Evolution of nuclear structure in neutron-rich odd-Zn isotopes and isomers

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Evolution

of

nuclear

structure

in

neutron-rich

odd-Zn

isotopes

and isomers

C. Wraith

a

_,

_{X.F. Yang}

b

,

∗

_,

_{L. Xie}

c

_,

_{C. Babcock}

a

_,

_{J. Biero ´n}

d

_,

_{J. Billowes}

c

_,

_{M.L. Bissell}

b

,

c

_,

K. Blaum

e

,

B. Cheal

a

,

L. Filippin

f

,

R.F. Garcia Ruiz

b

,

c

_,

_{W. Gins}

b

_,

_{L.K. Grob}

g

_,

_{G. Gaigalas}

h

_,

M. Godefroid

f

,

C. Gorges

i

,

H. Heylen

b

,

M. Honma

j

,

P. Jönsson

k

,

S. Kaufmann

g

,

M. Kowalska

l

_,

_{J. Krämer}

i

_,

_{S. Malbrunot-Ettenauer}

l

_,

_{R. Neugart}

e

,

g

_,

_{G. Neyens}

b

_,

W. Nörtershäuser

g

,

i

_,

_{F. Nowacki}

m

_,

_{T. Otsuka}

n

_,

_{J. Papuga}

b

_,

_{R. Sánchez}

o

_,

_{Y. Tsunoda}

p

_,

D.T. Yordanov

q

a_{OliverLodgeLaboratory,OxfordStreet,UniversityofLiverpool,Liverpool,L697ZE,UnitedKingdom} b_{KULeuven,InstituutvoorKern- enStralingsfysica,B-3001Leuven,Belgium}

c_{SchoolofPhysicsandAstronomy,TheUniversityofManchester,Manchester,M139PL,UnitedKingdom}

d_{InstytutFizykiimieniaMarianaSmoluchowskiego,UniwersytetJagiello´nski,ul.prof.StanisławaŁojasiewicza11,Kraków,Poland} e_{Max-Plank-InstitutfürKernphysik,D-69117Heidelberg,Germany}

f_{ChimieQuantiqueetPhotophysique,UniversitéLibredeBruxelles,B-1050 Brussels,Belgium} g_{InstitutfürKernchemie,UniversitätMainz,D-55128Mainz,Germany}

h_{InstituteofTheoreticalPhysicsandAstronomy,VilniusUniversity,Saul ˙etekioav.3,LT-10222Vilnius,Lithuania} i_{InstitutfürKernphysik,TUDarmstadt,D-64289Darmstadt,Germany}

j_{CenterforMathematicalSciences,UniversityofAizu,Tsuruga,Ikki-machi,Aizu-Wakamatsu,Fukushima965-8580,Japan} k_{SchoolofTechnology,MalmöUniversity,Sweden}

l_{ExperimentalPhysicsDepartment,CERN,CH-1211Geneva23,Switzerland} m_{IPHC,IN2P3-CNRSetUniversitédeStrasbourg,F-67037Strasbourg,France} n_{DepartmentofPhysics,UniversityofTokyo,Hongo,Tokyo113,Japan}

o_{GSIHelmholtzzentrumfürSchwerionenforschung,D-64291Darmstadt,Germany} p_{CenterforNuclearStudy,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan}

q_{InstitutdePhysiqueNucléaire,CNRS-IN2P3,UniversitéParis-Sud,UniversitéParis-Saclay,91406Orsay,France}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received10March2017

Receivedinrevisedform24April2017 Accepted29May2017

Availableonline1June2017 Editor:V.Metag

Keywords: Zinc

Magneticdipolemoment Quadrupolemoment Laser

Shellclosure

Collinear laserspectroscopy was performed on Zn (Z₌30) isotopesat ISOLDE, CERN.The studyof hyperfinespectraofnucleiacrosstheZnisotopicchain,

N

=33–49,allowedthemeasurementofnuclear spinsforthegroundandisomericstatesinodd-A neutron-richnucleiupto

N

₌50.Exactlyone long-lived (>10 ms) isomeric state has been established in each 69–79Zn isotope. The nuclear magnetic

dipolemomentsandspectroscopicquadrupolemomentsarewellreproducedbylarge-scaleshell–model calculationsinthe f5pg9 and

fpg

9d5 modelspaces, thusestablishingthe dominanttermintheirwave

function. The magneticmoment of the intruder Iπ_=1/2+ _isomerin 79_{Znis reproduced onlyif the}

ν

s1/2orbitalisaddedtothevalence space,asrealizedintherecentlydevelopedPFSDG-Uinteraction.

Thespinandmomentsofthelow-lyingisomericstatein73_{Znsuggestastrongonsetofdeformationat}

N=43,whiletheprogressiontowards79_{Znpointstothestabilityofthe}

_Z

_{=28 and}

_N

_{=50 shellgaps,}

supportingthemagicityof78_Ni.

©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Evaluatingtheaccuracyoflarge-scale shell–modelinteractions is dependent on experimental data in regions of shell closures.

*

Correspondingauthor.

E-mailaddresses:c.wraith@liverpool.ac.uk(C. Wraith), xiaofei.yang@fys.kuleuven.be(X.F. Yang).

ForelementswithZ

_≈

28,recentexperimentshaveaimedtoshed light onnuclear structureinthe neutron-richisotopes andhence assess the reliability of shell–model predictions. This region is known for beingrich in nuclear structuralchange, including the weaksub-shell closureatN

₌

40 observed innickel[1]and cop-per[2],thedevelopment ofcollectivitybeyondN

₌

40 inGa iso-topes[3]andthedoublymagicnatureoftheexoticnucleus78_Ni, http://dx.doi.org/10.1016/j.physletb.2017.05.085

0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

and31Ga isotopesshow that the fillingofthe

ν

g9/2 orbital after N

₌

40 inducesareorderingoftheprotonSPlevels p3/2and f5/2,

andhence a groundstate (g.s.) spin changeinduced by the ten-sorforce[3,5].Duetotheevenprotonnumberofzinc,theeffects ofthispredicted levelreordering on theg.s. properties ofodd-A Zn isotopes will be more subtle as their moments will be dom-inatedby the unpaired neutron. The tensorinteraction decreases thesize ofthe Z

₌

28 shell gapwithincreasing N, asthefilling ofthe

ν

g9/2 orbitinduces a reduction ofthe spin–orbit splitting

between the

π

f7/2 and

π

f5/2 levels [6]. This interaction

there-forehas strong implications onshell closures in thisregion, and mostnotably atclosuresfarfromstability,wherethe Z

₌

28 and N

₌

50 shellgapsprovideinformationontheeffectivenessofthe magicity of 78_{Ni [7,8]. Despite these predictions, mass}

measure-mentsof71–81_{ZnatISOLTRAPhavehighlighted thepersistence of}

the N

=

50 shell closure at Z

=

30 [9], while similar measure-ments at JYFLTRAP have indicated an increasing rigidity of the shellgapfromGatoNi [10].StudiesatRIBF of

β

-decayhalf-lives

of 76,77_Co, 79,80_{Co and} 81_{Cu, and E}

₍

₄+

1

)/

E

(

2+1

)

and B

(

E2

;

4+1

→

2+₁

)/

B

(

E2

;

2+₁

→

0+_g.s.

)

of80Znhavealsopointedtowardsadoubly

magicstructurefor78_Ni

_[11,12]

_.

In a previous publication [13] we reported the laser spec-troscopy results of an isomeric state in 79_{Zn, which was}

origi-nallyreported inRef. [14].Apreliminary analysisof thissystem, whichalsodisplaysasignatureofshapecoexistence,indicatedthe presence ofan intruder

ν

s1/2 state. Here, we report for thefirst

time a full theoretical analysis in the context of new measure-mentsfortheentireisotopicchain.Theobservednuclearmagnetic dipoleandspectroscopicquadrupolemomentsarecomparedwith large-scale shell–model calculations in different model spaces to evaluate the influence of proton excitations across Z

₌

28 and of neutrons across N

₌

50, and the evolution of nuclear struc-turealong theisotopic chain. Additionally, this Letter establishes firmlythegroundandlong-lived(

>

10 ms)isomericstatespinsof

odd-A ZnisotopesfromN

₌

33–49.Thedirectobservationoftheir hyperfine structure (hfs) solves a long-standing discussion about the (non-)existence of severallong-lived isomeric states in some oftheseisotopes[15–18,14].

2. Experimentalmethod

The experiment was completed at the collinear laser

spec-troscopysetup COLLAPS[19] atISOLDE,CERN.Radioactive fission fragmentswereproducedusingathickUCx target(45 g/cm2)

bom-barded withpulses of 1.4-GeVprotons. A neutron converter[20]

suppressed the production ofRb isobars,which contaminate the beam purity of neutron-rich Zn isotopes. The Zn yield was se-lectively enhanced by a factor of 100 using the Resonant Ion-ization Laser-Ion Source (RILIS) [21]. Zn ions were accelerated to 30 keV and mass selected using the high-resolution separa-tor (HRS). A gas-filled radio frequency quadrupole, ISCOOL [22],

Fig. 1. Hyperfinespectrafor63–79_{Znfrom the4s4p}3_Po

2 →4s5s3S1 transition, includingisomericstructures.See[13]forthefullhyperfinespectrumof79,79m_Zn.

delivered cooled and bunched ions to the collinear laser spec-troscopy setup, with a typical accumulation and release cycleof 200 ms. Theionbeamwas neutralisedin-flightthrough acharge exchange cell (CEC) filled with Na vapour, quasi-resonantly pop-ulating the atomic metastable 4s4p 3_Po

2 level at 32890.3 cm−1.

A co-propagating laser beamwas overlapped withthe emerging

atomicbeaminordertoresonantlyexcitetheZnatoms. Atuning potential appliedpriortotheneutralisationactedtoDoppler-shift the laser frequency observedby the atoms, allowing ascan over thehfsresonances.The481.1873 nm4s4p3_Po

2

→

4s5s3S1

transi-tionwas studiedusingacwfrequency-doubledtitanium-sapphire laser, lockedtoa wavelengthmeterwithuseofaninterferometer which was calibrated by a stabilized HeNe laser. A mass depen-denttimeofflightisassignedtoeachionbunch,witha5 µsgate placed on the photon signal fromlaser-ion bunchinteractions to reduce backgroundfromnon-resonantscatteredphotonsbya fac-tor of 4

×

104_{. Due to the relatively fast releaseof Zn from the}

target[23],thebackgroundwasfurthersuppressedbylimiting IS-COOLaccumulationandreleasecyclesto600 msaftereachproton pulse.

3. Experimentalresults

Opticalspectrafor63–79_Znareshownin

_{Fig. 1}

_{forthe481.2 nm}

line. A full hfs was fittedto each experimental spectrum with a

χ

2-minimisation fitting program to obtain the magnetic dipole, A,andelectricquadrupole, B,hfsconstants[24].Aslightly asym-metric lineshape occursfromenergylosses, eitherby the popu-lation of higher levels in the charge exchange process orby ad-ditional collisions. The line shape has been modelled using the

Fig. 2. LowenergyspectraofZnisotopesfromN₌41–49 arecomparedtothepredictionsfromshell–modelinteractions.Thechangeinenergyoftheconfirmedgroundand isomericstatesarehighlightedbydottedlines.Theverticaldashedlineinthe1/2+_{isomericstateof}79_{Znrepresentstheerroronthemeasuredenergy.}

Table 1

Spinsandhfsconstantsoftheupperandlowerstates ofthe481.2 nmline,for groundandisomericstatesof63–79_{Zn.NotethatB(}3_S

1)_≈0. A N I A(3S1)(MHz) A(3Po 2)(MHz) B(3P2o)(MHz) 63 33 3/2 −676.9(8) −286.0(13) +60(4) 65 35 5/2 +1114.0(23) +467.6(10) −7(6) 67 37 5/2 +1266.5(18) +531.2(11) +41(7) 69 39 1/2 +4033(9) +1691(5) – 69m _{39 9/2 −933.7(4) −392.1(2) −113(4)} 71 41 1/2 +3987(5) +1675(3) – 71m _{41 9/2 −844.5(9) −354.3(3) −76(5)} 73 43 1/2 +4044.0(27) +1696.9(16) – 73m _{43 5/2 −1233.9(14) −518.2(9) +125(6)} 75 45 7/2 −815.4(6) −342.3(4) +48(4) 75m _{45 1/2 +4034(6) +1695.5(29) –} 77 47 7/2 −938.1(7) −393.8(4) +141(5) 77m _{47 1/2 +4063(10) +1708(5) –} 79 49 9/2 −955.0(6) −400.6(3) +116(5) 79m _{49 1/2 −7362(6) −3093(4) –}

high-statisticsspectrumofaneven-A isotopeandwasfixedin fit-tingthespectraofallodd-A isotopes[25].

Unambiguous spin assignments could be made for all

nu-clei and isomers as only a single spin value reproduces all hfs peakspacingssimultaneously.The resultingspinassignmentsand hyperfine constants are shown in Table 1. Moments are cali-brated relative to those of 67_{Zn by using the hyperfine}

con-stants A

(

3P₂o

)

= +

531

.

987

(

5

)

MHz (given a negligible hyperfine

anomaly[26]) and B

(

3P₂o

)

= +

35

.

806

(

5

)

MHz[27].We usedthe

nuclearmagneticdipolemoment

µ

= +

0

.

875479

(

9

)

µ

N [28] and

anupdatedvalueforthequadrupolemoment,basedonnew calcu-lationsoftheelectricfieldgradient(EFG)forthe4s4p3_Po

1,2 states.

Applying both the non-relativistic Hartree–Fock and fully rela-tivisticDirac–Hartree–Fockmulticonfigurationmethods[29],using respectively ATSP [30] and GRASP [31] atomic structure codes, differentelectron correlation models were investigated andtheir consistency checked between the non-relativistic and relativistic approaches.Fromthisstudy,asetofA,EFGandQsvaluesare

pro-duced[32]fromwhichwederivedaquadrupolemomentvalueof Qs

= +

0

.

122

(

10

)

b.RecentlytheEFGofZninsolidZnhasbeen

re-calculatedusingahybridDensityFunctionalTheoryapproach[33]. Combiningthisvalue withthe experimental quadrupolecoupling constants measured by Potzel etal. [34], and corrected for ther-maleffects, anew quadrupolemoment value for 67_{Zn g.s., Q}

s

=

+

0

.

122

(

5

)

b,isdetermined in[33].Althoughthisvalue perfectly

agreeswiththepresentatomicestimation,theclaimederrorbars appeartobeveryoptimistic,takingthegeneraluncertaintyofthe DFT functionaldevelopments intoaccount. We thereforeadopted

thereferencevalue Qs

= +

0

.

122

(

10

)

b fortheg.s.of67Zn.All

ex-tractedmomentsareshownin

Table 2

.

4. Nuclearspinsofgroundandisomericstates

In Fig. 2 we present the experimental ground and isomeric statesin71–79_{Zn,forwhichfirmspin-assignmentshavebeenmade.}

The assigned parities are based on the measured magnetic

mo-ments,asdiscussedinthenextsection.

Whenfillingthe

ν

g9/2orbitalfromN

=

41 onwards,ag.s. spin I

₌

9

/

2 would be expected forthe odd-Zn isotopes, in the case

that no deformation or correlations are present. This is not the caseforanyoftheseisotopes,exceptfortheone-neutron–hole iso-tope79_{Zn.ThisisevidenceforthemagicnatureoftheN}

₌

_{50 shell}

andsuggeststhatthelighterZnisotopes exhibitsignificant corre-lationsintheir groundstates,leading tonon-trivialg.s. spins.For

71,73_{Zn,theg.s. spin-parity1}

_/

₂−_{thatwastentativelyassigned}

pre-viously[15]isconfirmed.The9

/

2+stateappearstobeisomericin 71_{Zn,andhasnotyetbeenobservedin}73_{Zn.Instead,a5}

_/

₂+

iso-mericstate isobserved[18].In75,77_{Zn,theg.s. spin is7}

_/

₂+ _and

the1

/

2−becomesnowalong-livedisomericstate.Finally,in79Zn,

having49neutrons,theg.s. spinisthe9

/

2+expectedfroma

non-interacting shell model picture with a hole inthe

ν

g9/2 orbital.

Along-livedisomeric state withspin-1/2 hasbeenestablished in this isotope, butits large negative magnetic moment excluded a negativeparityforthisisomer[13].

In

Fig. 2

wecomparethelowestenergylevelsinodd-A Zn iso-topeswithlarge-scale shell–modelcalculationsindifferentmodel spacesandusingdifferentinteractions. Thesimplestmodelspace starts froma 56_{Ni core, withprotonsandneutrons inthe f}

5/2

,

p

and g9/2 orbits. Two effective interactions are available in this

model space, JUN45 [35] and jj44b [3]. This model space is ex-tendedtoincludeprotonexcitationsfrom

π

f7/2acrossZ

=

28 and

neutronexcitations across N

=

50 into the

ν

d5/2 orbital. Two

in-teractionsareavailableinthisextendedmodelspace:themodified A3DA interaction (A3DA-m)[36] in the MonteCarlo Shell-Model (MCSM)[37]frameworkandthemodifiedLNPSinteraction (LNPS-m) that isused with theANTOINE code [38].To understand the structure of the newly found positive parity isomer in 79_{Zn, we}

usetherecentlydevelopedPFSDG-Uinteraction[39]intheproton pf andneutronsdgvalencespace.

As can be seen inFig. 2, noneof the calculationsreproduces correctly the energy level ordering of all ground and isomeric states in these isotopes. In the calculations with a 56_{Ni core}

(JUN45) theg.s. spin is predictedto be 9

/

2+ _{forall isotopes. By}

opening the proton shell to include excitations from the

π

f7/2

77 7/2 −0.9074(1) −0.876 −1.04 −0.964 +0.48(4) +0.421 +0.60 +0.487

77m _1/2− _{+0.562(2) +0.450 +0.50 +0.537 – – – –}

79 9/2+ _{−1.1866(10) −1.185 −1.49 −1.508 +0.40(4) +0.356 +0.546 +0.367}

79m _1/2+ _{−1.018(1) – −0.741 −0.603 – – – –}

a _{Tocalibrateacrosstheisotopechainthenuclearmomentsof}67_{Znareusedasreferences,withµandQstakenfrom[28]andthisworkrespectively,withdetailsgiven} in[32].PrecisehyperfineconstantsA(3P2)andB(3P2)[27]areused.

(A3DA-m and LNPS-m) the agreement becomes better for 77_Zn.

However, for the less exotic isotopes the level ordering is still not well reproduced. These interactions predict a positive-parity 1

/

2+levelin79Zn,althoughitappearsat1.8and1.5 MeV

respec-tively,well above the experimental energy of 1.10(15) MeV [14]. Themagneticmomentofthislevelmotivateda furtherextension ofthemodelspace, asrealizedinthePFSDG-Uinteraction.Inthis extendedmodelspacean isomeric1

/

2+ levelisfound atthe ex-perimentalenergy.

5. Groundandisomericstateg-factorsandwavefunctions

In the f5pg9 model space used for JUN45 and jj44b, we use g_seff

=

0

.

7g_sfree for magnetic moment calculations, and effective

chargeseeff

p

=

1

.

5e,eeffn

=

1

.

1e[35].Theseinteractions were used

inourpreviousworkonthenuclearmomentsandspinsoftheCu andGagroundstates[40,3],reproducingtheseobservablesrather well.TheLNPS-mandA3DA-minteractionsstartfroma40_Cacore

andincludealsothed5/2orbital,thususingafpg9d5 modelspace.

The neutron f7/2 orbit is blocked for the LNPS-m calculations,

butthishasnoinfluenceonthespectroscopyoftheneutron-rich (N

>

38) isotopes. Free g-factors canbe applied inthisextended

modelspace. Furthermore,theeffectiveneutroncharge canbe re-ducedtoeeff

n

=

0

.

46e becauseoftheinclusionofthe

ν

d5/2 orbital,

whiletheprotoncharge istakenaseeff

p

=

1

.

31e [38]. Thenuclear

moments have been calculated for the lowest lying energylevel withtheconfirmedspinassignment.

The nuclear magnetic moment provides a sensitive probe of

thewave functionofthestate. Bycomparingthemeasured mag-netic moments, andmore specifically the corresponding g-factor (g

=

µ

/

I) to the effective SPvalues of nearbyorbitals, the

lead-ing contributions to the wave functions can be deduced (Fig. 3). These values are also compared to the predictions of the shell– modelinteractions,fromwhichwecanextractthecalculatedmain contributioninthewavefunction.

The experimental g-factors for the 1

/

2− ground states of 69,71,73_{Znandtheisomericstatesin}75,77_{Znareingoodagreement}

withthe effectiveSP value for the

ν

p1/2 orbit. The

(

ν

p1/2)1 led

wave function configurationfor these statesis confirmed by the calculationsinthef5pg9 modelspacethatpredict a

>

50%

contri-butionfroma

ν

p1/2 holeconfigurationforthegroundstatesand

>

60% forthe isomers. The calculated magnetic moments appear

tosystematically underestimatethemeasured valuesofthe 1

/

2−

states.Furthertheoreticalinvestigationsareneededtounderstand this.

Fig. 3. Measured g-factorsofthegroundandisomericstatesof65–79_Zn.The ob-served results arecompared tothe effective SP values (parityinbrackets) and predictionsofshell–modelinteractions(seetextfordetails).

Thegroundstatesof65,67_Zn(N

₌

₃₅

_,

_{37)bothhavespin5}

_/

₂+

andtheir g-factorisingoodagreementwiththatforan unpaired neutronconfigurationinthe

ν

f5/2 orbital.Thehigh-spinstatesin

the 69–79_{Znisotopes,havingspins9}

_/

₂+_,5

_/

₂+ _and7

_/

₂+_,allhave

a g-factorthatisvery closeto thatforan unpairedneutron con-figurationinthe

ν

g9/2 orbital,suggestingthisistheleadingterm

intheirwavefunction.

For the isomeric 9

/

2+ states in 69,71Zn and the 9

/

2+ g.s. in 79_{Zn,a single unpaired g9}

/2 neutronconfigurationis expectedto

dominatethe wavefunction. Thatis confirmedbythe large-scale shell–modelcalculationsfromJUN45andjj44b,whichpredictthis configuration to have the largestcontribution indeed: about 50% in 69_{Zn (N}

₌

_{39), 40% in}71_Zn(N

₌

_{41) andnearly 100% in}79_Zn

(N

=

49).Theexcellentagreementofthecalculatedmagnetic mo-ments withthe observedvalue forthe 79_{Zng.s. with all}

interac-tions(Table 2),illustratesthepersistenceofN

=

50 asashellgap. Alsothevaluesforthe7

/

2+ groundstatesin75,77Znare well

re-produced by all large scale shell–modelcalculations. The leading termin theirwave function isa seniority-3

ν

(

g9/2

)

37/2

configura-tion, which makes up roughly half ofthe wave function in 75_Zn

and77_Zn.

The5

/

2+ _{isomericstatein}73_{Znalsohasag-factorthatagrees}

well with the value for an unpaired g9/2 neutron configuration.

Fig. 5. Positive-paritylevelsinN₌49 isotopesduetoneutronexcitationsacrossN₌50,comparedthecalculatedlevelswiththePFSDG-Uinteraction.Theverticaldashed lineinthe1/2+_{isomericstateof}79_{Znrepresentstheerroronthemeasuredenergy.}

Fig. 4. (a) High-spin state g-factors in relation to the effective SP value of geff(νg9/2).(b)Measuredspectroscopicquadrupolemomentsofthehighspinstates ofZnisotopescomparedtotheexpectedvaluesforaseniority-1(g9/2)n configura-tionandthespin-7/2+and5/2+seniority-3configurations.(Forinterpretationof

thereferencestocolourinthisfigure,thereaderisreferredtothewebversionof thisarticle.)

SPconfiguration.Thisexcludesthatthis5

/

2+ isomericstateisan

intruder isomer, dominated by a neutron excited into the

ν

d5/2

orbital. The fact that its g-factor is somewhat lower than that ofthe other high-spin statessuggests that some admixture with suchaconfigurationcannot beexcluded. In

Fig. 4

a,thehigh-spin g-factors are presentedon asmaller scale,inorder tobetter see how well each of the calculations agrees with the data. The di-vergenceofpredictionsfromtheLNPS-mandA3DA-minteractions fromexperimenttowards N

=

50 whileJUN45andjj44bconverge hintsatthepersistence ofthe Z

₌

28 and N

₌

50 shell gaps.All

Table 3

Calculatedenergies(MeV)andelectromagnetic momentsµ(µN)and Qs (b)for 79_Znand81_{GeusingthePFSDG-Uinteraction.Thesameeffectivechargesareused} asforLNPS-m.

A_{Z I}π _{E µexp µbare/µquenched Qs} ,exp Qs 79_{Zn 9/2}+ _{0.0 −1.1866 −1.03/−1.10 +0.40 +0.42}

1/2+ _{1.03 −1.018 −1.14/−0.91 – –}

81_{Ge 9/2}+ _{0.0 – −0.90/−0.95 – +0.60}

1/2+ _{0.31 – −1.15/−0.94 – –}

interactionspredictaveryfragmentedwavefunctionforthe5

/

2+

isomericstate in73_{Zn,withthelargestcontributioninJUN45}

be-inglessthan10%.

Forthe isomeric state in79_{Zn,the modelspacelimitations of}

the JUN45and jj44b interactions prevent anypredictions forthe positiveparity1

/

2+_{state.Thespinandpositiveparityofthislevel}

were tentativelyassigned in [14] andfirmly established by [13], basedon itsstrong negative g-factor, whichisincompatible with a p1/2 hole configuration (see Fig. 3). The larger modelspace of

the LNPS-m andA3DA-m interactions consider excitations across the N

₌

50 shellclosureinto the

ν

d5/2 orbitonly. In thismodel

space, a 1

/

2+ level is predictedat 1.8and 1.5 MeV respectively,

with g-factors gA3DA−m

= −

1

.

206 and gLNPS−m

= −

1

.

482, closer

to theobserved value, gexp

= −

2

.

038,butstill not in agreement.

In [13], a 1p–2h neutron excitation to a positive parity spin-1/2 state is suggested, witha large part of the wave function domi-natedbyasingleneutroninthes1/2 orbit.

Anewshellmodelinteractionhasbeendeveloped,suitableto calculatelevelsinisotopesaround N

=

50 withprotonslimitedto thepf shellandneutronstothesdg space[39],includingallspin– orbitpartners(allowingtheuseoffree g-factors). Thusthe inter-action is not suited to calculate levels in which neutrons inthe pf orbitsplayanimportantrole(suchasthe1

/

2−isomericstates

in75,77_{Zn).Therefore,we limitthecalculationstothe N}

₌

₄₉

iso-toneswithprotonsinthe pf shell,wherepositive-parityintruder orbitshave beenobservedbetween Z

₌

38 and Z

₌

30.In

Fig. 5

wecomparethecalculatedlowestpositiveparity9

/

2+,1

/

2+ and

5

/

2+ _{levels in} 85_Kr,83_Se, 81_Ge,79_Znand77_{Ni tothe}

experimen-taldata.Theenergiesfortheseintruderlevelsarewellreproduced for79_{Zn,giventypical shell–modeluncertainties(afew 100 keV)}

onenergypredictions.For77_{Ni,theseintruderlevelsarepredicted}

closeto2MeV,suggestingarathergooddoubly-magicnaturefor

78_{Ni.Fortheheavierisotonestheyappear200to500 keVtoolow,}

whichneedssomefurtherinvestigation.

The 1

/

2+ state appearsto be isomericin 79Zn and81Ge[41],

andthe intruder nature ofthis state is firmly established via its magnetic moment. Indeed, excellent agreement is observed

be-tween the calculated andobserved magnetic moment of the

normal-Fig. 6. Neutronoccupancynormalisedtothemaximumorbitalnucleonnumberfor thegroundandisomericstatesin79_{ZnfromthePFSDG-Uinteraction.}

izedneutronoccupancyinallsdg levels.Theg.s. wavefunctionis dominated byasingle neutronholeinthe g9/2 orbit(50%),buta

significantamountofneutronexcitationsintothesdspaceare ob-servedfortheisomericstate.Thatleadstoabetteragreementwith

theexperimental magneticandquadrupolemoment comparedto

theLNPS-mcalculations.Theisomericlevelhasalargeoccupancy ofthes1/2 level,butalsomorenp–nhexcitationsintothed5/2

or-bitalaswell asthehigher gd orbits.Themaincomponentinthe isomeric wave function is found tobe indeedofa 1p–2h nature (40%).

6. Quadrupolemomentsofgroundandisomericstates

The quadrupole moments of the high-spin states, shown in

Fig. 4b,are abletoshedfurtherlightonthesingle particle struc-tureaswell ascollectivityandstructural changesacross the iso-tope chain as the

ν

g9/2 orbit is filled. In Table 2, the A3DA-m

interaction is shown to most accurately predict the measured quadrupolemomentsofneutronrichisotopesfrom69–79_Zn,except

fortheg.s.of75_Zn.

Alreadystartingfrom69_{Zn,theneutronsgraduallyfillthe g} 9/2

orbital.In generalthequadrupole momentshould reflectthe na-ture of a single g9/2 neutron particle in 69Zn and single g9/2

neutron hole in 79_{Zn, as discussed for the magnetic moments}

measured in this work. In Fig. 4b it can be seen that the 1p configuration for the isomeric state in 69_{Zn has indeed the}

op-posite quadrupolemoment ofthe1h configurationforthe g.s.of

79_{Zn. The quadrupole moments forthe seniority-1}

₍

_ν

_g

9/2)n

con-figurations with spin-9/2 (69,71,79_{Zn) follow the expected linear}

increase,crossingzerointhemiddleoftheshell[42] (reddashed lineof

Fig. 4

b) whichcorresponds to A

=

74 in thepresentcase. Theexperimentalmagneticmomentsofthe7

/

2+ statesin75,77Zn

show a seniority-3

ν

(

g9/2)3_7/2+ configuration, explainingwhythe their quadrupole moments do not followthe straight line ofthe seniority-1cases.

Anestimateofthequadrupolemomentsofthe7

/

2+

seniority-3statescanbeobtainedusingtheeffectivesingle-particle quadru-polemomentobservedintheseniority-1cases,Qsp

= ⟨

J

| ˆ

Q

|

J

⟩

,the

applicable coefficients of fractional parentage [43] and the rela-tion[44,45],

⟨

Jn

(

I

)

| !

Q

|

Jn

(

I

)⟩ =

2 J

+

1

−

2n 2 J

+

1

−

2

ν

ν

"

J1

(−

1

)

J1+J+I

₍

_cfp

₎

2

×(

2I

+

1

)

#

J I J1 I J 2

$

⟨

J

_|!

Q

_|

J

_⟩

(1)

result, along with the increase of configuration mixing at Zn mentionedabove,witnessedbothinitsmagneticmomentandits quadrupole moment,thereforesignalsa rapidshape transitionat N

=

43 intheZnisotopes.Alow-energyCoulombexcitationstudy of zinc isotopes at REX-ISOLDE supports this conclusion. Here a suddenloweringof2+_statesatN

₌

_{40 andanincreaseinB(E2}

_↓

₎

strength towards N

₌

44 was associatedwithan increase in col-lectivity due to proton–neutron correlations anda weakening of the sub-shell closure [47,48]. An onset of collectivityis also

ob-served in the quadrupole moments of odd-A Ga isotopes when

N

>

40 [3], while no such increase in collectivityis observed in

the quadrupole moments of Cu isotones [40]. Therefore, Zn iso-topes are considered to lie within a transitional region between sphericalNianddeformedGenuclei[49].

7. Conclusion

In summary,thenuclear spins, magneticdipole moments and electricquadrupolemomentshavebeendeterminedfortheground and isomeric states in 63–79_{Zn by means of collinear laser}

spec-troscopy. Exactlyone long-lived(t1/2

>

10 ms) isomericstate has

been observed in all odd-A Zn isotopes from N

=

39–49. This

hasprovided an insightintothe neutronlevelsystematics asthe N

₌

50 shellclosureisapproached.

The magnetic dipole moments of ground andisomeric states

havebeencomparedtoavarietyoflarge-scaleshell–model calcu-lationsindifferentmodelspaces.Allstatesupto79_Zn(exceptfor

the 1

/

2+ _{isomeric level) are well described withinteractions}

as-suminga56_{Nicoreandneutronslimitedtothepf andg9}

/2orbits.

Extendingthemodelspacebothforprotonexcitationsacross Z

=

28 and neutron excitations across N

₌

50 does not significantly improve theagreement withexperiment, withtheir high-spin g-factorsdivergingfromtheexperimentalvaluesforN

₌

45–49 sug-gesting the preservation of these shell gaps when approaching

78_Ni.

Forthe 1

/

2+ intruder isomer,a newly developedshell–model

interactioninthepf

₊

sdgmodelspaceisneededtoreproducethe magnetic dipole moment of 79m_{Zn, which lies outside the f}

5pg9

andfpg9d5 modelspaces.ThePFSDG-Uinteractionsuggestsa

lead-ingwavefunctionconfigurationformedbya1p–2hexcitationfrom

ν

g9/2 to

ν

3s1/2, consistent with the spin-parity of the isomeric

state as 1

/

2+. A similar isomeric intruder level has been sug-gestedin81_{Ge[41]andafuturemagnetic momentmeasurement}

shouldconfirmits1p–2hintrudernature.Alsoin80_Gaalow-lying

short-livedintruder0+_{statehasbeeninferredfrom}

_β

_-decay

stud-ies[50].Thusfurtherstudiestoestablishthedeformationofthese proposedshape-coexistingstatesareneeded.

The quadrupole moments reveal a strong onset ofcollectivity from71m_Znto 73m_{Zn,wherethedeviationofthequadrupole}

mo-ment from the seniority-3 5

/

2+ prediction indicates substantial

describedmostaccurately bytheA3DA-minteraction,butin gen-eraltheyarewellreproducedbyallshell–modelinteractions.

Acknowledgements

The support and assistance from the ISOLDE technical group aregratefullyacknowledged.Thisworkwassupportedbythe

IAP-project P7/12, the FWO-Vlaanderen, GOA grant 15/010 from KU

Leuven,theBMBFContractsNos.05P15RDCIA,theMax-Planck So-ciety, the Science and Technology Facilities Council, and the EU FP7viaENSARNo. 262010. TheatomiccalculationsofEFGswere supported fromthe European Regional DevelopmentFund in the frameworkofthePolishInnovationEconomyOperationalProgram (contract no. POIG.02.01.00-12-023/08). PJ acknowledges support from the Swedish Research Council under contract 2015-04842. The Monte Carlo Shell-Model calculations were performed on K

computer at RIKEN AICS (hp150224, hp160211). This work was

supported in part by the HPCI Strategic Program (the origin of matterandtheuniverse)and“PriorityIssueonPost-Kcomputer” (Elucidationof the Fundamental Laws and Evolution of the Uni-verse)fromMEXTandJICFuS.

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