Nuclear charge radii of ^{62-80}Zn 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

aSchoolofPhysicsandAstronomy,TheUniversityofManchester,ManchesterM139PL,UnitedKingdom

bSchoolofPhysicsandStateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,China cKULeuven,InstituutvoorKern- enStralingsfysica,B-3001Leuven,Belgium

dOliverLodgeLaboratory,OxfordStreet,UniversityofLiverpool,Liverpool,L697ZE,UnitedKingdom

eInstytutFizykiimieniaMarianaSmoluchowskiego,UniwersytetJagiello´nski,ul.prof.StanisławaŁojasiewicza11,Kraków,Poland fMax-Planck-InstitutfürKernphysik,D-69117Heidelberg,Germany

gInstituteofTheoreticalPhysicsandAstronomy,VilniusUniversity,Sauletekioav.3,LT-10222Vilnius,Lithuania hChimiequantiqueetphotophysique,UniversitélibredeBruxelles,B1050Brussels,Belgium

iPhotonScienceInstituteAlanTuringBuilding,UniversityofManchester,ManchesterM139PY,UnitedKingdom jExperimentalPhysicsDepartment,CERN,CH-1211Geneva23,Switzerland

kInstitutfürKernphysik,TUDarmstadt,D-64289Darmstadt,Germany lInstitutfürKernchemie,UniversitätMainz,D-55128Mainz,Germany mSchoolofTechnology,MalmöUniversity,Sweden

nCenterforNuclearStudy,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan oDepartmentofPhysics,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan

pNationalSuperconductingCyclotronLaboratory,MichiganStateUniversity,EastLansing,MI 48824,USA qGSIHelmholtzzentrumfürSchwerionenforschung,D-64291Darmstadt,Germany

rInstitutedePhysiqueNucléaire,CNRS-IN2P3,UniversitéParis-Sud,UniversitéParis-Saclay,91406Orsay,France

a r t i c l e i n f o a b s t ra 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 shell}^gap, âs ^predicted ^bylarge-scale shell model calculations.It comprehensively explainsthechangesinisomer-to-groundstatemeansquarechargeradiiof⁶⁹⁻⁷⁹Zn,theinversionofthe odd-evenstaggeringaroundN=^{40 and}^theôdd-even^staggeringsystematicsoftheZnchargeradii.With twoprotonsabove Z=^28,^theôbserved^charge^radiiôf^the^Znîsotopic^chain^showâ^cumulativeêffect ofdifferentaspectsofnuclearstructureincludingsingleparticlestructure,shellclosure,correlationsand deformationsneartheproposeddoublymagicnuclei,⁶⁸Niand⁷⁸Ni.

©²⁰¹⁹^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (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-evenstaggering (OES),alonga givenisotopicchainremains amajorchallenge https://doi.org/10.1016/j.physletb.2019.134805

0370-2693/©²⁰¹⁹^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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[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 sensitivetothesubtlevariationofprotonexcitationsduetovary- 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 ¹⁷⁷⁻¹⁸⁵Hg 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-shellex- citations. With two protons outside of the Z =^{28 closed} ^shell andneutronsbetweenclosedshellsofN=^{28 and}^50,^the^Znîso- 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 ⁶²⁻⁸⁰Zn isotopes, and a successful interpretation oftheirtrendandtheir OESintermsofprotonexcitationsacross the Z=^{28 shell}^gap.^These^have^been^calculated^using^the^Monte 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 UC_x targetbombarded bya 1.4 GeV protonbeam.The Znisotopesre- 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 ³P₂^o metastable state ofZn I waspopulated intheneutrali- sationprocess, fromwheretheatoms wereresonantly excited to the4s5s ³S1 state by alaserbeamfromafrequency-doubledcw Ti:sapphirelaser.Thelaserwavelengthwaslockedat480.7254 nm tomatchtheDopplershiftedtransition. Fourphotomultipliersin-

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

3. Experimentalresults

The hyperfinespectra of the odd-mass ⁶³⁻⁷⁹Zn isotopes have been reported in [16], while the zero nuclear spin of even Zn isotopes resultsinasingleresonancespectrum.The observedhy- perfine spectra were fitted using a

χ

² minimisation procedure, generatingthehyperﬁne-structureA andB parametersoftheodd- massisotopes andisomers (asreportedin[16]),andthecentroid frequency

ν

ofall⁶²⁻⁸⁰Znisotopesandisomers.Theisotopeshifts (IS:δ

ν

⁶⁸^,^A₌

ν

^A₋

ν

⁶⁸)werecalculatedwithrespecttothecentroid of⁶⁸Zn(

ν

⁶⁸),aspresentedinTable1.Asystematicuncertaintyon thelaserfrequencyobservedbythemovingions,whichoriginates fromthevoltageuncertainty(about0.033%)onthestartingpoten- tial(30kV)atISCOOL,hasbeenintroduced.

The changes in meansquare charge radii δ^r²^were ^obtained fromtheISbasedontheequation[22,23]

δ ν

⁶⁸^,^A

₌

K_MSm_A

−

^m68

m_Am₆₈

+

^F

δ

^r²

⁶⁸^,^A

.

(1) Here KMS and F are the atomic mass-shift and field-shift factors, respectively, of the atomictransition used in this measure- ment. Since the mean square charge radii of five stable Zn iso- topesareknownexperimentallyfromacombinedanalysisofelec- tron scatteringandmuonicx-ray data[24],aKing-plotprocedure using these experimental δ^r²μe can be performed to evaluate the atomic factors [24–26]. As these evaluations of F and K_MS 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-initioap- 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 systematic way, inorder to optimise their computational strategy. They providea final F -factor, F= +³⁴⁶(3) MHz/fm²,inwhichthe uncertainty isestimated based onthe variation of the three different 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] and}^Ga ( Z=³¹⁾^[29],^we^thereforeûse^the^calculated^value^F= +³⁴⁶(35) MHz/fm² witha 10% uncertainty,andwe usethe Kingplotwith non-opticaldataδ^r²μeofstableisotopes[24] toextractthevalue of K_MS= +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 ⁶²⁻⁸⁰^Zn âre êxtracted, âs shown inTable1 andinFig. 1a.The systematicerrorquoted for δ^r²ârises^mainly^from^theuncertaintyintheatomicfactorsafter 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,whileadeviationfromthetrendisobservedifKMSfrom MCDHFisusedtoextracttheradii(blackdots).

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Table 1

Isotopeshiftsandchangesinmeansquarechargeradii of ⁶²⁻⁸⁰Zn δr²⁶⁸^,^A. Statistical errors are shown in curved brackets. Systematic errors in square brackets ariseprimarilyfromthe uncertaintyonthe beamen- ergy(forisotopeshifts)andonatomicfactorsKMSand F (forradii),respectively.

A I^π δν⁶⁸^,^A(MHz) δr²⁶⁸^,^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] 69^m 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] 71^m 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] 73^m 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] 75^m 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] 77^m 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] 79^m 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±^0.6^fm²^for clarity.TheblackdotspresenttheZnradiiextractedbyusingtheKMSfromMCDHF calculations.(b)Experimental^r²^for^ground^statesôf^the^Cu,^Znând^Gaîsotopes withthesphericalvolumecontributionr²0 from thedropletmodelsubtracted [21].

4. Discussion

The(sub-) shell effect hasbeen muchinvestigated in thisre- gion, as discussed for the Cu and Ga isotopes [3,29]. For this purpose, we plot the ‘residual’ ^r² ôf ^Cu, ^Zn, ^Ga îsotopes âfter subtractingthesphericalvolumecontribution^r²0 ofthedroplet model[21],asshowninFig.1b.Thegeneralparabolicshapeofthe

‘residual’chargeradii^r²− ^r²0 demonstratestheshelleffectex- pectednear N=^{28 and}^N=^50,^while^the ^local^minimum^of^the

^r²− ^r²0 around N=^40,^which^has ^been^attributed^to^a^weak subshell effectforCu [3],ismuchweaker for⁷⁰Znthanfor⁶⁹Cu.

The apparent ‘dip’ in theGaisotopic chain at N=^{40 is}^not ^due tothe subshelleffect,butarisesfroman inversionofthe OES[3, 29,33] and onsetof deformationappearing above N=^40, âsôb- servedinthenuclearmoments[34].ThustheZnradiiconfirmthe consistentpictureoftheN=40 subshelleffectwhichquicklydis- appears when going away from Z=^28, âs^described ^by ^various experimentalobservables:magneticandquadrupolemoments[16, 35–37],charge radii [3,29], nuclearmasses[38,39], E(2⁺) excita- tionenergies,andB(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 andaboveN=^{40 is}ôbserved^for^the^threeîsotopic^chains^(shaded regioninFig.1b).AninversionofthenormalOESaround N=⁴⁰ isclearlyobservedforGaisotopesandhintedforZnisotopes,but notapparent intheCuisotopes.Theslightincreaseincollectivity above N=^40,ôbservedⁱⁿ^theexperimentalquadrupolemoments of the odd Zn isotopes, and the B(E2;↑) ôf êven ônes, îs ^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,onecanattempttodescribeδ^r²ⁱⁿ^terms^of^changes 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} ^shell^for ^Zn.^However, ît îs ^known thattheprotonsingle particlelevelsaremodified withincreasing neutronnumbers[47]. Thisgivesrise toprotonexcitationsacross the Z=^{28 shell}^gap,âs^discussed^recently^for^the^Cuîsotopes^[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 69−⁷⁹ZnarepresentedinFig.2b.Thetrendintheseprotonoccupa- tionsiscomparedtothetrendintheexperimentalδ^r²ⁱⁿ^Fig.^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 usedanewlydevelopedp f sdg-fullinteraction[49] tocalculatethe protonoccupationnumber(seethebluediamondinFig.2b).This new interaction, with an extended model space in the full pro- tonandneutronp f sdg shell, predictsthenuclearmomentofthis 1/2⁺ state in ⁷⁹Zn as

μ

pfsdg-full= −¹.05

μ

N, in good agreement withtheexperimentalvalue

μ

exp= −¹.018(1)

μ

N [5].

Fig.2clearlyshowsaqualitativerelationshipbetweenthepro- ton occupation above Z =^{28 and} ^the ^relative ^nuclear ^size ^of groundandisomericstatesin⁶⁹⁻⁷⁷Zn.Thestatewithalargerpro- tonoccupationcoincideswiththestateoflargersize.Inparticular, itsolvesapuzzlevisibleinFig.2a:thechargeradiioftheI=¹/2⁻ andI=⁹/2⁺statesareintheoppositeorderfor⁶⁹Znand⁷¹Znal- 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 ⁶²⁻⁸⁰^Zn ^isotopes are converted into changes in the charge radii, δ^r²(p.occ), by

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Fig. 2. (a)Experimentalδr²comparedwith(b)protonoccupationnumbersabove Z=28 calculatedfromA3DA-minteractionforbothpositiveparitystatesand1/2⁻ statesin⁶⁹⁻⁷⁹Zn.Notethattheprotonoccupationnumberforthe1/2⁺ isomerin 79Zniscalculatedwithanewinteractionp f sdg-full(seethebluediamondinb), duetothemodelspacelimitofA3DA-minteraction.

Fig. 3. (a)Theδ^r²ôf⁶²⁻⁸⁰^Zn^(blue^square)^scaled^from^theêxcited^protonâcross Z=^{28 (see}^text^for^details)^compared^with^the^{‘residual’}^charge^radii^r²− ^r²0 (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 factor, f =⁰.172(7), estimated from the ratio of the isomer shift (δ^r²^g^,^m⁾ ^and^the ^occupationdifferencesof groundandisomeric states(δp^g^,^m)of⁶⁹⁻⁷⁷ZnfromFig.2.Notethat thevaluefor⁷³Zn 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− ^r²0 of⁶²⁻⁸⁰Zn(redcircle).Thisscalingismadeunder theassumptionthatthedifferencesinradiibetweentheprotonor- bits p f5/2g9/2d5/2 are negligiblecompared tothe difference with the f₇_/₂ orbitbelowthe Z=^{28 shell}^gap.

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

Z=^{28 have}^noticeableêffectsôn ^mean^square ^charge^radii âlong the entire Zn isotopic chain. For instance, in the mid-shell be- tweenN=^{40 and}^N=^50,^thereîsâ^reductionⁱⁿ^theexperimental chargeradiusatN=^{45 (black}ârrowⁱⁿ^Fig.^3a)^compared^toâdja- centisotopes,whichcanbeunderstoodfromthesuddendecrease inprotonexcitations.ApproachingtheN=^{50 neutron}^closed^shell, thecross-shellexcitationsaresuppressedasexpected(andasob- 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-mcalculationfailedtoreproducetheex- perimentalmagneticmoment of⁶³Zn[16],

μ

exp= −0.282(1)

μ

N and

μ

A3DA-m= +⁰.110

μ

N,which maybe the origin ofthe discrepancy.

Tobetter visualise theodd-eveneffectinthe charge radii,the experimental OESispresentedinFig.3bwithsolid circles,asthe difference³(^r²,^N)betweentheradiusoftheisotopewithneu- tron numberN andthemeanvalue oftheradii ofits neighbours withneutronnumbersofN+^1,^N−^1,^as^quantiﬁed^with^[50,51]:

³

(

^r²

,

^N

) =

^r²

^N

−

¹

2

(

^r²

^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.Âs^these^calculated^radii^wereôbtained fromscaling oftheprotonexcitation across Z=^{28 (Fig.}^2b),^this suggeststhatindeedtheinvertedOESeffectisrelatedto changes intheprotonexcitationsacross Z=^28.^Note^that^the ^low^proton excitationsaround N=^{40 (blue}^square ⁱⁿ^Fig.^3a)^led^toâ^wrong signof³(^r²,^N)at N=^{40 (blue}^square ⁱⁿ^Fig.^3b).^Due ^to^the parity change between two major shells at N=^40, ^the ^neutron excitationsare suppressed,asrecentlydemonstrated theoretically forthe⁶⁸Niand⁶⁹Cu[52],whichinitsturnleadtoasuppression ofthecorrelatedprotonexcitations. However,such effectisprob- ably overestimatedintheMCSM calculationfortheZnisotopeat N=^40.Nevertheless,theOESoftheexperimentalnuclearcharge radiiandscaledchargeradiishareasimilarrelativeamplitudeover thewholeZnisotopicchain,confirming thestrongconnectionbe- 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,^the^middle^shellôf^neutron ^f5/2 and g9/2 orbits,respectively.Thisphenomenonisalsohighlighted in theOES ofexperimental charge radii. Incontrast,approaching the closed shell N=^50, ^the ÔES îs ^suppressed ^for ^both êxperi- mentalchargeradiiandscaledradiifromprotonoccupations.

5. Summaryandconclusion

In summary, the changes in mean square charge radii of 62−⁸⁰Zn were extracted by laser spectroscopy. The variations in the charge radii of ⁶²⁻⁸⁰Zn were described in terms of proton

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excitations across the Z =^{28 shell} ^gap. ^The ^proton êxcitation probabilitycomprehensivelyexplainsthelocalvariationsofcharge radii, such as the size change between the isomeric and ground statesin⁶⁹⁻⁷⁹Zn,theunusualinversionofthenormalOESaround N=^40,ând^theÔESôf^the^charge^radiiôf⁶²⁻⁸⁰^Zn.^Thisôbserva- 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 HelmholtzInterna- 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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Nuclear charge radii of ^{62-80}Zn and their dependence on cross-shell proton excitations

Physics Letters B