Nuclear charge radii of Zn62-80 and their dependence on cross-shell proton excitations

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Physics

Letters

B

www.elsevier.com/locate/physletb

Nuclear

charge

radii

of

62

−

80

Zn

and

their

dependence

on

cross-shell

proton

excitations

L. Xie

a

,

X.F. Yang

b

,

c

,∗

,

C. Wraith

d

,

C. Babcock

d

,

J. Biero ´n

e

,

J. Billowes

a

,

M.L. Bissell

c

,

a

,

K. Blaum

f

,

B. Cheal

d

,

L. Filippin

h

,

K.T. Flanagan

a

,

i

,

R.F. Garcia Ruiz

c

,

a

,

W. Gins

c

,

G. Gaigalas

g

,

M. Godefroid

h

,

C. Gorges

k

,

l

,

L.K. Grob

j

,

k

,

H. Heylen

c

,

f

,

j

,

P. Jönsson

m

,

S. Kaufmann

k

,

M. Kowalska

j

,

J. Krämer

k

,

S. Malbrunot-Ettenauer

j

,

R. Neugart

f

,

l

,

G. Neyens

c

,

j

_,

_{W. Nörtershäuser}

k

_,

_{T. Otsuka}

n

,

o

,

c

,

p

_,

_{J. Papuga}

c

_,

_{R. Sánchez}

q

_,

_{Y. Tsunoda}

n

_,

D.T. Yordanov

r

a_{SchoolofPhysicsandAstronomy,TheUniversityofManchester,ManchesterM139PL,UnitedKingdom}

b_{SchoolofPhysicsandStateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,China} c_{KULeuven,InstituutvoorKern- enStralingsfysica,B-3001Leuven,Belgium}

d_{OliverLodgeLaboratory,OxfordStreet,UniversityofLiverpool,Liverpool,L697ZE,UnitedKingdom}

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

g_{InstituteofTheoreticalPhysicsandAstronomy,VilniusUniversity,Sauletekioav.3,LT-10222Vilnius,Lithuania} h_{Chimiequantiqueetphotophysique,UniversitélibredeBruxelles,B1050Brussels,Belgium}

i_{PhotonScienceInstituteAlanTuringBuilding,UniversityofManchester,ManchesterM139PY,UnitedKingdom} j_{ExperimentalPhysicsDepartment,CERN,CH-1211Geneva23,Switzerland}

k_{InstitutfürKernphysik,TUDarmstadt,D-64289Darmstadt,Germany} l_{InstitutfürKernchemie,UniversitätMainz,D-55128Mainz,Germany} m_{SchoolofTechnology,MalmöUniversity,Sweden}

n_{CenterforNuclearStudy,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan} o_{DepartmentofPhysics,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan}

p_{NationalSuperconductingCyclotronLaboratory,MichiganStateUniversity,EastLansing,MI 48824,USA} q_{GSIHelmholtzzentrumfürSchwerionenforschung,D-64291Darmstadt,Germany}

r_{InstitutedePhysiqueNucléaire,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:

Received10April2019

Receivedinrevisedform23July2019 Accepted23July2019

Availableonline25July2019 Editor:D.F.Geesaman

Keywords:

Zinc

Nuclearchargeradii Shellclosure Nucleardeformation Correlations

Nuclearchargeradiiof62−80Znhavebeendeterminedusingcollinearlaserspectroscopyofbunchedion beamsatCERN-ISOLDE.Thesubtlevariationsofobservedchargeradii,bothwithinoneisotopeandalong the full rangeofneutronnumbers,are foundto bewelldescribed intermsofthe protonexcitations across the Z=28 shellgap, as predicted bylarge-scale shell model calculations.It comprehensively explainsthechangesinisomer-to-groundstatemeansquarechargeradiiof69−79_{Zn,theinversionofthe}

odd-evenstaggeringaroundN₌40 andtheodd-evenstaggeringsystematicsoftheZnchargeradii.With twoprotonsabove Z=28,theobservedchargeradiioftheZnisotopicchainshowacumulativeeffect ofdifferentaspectsofnuclearstructureincludingsingleparticlestructure,shellclosure,correlationsand deformationsneartheproposeddoublymagicnuclei,68Niand78Ni.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

The nuclear charge radius is one of the most fundamental

propertiesof the atomicnucleus, and thus an important

observ-*

Correspondingauthor.

E-mailaddress:xiaofei.yang@pku.edu.cn(X.F. Yang).

able forunderstanding variousaspects of nuclear structure:shell andsubshell effects [1],configuration mixing[2], correlations[3] as well as nuclear deformation and shape coexistence [4,5]. Al-thougheffortsaremadetosuccessfullydescribegeneraltrendsof chargeradii usingvariousnuclearmodels,anaccurate description ofchargeradiiandtheirlocalvariations,e.g.theodd-even stagger-ing (OES),alonga givenisotopicchainremains amajorchallenge

https://doi.org/10.1016/j.physletb.2019.134805

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

[6–8].Forexample,significanteffortshavebeenmadetoestablish a nucleartheory that accurately describes theparabolic shapeof thechargeradii andthepronouncedOESintheCaisotopicchain

from N

=

20 to N

=

28 [9] and more recently from N

=

16 to

N

=

32 [7,10,11].

TheOESeffectisubiquitousbutstill remainstobean intrigu-ing featureofnuclear charge radii,signalling a wealthofnuclear information.Ingeneral,theOESreferstothefactthatchargeradii ofmostodd-N isotopes are smallerthan the averageofadjacent even-N isotopes.Thishasbeenexplainedbythepairingeffect.The unpaired neutronin an odd-N isotopeblocks a certain orbitand thussuppressesthepairscattering[10,12,13],whichinturnleads toareduction inprotonpairscattering.The resultingdecreaseof occupationprobability oflessbound protonorbits givesrise toa smallerchargeradius.Therefore,theOESofchargeradiishouldbe sensitivetothesubtlevariationofprotonexcitationsdueto vary-ing neutron numbers, andthus reflect the effect of correlations. Substantial experimentalandtheoretical investigations havebeen applied recentlytounderstand theOESfeature ofnuclear charge radii, butmostly in specific regions where the OESeffect is un-usually large, such as for the light-mass 40−48Ca isotopes [10,9,

11],andmore recentlyforthe mostnotable example,known for many years,the neutron-deficient 177−185_{Hg isotopes [14].}

How-ever,theseexceptionalcasesarenotrepresentativeforthegeneral caseofmuchsmallerOESinmostotherisotopicchainsacrossthe nuclearchart.

In themedium mass Ni region, the localfluctuation and OES of the nuclear charge radii are more typical, and thus suitable fora more fundamental understanding ofthe subtle correlations betweenminorchangesofchargeradii andprotoncross-shell ex-citations. With two protons outside of the Z

=

28 closed shell andneutronsbetweenclosedshellsof

N

=

28 and50,theZn iso-topesoccupy atransitional region betweensingle particle-likeNi isotopes anddeformed Ge isotopes. Therefore,they are expected to exhibit the combined effects of shell closures and deformed shapes, whichcanbe reflected inthevarious subtlevariationsof theirchargeradii.

Thisletterreportsonthemeasurementofnuclearmeansquare charge radii of 62−80_{Zn isotopes, and a successful interpretation}

oftheirtrendandtheir OESintermsofprotonexcitationsacross the Z

=

28 shellgap.ThesehavebeencalculatedusingtheMonte CarloShellModel (MCSM)withthe A3DA-minteraction ina full proton-neutron p f g9/2d5/2 modelspace[15].Thisinteractionwas

usedbeforetosuccessfullyreproducethemagneticandquadrupole moments of theseZn isotopes and their long-lived isomers [16], illustrating that the model correctly reproduces the ground and isomericstatewavefunctions.

2. Experimentalmethod

The experiment was performed atthe COLLAPS setup [17] at

ISOLDE-CERN. The Zn isotopes were produced from a thick UCx

targetbombarded bya 1.4 GeV protonbeam.The Znisotopes re-leased fromthe target were selectively ionised by the resonance ionisation laser ion source RILIS [18]. Extracted Zn+ ions were acceleratedto 30 keVand mass separated. The ions were deliv-ered to the COLLAPS setup typically as 5 μs bunches after 200 ms accumulation time in the radio frequency quadrupole cooler and buncher ISCOOL [19,20]. The ions were neutralised by pas-sagethroughsodium vapourina chargeexchange cell(CEC).The 4s4p 3P₂o metastable state ofZn I waspopulated inthe neutrali-sationprocess, fromwheretheatoms wereresonantly excited to the4s5s 3S1 state by alaserbeamfromafrequency-doubledcw

Ti:sapphirelaser.Thelaserwavelengthwaslockedat480.7254 nm tomatchtheDopplershiftedtransition. Fourphotomultipliers

in-stalled at the detection region were used to record the emitted fluorescencephotonsfromthelaser-excitedatomsasafunctionof atuningvoltageappliedtotheCEC.Moredetailsaboutthe exper-imentalset-upcanbefoundin[5,16].

3. Experimentalresults

The hyperfinespectra of the odd-mass 63−79_{Zn isotopes have}

been reported in [16], while the zero nuclear spin of even Zn isotopes resultsinasingleresonancespectrum.The observed hy-perfine spectra were fitted using a

χ

2 _{minimisation procedure,}

generatingthehyperfine-structure

A and B parameters

ofthe odd-massisotopes andisomers (asreportedin[16]),andthecentroid frequency

ν

ofall62−80Znisotopesandisomers.Theisotopeshifts (IS:

δ

ν

68,A

₌

_ν

A

₋

_ν

68_{)werecalculatedwithrespecttothecentroid}

of68Zn(ν68_{),aspresentedinTable1.Asystematicuncertaintyon}

thelaserfrequencyobservedbythemovingions,whichoriginates fromthevoltageuncertainty(about0.033%)onthestarting poten-tial(30kV)atISCOOL,hasbeenintroduced.

The changes in meansquare charge radii

δ



r2



were obtained fromtheISbasedontheequation[22,23]

δ

ν

68,A

₌

_K

MS

mA

−

m68

mAm68

+

F

δ



r2



68,A

.

(1)

Here KMS and F are the atomic mass-shift and field-shift

fac-tors, respectively, of the atomictransition used in this measure-ment. Since the mean square charge radii of five stable Zn iso-topesareknownexperimentallyfromacombinedanalysisof elec-tron scatteringandmuonic

x-ray

data[24],aKing-plotprocedure using these experimental

δ



r2



μe can be performed to evaluate

the atomic factors [24–26]. As these evaluations of F and KMS

factors have rather large error bars in the case of Zn [25,24], we take advantage of the recent progress in multi-configuration Dirac-Hartree-Fock(MCDHF)calculationsbasedonanab-initio ap-proach to better quantify the F -factor [27]. This methodhas in-deed proven to be very successfulin calculatingthe F -factor for a range ofelements [3,28–31]. Forthe caseofZn, Filippinetal., [32] have explored different electron correlations in a system-atic way, inorder to optimise their computational strategy. They providea final F -factor, F

= +

346

(

3

)

MHz/fm2_,inwhichthe

un-certainty isestimated based onthe variation of the three differ-ent correlation models [32]. However, the calculated mass shift,

KMS

= +

14

(

7

)

GHz u,in commonwithother systems [3,29], has

a significant discrepancy with the value deduced from a

King-plot analysis, leading to charge radii which do not conform to regional systematics.Aswiththe caseofCu ( Z

=

29) [3] andGa ( Z

=

31)[29],wethereforeusethecalculatedvalue

F

= +

346

(

35

)

MHz/fm2 witha 10% uncertainty,andwe usethe Kingplotwith non-opticaldata

δ



r2



μeofstableisotopes[24] toextractthevalue

of KMS

= +

49

(

17

)

GHz u. In this analysis, the F -value from the

calculationwasusedasaconstraintbutallowedtovarywithinthe 10% uncertainty.Withtheseempiricalatomicfactors,thechanges in mean square charge radii

δ



r2



for 62−80Zn are extracted, as shown inTable1 andinFig. 1a.The systematicerrorquoted for

δ

r2

_

_{arisesmainlyfromtheuncertaintyintheatomicfactorsafter}

removing the correlations between KMS and F during the

King-plot procedure [8]. The systematic error on the IS, due to the uncertainty of the beam energy,has no effect on the final

δ



r2



systematicerrorasthe atomicfactorsallow their influencetobe cancelled through the King-plot procedure. By comparison with the Cu andGa isotopicchains shown inFig. 1a,the Zn radii are consistent withthegeneral trendofcharge radii ofneighbouring isotopes,whileadeviationfromthetrendisobservedif

K

MSfrom

Table 1

Isotopeshiftsandchangesinmeansquarechargeradii of 62−80_{Zn δr}2_68,A_{. Statistical errors are shown in}

curved brackets. Systematic errors in square brackets ariseprimarilyfromthe uncertaintyonthe beam en-ergy(forisotopeshifts)andonatomicfactorsKMSand

F (forradii),respectively.

A Iπ δν68,A_{(MHz) δr}2_68,A_(fm2₎ 62 0+ −239.5(11)[99] −0.493(3)[52] 63 3/2− −191.2(32)[87] −0.389(9)[43] 64 0+ −141.2(12)[66] −0.279(4)[34] 65 5/2− −121.8(23)[51] −0.257(7)[25] 66 0+ −63.6(15)[38] −0.121(4)[16] 67 5/2− −41.4(21)[16] −0.089(6)[8] 68 0+ 0 0 69 1/2− 19.5(20)[15] 0.026(6)[9] 69m _9/2+ _{35.7(11)[15] 0.073(3)[8]} 70 0+ 69.5(9)[29] 0.142(3)[15] 71 1/2− 108.8(24)[44] 0.227(7)[23] 71m _9/2+ _{96.3(11)[43] 0.191(3)[23]} 72 0+ 140.6(10)[57] 0.292(3)[30] 73 1/2− 158.9(12)[71] 0.318(3)[37] 73m _5/2+ _{160.4(19)[71] 0.322(6)[37]} 74 0+ 187.9(13)[83] 0.375(4)[44] 75 7/2+ 187.7(10)[96] 0.349(3)[51] 75m _1/2− _{195.8(21)[96] 0.373(6)[51]} 76 0+ 221.3(14)[108] 0.421(4)[57] 77 7/2+ 236.0(16)[120] 0.440(5)[64] 77m _1/2− _{241.2(38)[120] 0.455(11)[64]} 78 0+ 255.7(11)[131] 0.474(3)[70] 79 9/2+ 259.3(10)[142] 0.461(3)[77] 79m _1/2+ _{320.6(29)[142] 0.639(8)[75]} 80 0+ 268.4(12)[161] 0.465(4)[84]

Fig. 1. (a)ChangesinmeansquarechargeradiifortheZnisotopescomparedwith neighbouring CuandGaisotopicchains,whichareverticallyoffsetby±0.6fm2_for

clarity.TheblackdotspresenttheZnradiiextractedbyusingtheKMSfromMCDHF

calculations.(b)Experimentalr2_{forgroundstatesoftheCu,ZnandGaisotopes}

withthesphericalvolumecontributionr2_

0 from thedropletmodelsubtracted

[21].

4. Discussion

The(sub-) shell effect hasbeen muchinvestigated in this re-gion, as discussed for the Cu and Ga isotopes [3,29]. For this purpose, we plot the ‘residual’



r2



of Cu, Zn, Ga isotopes after subtractingthesphericalvolumecontribution



r2



0 ofthedroplet

model[21],asshowninFig.1b.Thegeneralparabolicshapeofthe

‘residual’chargeradii



r2

_

_{− }

_r2

_

0 demonstratestheshelleffect

ex-pectednear N

=

28 andN

=

50,whilethe localminimumofthe



r2



− 

r2



0 around N

=

40,whichhas beenattributedtoaweak

subshell effectforCu [3],ismuchweaker for70_Znthanfor69_Cu.

The apparent ‘dip’ in theGaisotopic chain at N

=

40 isnot due tothe subshelleffect,butarisesfroman inversionofthe OES[3,

29,33] and onsetof deformationappearing above N

=

40, as ob-servedinthenuclearmoments[34].ThustheZnradiiconfirmthe consistentpictureofthe

N

=

40 subshelleffectwhichquickly

dis-appears when going away from Z

=

28, asdescribed by various

experimentalobservables:magneticandquadrupolemoments[16,

35–37],charge radii [3,29], nuclearmasses[38,39], E

(

2+

)

excita-tionenergies,and

B

(

E2

)

transitionrates[40–43].

In addition to the observed disappearing shell effect,nucleon correlations or deformation should contribute to the ‘residual’ charge radii. As an example, a different behaviour of OES below andabove

N

=

40 isobservedforthethreeisotopicchains(shaded regioninFig.1b).AninversionofthenormalOESaround N

=

40 isclearlyobservedforGaisotopesandhintedforZnisotopes,but notapparent intheCuisotopes.Theslightincreaseincollectivity above N

=

40,observedintheexperimentalquadrupolemoments of the odd Zn isotopes, and the B

(

E2

;

↑)

of even ones, is con-sidered asone possible explanation [16,44,45,43]. An increase in deformation was also observed inthe Gaisotopic chain [37] but notintheCuisotopicchain[46].

To assessthe contribution ofcorrelations tothe experimental chargeradii,onecanattempttodescribe

δ



r2

_

_{intermsofchanges}

inproton orbitoccupationprobabilities resultingfromcross-shell excitations. This approach has been adopted recently to explain the pronounced OES in the charge radii of the Hg isotopes [14]. Anaiveshellmodelpicturewillpredictaconstantprotonnumber of 2above the Z

=

28 closed shellfor Zn.However, it is known thattheprotonsingle particlelevelsaremodified withincreasing neutronnumbers[47]. Thisgivesrise toprotonexcitationsacross the Z

=

28 shellgap,asdiscussedrecentlyfortheCuisotopes[35,

48].Suchexcitationscanbequantified fromtheshellmodelwith alarge modelspace.MCSMusingtheA3DA-minteraction[15] in a f pg9/2d5/2 modelspacehasbeenwidely usedinthe Niregion

[16,44,35] to describe nuclear moments.In orderto examine the sensitivityofchargeradiito protonexcitationsacross Z

=

28,the calculatedprotonoccupationsforthe1/2−andhigh-spinstatesof

69−79_{ZnarepresentedinFig.2b.Thetrendintheseproton}

occupa-tionsiscomparedtothetrendintheexperimental

δ

r2

_

_inFig.2a.

Forthe I

=

1

/

2+ isomericstate of79Zn,sincea largepartof the contributiontoitsconfigurationcomesfromtheneutronintruder

s1/2 orbitwhich is out of the model space (proton and neutron

in p f d5/2g9/2 shells) of the A3DA-m interaction [5,16], we have

usedanewlydeveloped

p f sdg-full

interaction[49] tocalculatethe protonoccupationnumber(seethebluediamondinFig.2b).This new interaction, with an extended model space in the full pro-tonandneutron

p f sdg shell,

predictsthenuclearmomentofthis 1/2+ state in 79_{Zn as}

_μ

pfsdg-full

= −

1

.

05

μ

N, in good agreement withtheexperimentalvalue

μ

exp

= −

1

.

018

(

1

)

μ

N [5].

Fig.2clearlyshowsaqualitativerelationshipbetweenthe

pro-ton occupation above Z

=

28 and the relative nuclear size of

groundandisomericstatesin69−77_{Zn.Thestatewithalarger}

pro-tonoccupationcoincideswiththestateoflargersize.Inparticular, itsolvesapuzzlevisibleinFig.2a:thechargeradiiofthe

I

=

1

/

2− and

I

=

9

/

2+statesareintheoppositeorderfor69_Znand71_Zn

al-thoughtheysharesamespinsandsimilarmagneticmoments[16]. Furthermore, the sensitivity of local changes of charge radii to the protonoccupation can be explored qualitatively along the whole Zn isotopic chain.For thispurpose, theproton excitations across the Z

=

28 major shell closure for all 62−80Zn isotopes are converted into changes in the charge radii,

δ

r2

_

Fig. 2. (a)Experimentalδr2_{comparedwith(b)protonoccupationnumbersabove}

Z=28 calculatedfromA3DA-minteractionforbothpositiveparitystatesand1/2− statesin69−79_{Zn.Notethattheprotonoccupationnumberforthe1/2}+ _isomerin

79_{Zniscalculatedwithanewinteractionp f sdg-full(seethebluediamondinb),}

duetothemodelspacelimitofA3DA-minteraction.

Fig. 3. (a)Theδr2_of62−80_{Zn(bluesquare)scaledfromtheexcitedprotonacross}

Z=28 (seetextfordetails)comparedwiththe‘residual’chargeradiir2_{− r}2_ 0

(redcircle)takenfromFig.1b.Theerrorbarsaresmallerthanthesymbols.(b)The odd-evenstaggering(OES)ofexperimentalchargeradii(redcircle)andthecharge radii(bluecircle)scaledfromtheprotonoccupations,asshownin(a),seetextfor details.

multiplying the proton excitations with a constant scaling fac-tor, f

=

0

.

172

(

7

)

, estimated from the ratio of the isomer shift (

δ

r2

_

g,m_{) andthe occupationdifferencesof groundandisomeric}

states(

δ

pg,m_)of69−77_{ZnfromFig.2.Notethat thevaluefor}73_Zn

is not taken into account for the determination of f , due to its largedeformation[44].Theresultsofthisprocedureareshownby the blue squares in Fig. 3a, compared with the ‘residual’ charge radii



r2

_

_{− }

_r2

_

0 of62−80Zn(redcircle).Thisscalingismadeunder

theassumptionthatthedifferencesinradiibetweentheproton or-bits p f5/2g9/2d5/2 are negligiblecompared tothe difference with

the f7/2 orbitbelowthe Z

=

28 shellgap.

Althoughafullyquantitativeanalysisisimpossiblewithout de-tailedcalculationsoftheradiiofthespecificsingleparticleorbits, themagnitudeoftheodd-eveneffectinexperimentalchargeradii agreeswiththatfromprotonorbitoccupationprobabilities,ascan be seen in Fig. 3a. Subtle changes in proton occupations above

Z

=

28 havenoticeableeffectson meansquare chargeradii along the entire Zn isotopic chain. For instance, in the mid-shell be-tween

N

=

40 and

N

=

50,thereisareductionintheexperimental chargeradiusat

N

=

45 (blackarrowinFig.3a)comparedto adja-centisotopes,whichcanbeunderstoodfromthesuddendecrease inprotonexcitations.Approachingthe

N

=

50 neutronclosedshell, thecross-shellexcitationsaresuppressedasexpected(andas ob-servedalsofortheCuisotopes[35]),resultinginareductionofthe OES,asreflectedintheexperimentalchargeradii.AroundN

=

40, theaforementionedinversionoftheOESofradiiinFig.1b)isalso nicelydescribedbythechangesofprotonoccupation.Thereisonly one exception observed around N

=

33, where radii scaled from the protonoccupationexhibitsausual odd-eveneffectwhilethis is nearly invisible in the experimental charge radii. This is pos-sibly due to the fact that the 3/2− ground state in 63Zn has a rather mixed configuration from neutron f5/2 and p3/2, as

con-cluded fromits magneticmoment andlargequadrupole moment

[16].However,theA3DA-mcalculationfailedtoreproducethe ex-perimentalmagneticmoment of63Zn[16],

μ

exp

= −

0

.

282

(

1

)

μ

N and

μ

A3DA-m

= +

0

.

110

μ

N,which maybe the origin ofthe dis-crepancy.

Tobetter visualise theodd-eveneffectinthe charge radii,the experimental OESispresentedinFig.3bwithsolid circles,asthe difference



3

₍

_

_r2

_,

_N

₎

_{betweentheradiusoftheisotopewith}

neu-tron numberN and themeanvalue oftheradii ofits neighbours withneutronnumbersof

N

+

1,

N

−

1,asquantifiedwith[50,51]:



3

(



r2

,

N

)

= 

r2



N

−

1

2

(



r

2

_

N−1

_{+ }

_r2

_

N+1

_).

₍₂₎

A value



3

₍

_

_r2

_,

_N

₎

_>

_{0 for an odd-N isotope represents an}

inversion of the normal OES behaviour. The hinted inversion in the OES at N

=

41 is clearly visible in this representation. To understand its origin, we present in Fig. 3b also the calculated



3

₍

_

_r2

_,

_N

₎

_{withopensquares,extractedfromthecalculatedradii}

using the proton occupations above Z

=

28 (the blue squares in Fig. 3a). The OES from the calculated radii shows also an inver-sionintheOESatN

=

41.Asthesecalculatedradiiwereobtained fromscaling oftheprotonexcitation across Z

=

28 (Fig.2b),this suggeststhatindeedtheinvertedOESeffectisrelatedto changes intheprotonexcitationsacross Z

=

28.Notethatthe lowproton excitationsaround N

=

40 (bluesquare inFig.3a)ledtoawrong signof



3

(



r2

,

N

)

at N

=

40 (bluesquare inFig.3b).Due tothe parity change between two major shells at N

=

40, the neutron excitationsare suppressed,asrecentlydemonstrated theoretically forthe68_Niand69_{Cu[52],whichinitsturnleadtoasuppression}

ofthecorrelatedprotonexcitations. However,such effectis prob-ably overestimatedintheMCSM calculationfortheZnisotopeat

N

=

40.Nevertheless,theOESoftheexperimentalnuclearcharge radiiandscaledchargeradiishareasimilarrelativeamplitudeover thewholeZnisotopicchain,confirming thestrongconnection be-tween proton excitationsacross Z

=

28 and nuclear charge radii. Fig.3b alsoillustratesthat,aroundtheneutronmid-shell,theOES ofcharge radiicalculatedfromprotonoccupationsispronounced, e.g. around N

=

34 and N

=

45,themiddleshellofneutron f5/2

and g9/2 orbits,respectively.Thisphenomenonisalsohighlighted

in theOES ofexperimental charge radii. Incontrast,approaching the closed shell N

=

50, the OES is suppressed for both experi-mentalchargeradiiandscaledradiifromprotonoccupations.

5. Summaryandconclusion

In summary, the changes in mean square charge radii of

62−80_{Zn were extracted by laser spectroscopy. The variations in}

excitations across the Z

=

28 shell gap. The proton excitation probabilitycomprehensivelyexplainsthelocalvariationsofcharge radii, such as the size change between the isomeric and ground statesin69−79_{Zn,theunusualinversionofthenormalOESaround}

N

=

40,andtheOESofthechargeradiiof62−80Zn.This observa-tionprovidesstrongevidencethat thechargeradiusisasensitive reflectionofthecross-shellprotonexcitations(whicharestrongly correlatedto the neutron numbers), offeringa new approach for theinterpretationofnuclearchargeradii.

Acknowledgements

Weacknowledge the supportof the ISOLDEcollaboration and

technical teams. This work was supported by the National Key

R&D Program of China (Contract No. 2018YFA0404403), the Na-tional Natural Science Foundation of China (No.11875073), the UKScience andTechnology FacilitiesCouncil grantsST/L005670/1

and ST/L005794/1, the JSPS and FWO under the Japan-Belgium

Research Cooperative Program, the IAP-project P7/12, the FWO-Vlaanderen,GOAgrant15/010fromKULeuven,theBMBFContract No. 05P15RDCIA, theMax-Planck Society, the Helmholtz Interna-tionalCenter forFAIR (HIC for FAIR), the EU FP7 via ENSAR No.

262010, the HPCI Strategic Program (The origin of matter and

the universe) and “Priority Issue on post-K computer” (Elucida-tionoftheFundamentalLawsandEvolutionoftheUniverse)from

MEXTand JICFuS, and the FWO-FNRS Excellence of Science

Pro-gramme(Grant No.EOS-O022818F). TheMCSM calculationswere

performedontheKcomputeratRIKENAICS(hp150224,hp160211, hp170230).

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