignificantlychange

the spectroscopic factor deduced using just L1, i.e. S1

≈

S. The

overalluncertaintiesassignedtothespectroscopicfactorsaresome 20%(dominatedoverwhelminglybythereactioncalculations)[35]. Theinferredspinandparityassignmentsarediscussedbelow.

The25Naprojectilehasastructure,inthesimplestshellmodel picture,ofthree0d5/2 protonscoupledto5

/

2+andaclosed0d5/2

neutronorbital.Thepositiveparityorbitals1s1/2and0d3/2,aswell

asthenegativeparityorbitals0 f7/2,1p3/2,1p1/2

. . .

arethus

avail-ableforneutrontransfer.AsshowninFig. 2,theknownlow-lying positiveparitystatesbelow450 keV[16,20]arepopulated.As dis-cussedbelow, thedataalsoshow clearly that thereispopulation ofnegativeparitystates,aswouldbe expectedfromtheprevious (d, p)studies of25,27_Ne[12,13], 27_{Mg[37] and}28_{Al [38,37,39]. In}

order tointerpret theresults,shell modelcalculations havebeen performed including all 0hω

_¯

sd-shell configurations for positive parity statesand all 1

_¯

hω excitationsin an spsdp f basis for neg-ativeparity states.The programOXBASH [40] was used withthe USD-A[32]andWBP-M[13]interactionsrespectively.TheWBP-M interaction, which describes the neighbouring nuclei 25,27Ne and

29_{Mginaconsistentmanner[13],isamodificationoftheWBP}

JID:PLB A ID:32023 /SCO Doctopic: Exper iments [m5Gv1.3; v 1.180; Pr n:2/06/2016; 15:15] P .4 (1-7) 4 G.L. W ilson et al. / Ph y sics Le tt ers B ••• ( •••• ) ••• – ••• 1 66 2 67 3 68 4 69 5 70 6 71 7 72 8 73 9 74 10 75 11 76 12 77 13 78 14 79 15 80 16 81 17 82 18 83 19 84 20 85 21 86 22 87 23 88 24 89 25 90 26 91 27 92 28 93 29 94 30 95 31 96 32 97 33 98 34 99 35 100 36 101 37 102 38 103 39 104 40 105 41 106 42 107 43 108 44 109 45 110 46 111 47 112 48 113 49 114 50 115 51 116 52 117 53 118 54 119 55 120 56 121 57 122 58 123 59 124 60 125 61 126 62 127 63 128 64 129 65 130 Table 1

Excitationenergies(Ex)andproposed Jπ for26Nalevelsinthepresentwork,withangularmomentumtransfersanddeducedspectroscopicfactors(±20%)§.TheL-transferdominatingtheyieldisdenotedbyL,orL1where

twoL-valuesarepossible;thesecondvalueisthendenotedbyL2.ValuesofS andS1,2wereobtainedbyfittingcrosssectionsusingasingleLandasumoftwoLcontributions,respectively,assumingorbitals(nlj).Shellmodel

spectroscopicfactorsSS M_andSS M

1,2 areshownforeachfittedorbital(nlj)and,forcompleteness,itsspin-orbitpartneralso.NumberingofstatesasinFig. 4.

No. Exa) ExS Mb) Jπc) JπS M

Single L analysis Two L analysis (where applicable)

L nlj S SS M _L 1 n1l1j1 S1 SS M1 L2 n2l2j2 S2 SS M2 0 0 3+ 3+1 * 1s1/2 0.61 * 1s1/2 0.61 * 0d3/2 0d5/2 0.01 0.01 0.082d) _{0.077 1}+ ₁+ 1 * 0d3/2 0d5/2 0.29 0.11 (i) 0.232 0.149 2+ 2+₁ 0 1s1/2 0.13 0.15 0 1s1/2 0.10 0.15 2 0d3/2 0d5/2 0.19† 0.10 0.09 (ii) 0.405 0.416 2+ 2+₂ 0 1s1/2 0.33 0.27 0 1s1/2 0.30 0.27 2 0d5/2 0d3/2 0.13† 0.03 0.03 1.507 1.409 1+ 1+₂ * 0d3/2 0d5/2 0.09 0.10 (iii) 1.805 1.676 (3+) 3+2 2 0d3/2 0d5/2 0.37 0.33 0.02 2 2 0d3/2 0d5/2 0.33† 0.33 0.02 0 1s1/2 0.01‡ 0.00 (iv) 2.116 2.241 5+ 5+1 2 0d5/2 0.16 0.08 (v) 2.225 2.048 (4+) 4+₂ 2 0d3/2 0d5/2 0.43 0.51 0.01 2.843 2.936 (2−) 2−1 * 0f7/2 0f5/2 0.20 0.00 * 0f7/2 0f5/2 0.20 0.00 * 1p3/2 1p1/2 0.05 0.04 (vi) 3.135 3.228 3− 3−1 1 1p3/2 1p1/2 0.07† 0.15 0.02 1 1p3/2 1p1/2 0.06† 0.15 0.02 3 0f7/2 0f5/2 0.10‡ 0.13 0.00 (vii) 3.511 3.513 4− 4−1 1 1p3/2 0.30 0.44 1 1p3/2 0.25 0.44 3 0f7/2 0f5/2 0.51† 0.00 0.00 4.305 4.401 (5−) 5−1 * 0f7/2 0f5/2 0.46 0.00 4.917 4.881 (6−) 6−1 * 0f7/2 0.61 5.009 (3−,4−) *

§Dominated byreactiontheorycontribution;statisticalerrorstypicallyseveralpercentexceptwherenotedas10%(†)or35%(‡). *Extraction ofthesedifferentialcrosssectionsbeyondscopeofpresentanalysis(seetext).

a) _{Present work,excitationenergyinMeV(±1 keV)deducedfromDoppler-correctedgamma-rayenergies.}

b) _{Excitation energyinMeV,calculatedusingtheshellmodel(SM)interactionsUSD-A(π= +)[32]andWBP-M(π= −)[13](seetext).} c) _{Inferred inpresentwork(seetext)exceptg.s.[16]andfirstfourexcitedstates[20,18,19].}

d)

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Fig. 4. (Colouronline.)Differential crosssectionsforthereactiond(25_{Na, p)at5.0MeV/nucleon.TheresultsofADWAreactioncalculationsarealsoshown,normalisedtothe}

data,fortheangularmomentumtransfersindicatedandlistedinTable 1(dashedline=fitwithsingleangularmomentum,labelledasLorasL1whereanotherfitisalso

shown,fullline=sumoftwocontributionsL1andL2).

ofthe f p-shellorbitals.Infact,earlierworkbyBenderand cowork-ersalsoapplied asimilar interactioncalledWBP-athat improved theagreementwiththeshellmodelforstatesinnearby(andonly slightly higher Z ) isotopes of Al [42] and P [43,44]. Excitation energies for the WBP-M and USD-A calculations were computed relative to the (positive parity) ground state calculated with the sameinteraction.Theassociationofexperimentallyobservedstates withshellmodelstates,indicatedinTable 1andFig. 5,wasbased ontheobservedL-transfer,theexcitationenergyandthe gamma-decayselectivity(Fig. 6)asdiscussedbelow.

Above

∼

2.5 MeV excitation, no states of positive parity are expectedto be strongly populated, according to the shell model calculations.Thestatesseenhereathigherenergiesaretherefore likelytohavenegative parity.Ofthese, themosteasily identified isthestronglypopulatedstateat3.511MeVwhichisobservedto havea yield dominated by L

=

1 neutron transfer atlarge labo-ratoryangles(Fig. 4). Theonlyobservedgamma-decaybranchfor thisstate istothe3+ groundstate,inlinewiththefavoured de-caypatternfor thelowest 4− state inthe isotone28Al [38].This stateisthusassignedtobethe4−₁ statein26_Na.

There are two strongly populated higher lying levels that gamma-decay via the 3.511 MeV level (Fig. 6). In terms of pre-dictedlevels inthisenergyrange,theobviouscandidatesare the lowest5− and6− states(Table 1).Thesecouldreasonablybe ex-pectedtogamma-decay viathe4−state,accordingtothepattern observed[39]in28Al.

Thedecaysofboththe proposed5− and6− statesproceedin part(20% and31% respectively [28]) via the state at2.116 MeV. GiventhatthislevelispopulatedviaanL

=

2 transfer(Fig. 4)and thatitisfed bythesehigherlyingnegative paritystates,ithasa likely J π assignmentofgreater than4,andacomparisonof pos-siblespinswithshell modelcalculationsindicates an assignment of5+ (supportedbyboth theenergyandtheweakspectroscopic factor).Indeed,there isan analogousstate at2.581 MeV in28_Al,

perhapsweaklypopulated inthedecayofthe6− state[39],that hasa5+assignment[45,46].

The two reasonably strong statesseen justbelow the 4− are mostnaturally associatedwiththe2− and3− statespredictedin theshellmodel(seeTable 1).Inparticular,theidentificationofthe 3− at3.135MeV isconfirmedby its gamma-decaybranch tothe lowestlying 1+ state at1.507 MeV asoccurs in28_{Al (Table 28.6}

ofref.[46])).Thisis furthersupported by the mixedL1

=

1 plus

L2

=

3 differentialcrosssection(Fig. 4).

Fig. 5. (Colouronline.) Levelscheme of26_{Naasdeducedfromthepresentwork}

compared to the results ofshell model calculations employingthe USD-A and WBP-M interactions(seetext).Thelengthsofthecolouredlinescorrespondtothe spectroscopicfactorsasfollows:reds-wave,blue p-wave,greend-wave, orange

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6 G.L. Wilson et al. / Physics Letters B•••(••••)•••–•••

1 66 2 67 3 68 4 69 5 70 6 71 7 72 8 73 9 74 10 75 11 76 12 77 13 78 14 79 15 80 16 81 17 82 18 83 19 84 20 85 21 86 22 87 23 88 24 89 25 90 26 91 27 92 28 93 29 94 30 95 31 96 32 97 33 98 34 99 35 100 36 101 37 102 38 103 39 104 40 105 41 106 42 107 43 108 44 109 45 110 46 111 47 112 48 113 49 114 50 115 51 116 52 117 53 118 54 119 55 120 56 121 57 122 58 123 59 124 60 125 61 126 62 127 63 128 64 129 65 130

Fig. 6. (Colouronline.) Decayschemeof26_{Naasdeducedfromthepresentwork,}

includingthegamma-raybranchingratios.

The spectroscopic factors extracted from the proton differen-tialcrosssectionsarecomparedtotheshellmodelpredictionsin

Table 1 andFig. 5. The 1s1/2 strength that leads to 2+ states is

concentrated in the two known statesbelow 0.5 MeV andsums toapproximately 0.45inboth theoryandexperiment.The tenta-tiveidentificationsof3+₂ and4+₂ statesarebasedonacomparison withthe shell modelcalculations asfollows. The observed 0d3/2

strength leading to J π

=

3+ is concentrated in one state near 1.8 MeV with a spectroscopic strength in very good agreement withthepredictions. The 0d3/2 strengthleading to the4+ states

hasacomparablemagnitudeintheory andexperimentandis lo-catedcloseto 2 MeV,so that theexperimentis compatiblewith thestrength beingconcentrated inthesecond 4+ state.We note thattheUSD-Ainteraction[32]predictstheexcitationenergiesfor positiveparitystatestowithin

∼

150keV,inlinewithtypicalshell modelaccuracy.WhenweinsteadusedtheWBP-Minteractionto calculatetheenergiesofstateswithastrong0d3/2neutron

charac-ter(namelythe3+ and2+ states),thenthepredictionslayabout 0.4MeV lower than experiment. This is becausethe WBP-M in-corporates theUSD interaction [47] tocompute the 0

_¯

hωpositive paritylevelsandthisisknowntounderestimate0d3/2neutron

en-ergies[12].

The spectroscopic factors deduced forthe 4− state indicate a comparablestrength to that predicted for the 1p3/2 transfer,

al-beitsomewhat weaker. However,theshellmodelfailscompletely toreproducethesubstantial0 f7/2 strength.Theexcitation energy

isgivenaccuratelyby theWBP-M calculation,asarethoseofthe othernegativeparitystates,within100keV( J π

=

2−

,

3−

,

5−

,

6−). Theselatterstatesare allpredictedtohaveastructure that over-lapssubstantiallywiththatofaneutroninthe0 f7/2 orbital

cou-pledtothe0d5/2protonofthe25Nagroundstate.Itisworthwhile

notingthatthe3−stateispredictedalsotohaveasimilar spectro-scopicstrengthforthecouplingwitha1p3/2neutron.Becauseofa

betterkinematicmatching,theL

=

1 transferdominatestheyield; a similar situationis observed forthelowest 3− state in28_{Al as}

populatedin(d, p)[48,49,45].In28_{Al,the0 f}

7/2 measured

spectro-scopic factoractuallyexceedsthat ofthe1p3/2 orbitalbyafactor

of three[48] (Table 2). Another3− state in 26_{Na ispredicted by}

the WBP-M calculationsto haveapproximatelyequal mixingand to lie at4.462 MeV, whilst a predominantly 1p3/2 neutronstate

occursat4.774MeV.Thesestatesmaybepopulatedbuthavenot beenidentifiedinthepresentanalysis.

In the caseof the 4− state in 26_{Na, the deduced1p}

3/2

spec-troscopicfactoristwiceaslargeasthatreportedfor28_Alwhereas

the0 f7/2 spectroscopicfactoriseffectivelyunchanged(Table 2).In

contrast,forthe3−state,thespectroscopicfactorsarethreetimes and six times lower, respectively, than in 28_{Al [48,46]. A clearer}

picture emerges from Table 2 if the relative magnitudes of the 1p3/2 and0 f7/2 spectroscopicfactors foreach ofthe 26Nastates

arecomparedwiththebehaviourin28_{Al.Forboththe3}−_and4−

statesin26_Na,the1p

3/2spectroscopicfactorishalfthemagnitude

ofthat for0 f7/2.In contrast,theanalogousstatesin28Alexhibit

1p3/2 spectroscopic factors that are three to five times smaller.

This demonstrates an enhanced role emerging for the 1p3/2

or-bital in the structure of the low-lying negative parity states in

26_{Naascomparedto}28_{Al.Indeed,inthecaseof}28_Althe

spectro-scopicfactors(Table 2)indicatethatthestateswithpredominantly 1p3/2 structurelieintheregionof4.8MeV,significantlyabovethe

0 f7/2-dominated states which are closer to 4.0 MeV (Table 2 of

ref.[48]).It wouldbe veryinteresting ifthespectroscopicfactors forthehigherlying2− and3− statesin26_{Nacouldbe measured}

andcompared.Asisevident inFig. 5,atheory-basedcomparison betweenthe1p3/2 and0 f7/2 strengths in26Naindicatesthat the

levelswitha1p3/2 structureareonaveragearound1 MeVbelow

those with 0 f7/2 structure (in fact, 0.83 MeV whenweighted by

the spectroscopicfactors),an inversionthat isinaccord withthe systematicsofFig. 1.

In conclusion, as noted in the introduction and illustrated in

Fig. 1, the ordering of levels in nuclei with A



25–30 evolves dramaticallyastheybecome moreneutron-rich,drivenlargelyby the interaction betweenprotons in the 0d5/2 orbital and the

va-lence neutrons. Importantlyinthis context,the resultspresented hereconfirmthattheevolutionisalsomanifestin26_Na.In

partic-ular,the low-lying3− and4− statesin26_{Naare foundtoexhibit}

an enhanced influence ofthe1p3/2 neutron orbital,compared to

theisotone 28_{Al.In additiontheWBP-Mshellmodelcalculations,}

in whichthe f p-shellorbitalsare loweredto reduce the N

=

20 gapby0.7MeV, succeedinreproducingtheenergies ofthe nega-tiveparitystatesin26_{Naastheydointheneighbouringneonand}

magnesium isotopes[12,13].From atheoreticalperspective,a less adhoc descriptionofthetransitionintotheislandofinversion rep-resentsaninterestingandimportantchallenge.

Acknowledgements

The assistance of our late colleague and friend R.M. Church-man inpreparingtheexperimentis gratefullyacknowledged.The efforts of the ISAC operations team in supplying the 25_{Na beam}

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G.L. Wilson et al. / Physics Letters B•••(••••)•••–••• 7

1 66 2 67 3 68 4 69 5 70 6 71 7 72 8 73 9 74 10 75 11 76 12 77 13 78 14 79 15 80 16 81 17 82 18 83 19 84 20 85 21 86 22 87 23 88 24 89 25 90 26 91 27 92 28 93 29 94 30 95 31 96 32 97 33 98 34 99 35 100 36 101 37 102 38 103 39 104 40 105 41 106 42 107 43 108 44 109 45 110 46 111 47 112 48 113 49 114 50 115 51 116 52 117 53 118 54 119 55 120 56 121 57 122 58 123 59 124 60 125 61 126 62 127 63 128 64 129 65 130 Table 2

Mixingbetween1p3/2and0f7/2configurationsin26Na,comparedwiththeisotone28Al.Valuesof(2J+1)Sfrom[48]areconvertedtoSusingtheconfirmedspins[46].

26_{Na, present work} 28_{Al, ref.[48]}

Jπ _E xa) S1(1p3/2)b) S2(0f7/2)b) Exa) S1(1p3/2) S2(0f7/2) 3− 3.135 0.06 0.01 0.10 0.03 3.591 0.19 0.60 4− 3.511 0.25 0.01 0.51 0.05 3.465 0.11 0.62 3− 4.691 0.31 0.08 2− 4.766 0.41 0.15 2− 4.905 0.24 0.06 3− 5.134 c)

a) _{Excitation energyinMeV.} b) _{Statistical errorinitalics.} c) _{Beyond E}

xrangeof[48].

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