Tl and Bi nuclei Contrasting properties of particle-particle and hole-hole excitations in Physics Letters B

N. Cieplicka-Ory ´nczak

^a,∗

, C. Michelagnoli

^b

, A. Gargano

^c

, B. Fornal

^a

, S. Leoni

^d,e

,

G. Benzoni

^d

, A. Blanc

^b

, S. Bottoni

^d,e

, F.C.L. Crespi

^d

, Ł.W. Iskra

^d

, M. Jentschel

^b

, U. Köster

^b

, P. Mutti

^b

, N. Pietralla

^f

, E. Ruiz-Martinez

^b

, V. Werner

^f

aInstituteofNuclearPhysics,PolishAcademyofSciences,Radzikowskiego152,PL-31342Kraków,Poland bInstitutLaue-Langevin,71avenuedesMartyrs,38042GrenobleCedex9,France

cINFNSezionediNapoli,ViaCintia,80126Napoli,Italy dINFNSezionediMilano,ViaCeloria16,20133Milano,Italy eUniversitàdegliStudidiMilano,ViaCeloria16,20133Milano,Italy

fTechnischeUniversitätDarmstadt,Karolinenplatz5,64289Darmstadt,Germany

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received25October2019

Receivedinrevisedform5December2019 Accepted13January2020

Availableonline15January2020 Editor:D.F.Geesaman

Keywords:

Nuclearstructure²⁰⁶Tl,²¹⁰Bi γ γ-coin.²⁰⁶Tl

Branchingratios²⁰⁶Tl Deducedlevelsand J^π206Tl

Comparisonwithshell-modelcalculations

A complete-spectroscopy investigation oflow-lying, low-spin states inthe one-proton-hole and one- neutron-hole nucleus ²⁰⁶Tl hasbeen performedby usingthermal neutroncapture and γ-coincidence technique withthe FIPPSGearrayatILL Grenoble.The newexperimental results,togetherwithdata for theone-proton-particleand one-neutron-particle nucleus²¹⁰Bi(takenfromapreviousstudydone at ILL in the EXILL campaign), allowed for an extensive comparison with predictions ofshell-model calculationsperformedwithrealisticinteractions.Nophenomenologicaladjustmentswereintroducedin thecalculations.In²¹⁰Bi,stateenergies,transitionmultipolaritiesanddecaybranchingsagreewellwith theoryforthethreewellseparatedmultipletsofstateswhichdominatethelow-lyingexcitations.Onthe contrary,in²⁰⁶Tlsignificantdiscrepanciesareobserved:inthesameenergyregion,sixmultipletswere identified,withasignificantmixingamongthembeingpredicted,asaconsequenceofthesmallerenergy separationbetweentheactiveorbitals.Thediscrepanciesin²⁰⁶Tlareattributedtothelargeruncertainties inthe determination oftheoff-diagonal matrix elementsof therealistic shell-modelinteraction with respectto thecalculated diagonalmatrix elements,theonlyones playingamajorrole inthecase of 210Bi. The work pointsto the need ofmoreadvanced approaches inthe construction ofthe realistic interactions.

©^{2020TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

Odd-oddtwo-valence-particles/holes systemsaround themost magic of all nuclei, ¹³²Sn and ²⁰⁸Pb, are ideal to test advanced shell-model approaches. Unfortunately, the one-proton-hole and one-neutron-hole nucleus ¹³⁰In and the one-proton-particle and one-neutron-particlenucleus¹³⁴Sb aredifficultto reachforspec- troscopic studies. On the contrary, the accessibility of low-lying excitationsinthe corresponding (with respect tothe ²⁰⁸Pbcore) 206Tl and²¹⁰Bi nuclei, in neutron capture and transfer reactions with stable beams, make them unique systems to benchmark theproton-neutronshell-modelinteractionsderivedfromthebare nucleon-nucleonpotential.

*

Correspondingauthor.

E-mailaddress:natalia.cieplicka@ifj.edu.pl(N. Cieplicka-Ory ´nczak).

In this work, we aim at obtaining experimental results on the low-energy structuresin ²⁰⁶Tl populated in thermal neutron capture reaction and, together with existing similar data on the 210Binucleus,comparethemtotheoreticalpredictionsusingshell- modelcalculationsbasedoneffectiveinteractionsderivedfromthe realisticnucleon-nucleonCD-Bonnpotential.Forthefirsttime,not only energy spectra, butalso decay branchings were considered.

A detailedcomparisonof the experimental excitation energies of 210Bi withshell-model resultsis reported in Ref. [1], where cal- culations were performed by employing the pioneering realistic interactiondevelopedbyKuo-Herling [2] withtheempiricalmod- ifications introduced inRef. [3] and later works.Here, we intend toascertainthereliabilityofmodernrealisticeffectiveinteractions in the description of the low-lying excitations of nuclei around 208Pb,withoutintroducing anyphenomenologicaladjustments,so to better evaluate their predictive power. The results we obtain https://doi.org/10.1016/j.physletb.2020.135222

0370-2693/©^{2020TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. Partiallevelscheme(upto1.5 MeV)of²⁰⁶Tlpopulatedinthethermalneutroncapturereactionon²⁰⁵Tl(left),comparedtoshell-modelrealisticcalculations(right).

The4⁻level,notobservedinthepresentdata,ismarkedbyanasterisk.

Fig. 2. Thepartiallevelscheme(upto1.5 MeV)of²¹⁰Bipopulatedinthethermalneutroncapturereactionon²⁰⁹Bi(left) [1] comparedtotheshell-modelrealisticcalculations discussedinthiswork(right).The(10⁻),(1⁻),(8⁻),(7⁻),(6⁻),(7⁻),(9⁻)levels,notobservedintheworkofRef. [1],aremarkedbytheasterisks.

for²¹⁰Bi,withtwo-valenceparticles outside²⁰⁸Pb, havebeen, in part,presentedinRef. [4].There, itwas shownthat oureffective interaction isable toreproduce remarkablywell the lowest-lying multipletandinparticulartopredictthecorrectground-statespin, J π=^{1−,asarising from}core-polarization effectsinduced bythe nucleon-nucleonpotential–theyareresponsiblefortheinversion ofthe1⁻and0⁻states.Inthepresentpaper,weextendthecom- parison betweentheory and experimentfor ²¹⁰Bi by considering higher-lying states anddecay branchings, andwe also report re- sultsfor²⁰⁶Tl, withtwo-valenceholeswithrespect to ²⁰⁸Pb. We shallseethatwhile in²¹⁰Bi,state energies,transitionmultipolar- ities anddecaybranchingsagreewell withtheory,inthe caseof 206Tlsignificantdiscrepanciesareobserved.Theyareattributedto larger uncertainties in the determinationof the off-diagonalma- trixelements oftherealistic shell-modelinteractionwithrespect tothecalculateddiagonal matrixelements,whichplay themajor roleinthecaseof²¹⁰Bi.

In²⁰⁶Tl,almost allstates(12 outof13reportedinthispaper) up to 1.5 MeV excitation energy were observed in transfer reac- tions, beta-decay and previous thermal neutron capture studies, andwere interpreted asmembers ofsix multiplets involvingthe protons_1/2,d_3/2andneutron p_1/2, p_3/2 and f_5/2 orbitals [5] (see

Fig.1).However, informationon

γ

decaysandspin-parityassign- mentswaslargelymissing.Onthecontrary,completespectroscopy of ²¹⁰Bi was recently achieved in a cold neutron capture study carried out atILL, during the EXILL campaign [1,6]. Here, in the excitation energy region below 1.5 MeV,21 stateshave been lo- cated (15 with firm spin-parity assignments) and their

γ

-decay patternhas beenestablished, asshowninFig. 2.In thiscase, all negativeparitystates(20intotal)belongtothelowestthreemul- tiplets

π

h9/2

ν

g9/2,

π

h9/2

ν

i11/2and

π

f7/2

ν

g9/2.

The ²⁰⁶Tl and²¹⁰Biisotopeswereinvestigatedintwoseparate neutron-capture experiments,performedatInstitutLaue-Langevin (ILL)inGrenoble,France.

The coincidence measurements of

γ

rays from the thermal- neutron capture on ²⁰⁵Tl were performed with the newly con- structeddetectionsystem–FIPPS(FIssionProductPromptgamma- ray Spectrometer) [7]. FIPPS is an array consisting of 8 HPGe clovers (fora total of32 HPGe crystals), arranged inannular ge- ometry atevery 45^◦ aroundthe target, whichwas inthis casea sampleof99.9%enriched ²⁰⁵Tlisotope,withtotalweightof∼^{2 g.}

Digital electronics was used to collect and process the signals fromthedetectors.Eacheventcontainedinformationon

γ

-rayen- ergy, time and identification number of the specific crystal that

modelcalculations,discussedinthiswork.

fired. The data were stored triggerless and sorted offline into a

γ γ

-coincidencematrixandacube [8].

Atotalnumber of22primary

γ

rays(10 new) fromthecap- turestatewasobservedin²⁰⁶Tl.Theypopulate21excitedstates,8 ofwhichare reportedforthefirst time.Thefull

γ

-decayscheme fromthe capturestate andtheanalysisofthe

γ

-ray angularcor- relations will be discussed in Ref. [9], while preliminary results, including the coincidence spectra, have been already presented in [10]. In this paper, we would like to discuss only the states up to 1.6 MeV in the ²⁰⁶Tl isotope, as presented in Fig. 1. They arise from the couplings between one-valence-proton-hole and one-valence-neutron-hole excitations. As the

γ

decay originates from the capture state, which in this case may have 0⁺ or 1⁺ spin-parityvalues,onlyverylow-spin excitations,withspinsfrom 0to3,were populated.The

γ

-angularcorrelation analysisofthe present data allowed to firmly establish the spins of the 801-, 998-,and1360-keV statesas3⁻, 2⁻,and0⁻,respectively.More- over,this analysishelpedto assignthe spin-parity valuesforthe 1117-, 1332-, and 1648-keV excitations as (1⁻), (1⁻), and (2⁻), whichwere previouslyreportedas(1⁻,2⁻).Furthermore,thespin value (2⁻) was hereproposed to the excitationat 1400 keV,the

γ

decayofwhichwaspreviouslynotreported.Amongtheconsid- eredstates,theexcitationat1487 keVwith J π= (¹⁻)wasnewly established.We note thatthis maybethe samestate asthe one whichwasreportedinNNDCat1490 keV.Further,thepresenceof thelevelsplacedat939,1080,1206,1453,and1631intheprevi- ousneutroncaptureexperiment [11,12] wasnotconfirmed.

In ²¹⁰Bi, states with spins from 0 to 9 were studied in the cold-neutron-capture reaction with the EXILL setup described in Ref. [13]. Inthatwork, 64primary

γ

rays fromthecapturestate wereobserved:theypopulate70discretestates,33ofwhichwere newly identified. Details of the experiment and of the analysis aredescribedinRefs. [1,6],whereacomparisonwithshell-model calculationsbased on phenomenological interactions is also pre- sented. In this work, we focus on the lower lying levels (up to 1.5 MeV) in ²¹⁰Bi, asshown in Fig. 2, originatingonly from the couplings between one-valence-proton and one-valence-neutron excitations.

Shell-model calculations have been performed for ²¹⁰Bi and 206Tl using a realistic two-body effective interaction. As model space, we have considered one proton major shell andone neu- tron major shell above and below ²⁰⁸Pb, respectively, for ²¹⁰Bi and²⁰⁶Tl.Theadoptedspacesare showninFig.3,wherewealso reportthesingle-particleandsingle-holeneutronandprotonener- gies,that aretakenfromtheexperimentalspectra ofone-valence particle/hole nuclei, namely from ²⁰⁹Pb and ²⁰⁹Bi for ²¹⁰Bi and 207Pband²⁰⁷Tlfor²⁰⁶Tl [5].

The neutron-protonmatrix elements of the Hamiltonianhave been derived by using the perturbative many body theory [14]

withintheparticle-particleformalismfor²¹⁰Bi,andthehole-hole

Fig. 4. (a)Thethreelowestlyingmultipletsof²¹⁰Bibelow1.5 MeVexcitationen- ergy,calculatedandmeasured inthethermalneutroncapturereactionon ²⁰⁹Bi (fullcircles)orotherreactions(opencircles).The7⁻state,locatedinourprevious workat1527 keV [1],belongstothesecondmultiplet(πh9/2νi11/2),assuggested bythebranchingratios(seetext).(b)Thesixlowestlyingmultipletsof²⁰⁶Tlbelow 1.6 MeVexcitationenergy,calculatedandmeasuredinthethermalneutroncapture reactionon²⁰⁵Tl(fullcircles)orotherreactions(opencircle).

one for ²⁰⁶Tl. We start from the realistic CD-Bonn free nucleon- nucleon potential [15] and use the V_low−k approach [16], witha cutoffmomentum = 2.2 fm⁻¹,tointegrateoutitshigh-momentum components. Then, the smooth V_low−k potential is used within the Q -boxˆ foldeddiagramexpansion,includingalldiagramsupto secondorderinV_low−k,toderivetheeffectiveshell-modelinterac- tion.Inthisway,thebarematrixelementsofthenucleon-nucleon potential are renormalizedto take intoaccount thecontributions arisingfromtheneutronandprotonexcitationsacrossthe126and 82shells.Moredetailsonthederivationoftheeffectiveinteraction usedfor²¹⁰Bicanbefoundin [4].

Experimental and calculated levels of ²¹⁰Bi are compared in Fig. 2 (the 10⁻ state, not observed in the (n,

γ

) experiment of Ref. [1],istakenfromRef. [5]).Weseethatexperimentalenergies are satisfactorily reproducedby theory – state energydifferences betweentheoryandexperimentrangefromafewkeVtoamaxi- mum of∼^{200 keVforthe10−state at669 keV,withastandard} deviation of80 keV only. In particular, the calculations correctly reproduce the 1⁻ experimental ground state, which was a long- standingproblem,asdiscussedin [4].

Up to about 1.5 MeV excitation energy, three long multiplets can be identified in ²¹⁰Bi, as shown in Fig. 4(a). These multi- plets, that exhibit the typical downwardparabolicbehavior, arise fromthe

π

0h9/2

ν

0g9/2,

π

0h9/2

ν

0i11/2,and

π

1 f7/2

ν

0g9/2configu- rations.Themembersofthelowest-lyingmultipletarealmostpure –the

π

0h_9/2

ν

0g_9/2 configurationcontributionis>91%.Members oftheother twomultipletsareinsteadcharacterizedbysomead- mixtures,whichareparticularlyrelevantforthe1⁻_2,3,2⁻_2,3,and6⁻_2,3 states, where dominant components range from 52 to 61%. The percentagesofthevariousconfigurationsforthestatesof²¹⁰Biare showninpanels(g)-(i)ofFig.5.Nostatesarisingfromhigheren- ergymultiplets appearbelow1.5 MeV,exceptforthelowest-spin member,3⁺,ofthe

π

0h_9/2

ν

0 j_15/2 configuration,thathavingpos- itiveparitycannotadmixwiththestatesofthethreelowest-lying multiplets. Itisworth mentioning,that a goodoverallagreement betweenthecalculatedandexperimentalspectraof²¹⁰Bi–witha standarddeviationofabout150 keV–wasalsoobtainedinRef. [3]

Fig. 5. Percentageofthemainconfigurations(>10%)inthesixlowestmultiplets calculatedfor²⁰⁶Tl(a)-(f)andthethreelowestmultipletscalculatedfor²¹⁰Bi(g)-(i).

byusingtheKuo-Herlinginteractionwithonlythebareandcore- polarization contributions, the latter being scaled by a factor of 0.92.However,toreproducetheinversionofthe1⁻and0⁻ states andtoimprove,ingeneral,theagreementwithexperiment,other modifications of the Kuo-Herling interaction were proposed by varying selected two-body matrix elements, as done in [3] and laterworks.Thespectrumresultingfromthisphenomenologically- adjustedinteraction,showninRef. [1],hasaverygoodagreement withtheexperimentforthestateswhichwereusedinthefitting procedurewhile forother excitationsthe agreementis similarto theoneobtainedinthepresentcalculations.

Experimental and calculated excitation energies for ²⁰⁶Tl are compared in Fig. 1.In this case, agreement between experiment and theory is not as good as for ²¹⁰Bi. Discrepancies between experimental energies and calculated levels range from ∼^{40 to} 300 keV, andthe standard deviation increases to 180 keV, with discrepancies larger than 200 keV for the four lowest-lying 1⁻ states.As in previous shell-model calculations [17,18], we finda J=^{1 state almost} degenerated withthe 0⁻ groundstate, while experimentallythe0⁻groundstate iswellseparatedfromthe1⁻ yraststate.

Bylookingatthecompositionsofthewavefunctionsfor²⁰⁶Tl, wecan identifyfourdoubletsandtwo multipletsbelow1.5 MeV, which are reported in Fig. 4(b). As shown in panels (a)-(f) of Fig. 5, their members are characterized by a significant configu- rationmixing,namelytheyreceivesizablecontributionsfromcon- figurationsotherthanthedominantone.

Fig. 6. Comparisonbetweenexperimentalandcalculatedbranchingratiosin²¹⁰Bi and²⁰⁶Tl.

The morecomplexstructure observedin²⁰⁶Tl withrespectto that of²¹⁰Bi,arisesfromthedifferentfeaturesoftheshell-model orbitalswhichareactiveinthetwocases.

Considering the single-particle energy spectrum of ²¹⁰Bi (see Fig.3left),theunperturbedenergiesofthethreelowest-lyingmul- tiplets, reportedinFig.4(a),are separatedby∼^{700 keVfromthe} higher-lyingnegative-parity

π

0h_9/2

ν

2d_5/2multiplet,andasignifi- cantgapof∼^{700 keVexistsbetweenthe}lowest-lyingandthenext two multiplets. Such multiplets are, therefore, scarcely affected by the off-diagonal matrixelements of the two-bodyinteraction, whosevaluesarenot largerthan300 keV,mostofthem beingof theorderofafewtensofkeV.Anon-negligibleadmixtureisfound forthe

π

0h9/2

ν

0i11/2,and

π

1 f7/2

ν

0g9/2configurationsonly.

Inthecaseof²⁰⁶Tl,theenergygapsbetweentheunperturbed first 6 low-lying multiplets shown in Fig. 4(b) (see Fig. 3 right) rangefrom200to300 keV, andthenext negative-parityconfigu- ration,

π

2d5/2

ν

2p1/2,liesonly400 keVabove.As aconsequence, theeigenvaluesandthecompositionofthestatesin²⁰⁶Tlarevery sensitive totheoff-diagonalmatrixelements ofthetwo-bodyin- teraction.Therefore,afinetuningofthelatterwouldbeneededto improvetheagreementwithexperiment.

Togain furtherinsight intothestructure ofthestates ofboth nuclei, wehaveconsideredthedecaybranchings,whichmaypro- vide information on the wave function fragmentation. In Fig. 6, experimental and calculated branching ratios for ²¹⁰Bi and ²⁰⁶Tl are comparedinafew selectedcaseswhichare representativeof themultiplets discussedabove.Amoreextendedcomparisonwill begiveninRef. [9].

Panels on the left show the decay branchingsfor the 4⁻₁, 2⁻₂ and2⁻₃ statesof²¹⁰Bi,whilepanelsontherightrefer tothe2⁻₂, 2⁻₃ and 2⁻₄ states of ²⁰⁶Tl. As observed for the excitation ener- gies,thequalityoftheagreementbetweentheoryandexperiment is very good in ²¹⁰Bi.This resultmakes usconfident that calcu- latedbranching ratios canhelp assessing spin-parityassignments ofthelowestlyingstatesin²¹⁰Bi.Inthisway,firmspin-parityas- signment of3⁻, 2⁻ and3⁻ could be madeto the levels located experimentallyat1175,1197,and1374 keV,respectively(previous assignments were:(2⁻), (1,2), and(3⁻)), havingtheir theoretical counterparts at1147 keV,1162 keV (cf.Fig.6(c)),and1416 keV.

The 1165-keV state, observed in the past in a neutron-capture measurement [19] and assignedas 1⁻,was not observed in our databutitwasaddedforcompleteness.

above,arefoundtobehighlyfragmented,withadmixtureofvari- ousconfigurations.Thismakesthe²⁰⁶Tlnucleusanidealcasefor an extended test of the quality of the two-body effective inter- action, with emphasis on the non-diagonal matrix elements. As seen in Fig. 6(d)-(f), pronounced differences are found between experimental andtheoretical branching ratios, qualitatively much largerthan the deviationsobserved forstate energies. Forexam- ple,inthecaseofthe2⁻₃ locatedat998 keV(predictedbytheory 158 keVbelow),thestrongestexperimental branchistheM1de- cayto the1⁻₂ state at649 keV,whilea strongM1branch tothe 2⁻₁ state is expected. The comparison between experiment and shell-modelcalculationswithstate-of-the-artrealistic interactions forthetwoverysimplesystems²⁰⁶Tand²¹⁰Birevealslimitations inthe procedure of the off-diagonalmatrix elements determina- tion,thelatterbeingresponsible fortheconfigurationmixing. An improvementinthedeterminationofthenon-diagonalmatrixel- ementsoftheshell-modelinteractionisthereforeneededinorder toincreasethereliabilityofourcalculations.

Toconclude,predictionsofshell-modelcalculations,performed withrealisticinteractions,withoutintroducinganyphenomenolog- icaladjustments,were testedon²¹⁰Biand²⁰⁶Tlnuclei,whichare unique systems to benchmarkproton-neutron interactions in the particle-particleandhole-holespaces,withrespectto thedoubly magic ²⁰⁸Pb core. Experimental low-lying, low-spin states,popu- latedin neutron capture reactions at ILL (Grenoble), allowed for anextensive comparisonwiththeory.Forthefirst time,not only statesenergies, butalso

γ

branching ratios were considered, re- sultinginaratherstringenttestoftheshell-modelwavefunctions calculatedwithrealisticinteractions.

Strikingdifferencesare found between ²¹⁰Bi and²⁰⁶Tl. Inthe caseof ²¹⁰Bi, state energies, transition multipolarities anddecay branchingsforallstatesbelow1.5 MeV(belongingtothreerather puremultiplets)areverywellreproducedbytheory.Incontrast,in the ²⁰⁶Tl nucleus much larger discrepancies betweentheory and

amajorstepforwardinourbasicunderstandingofnuclearforces inthenuclearmedium.

This work was supported by the Italian Istituto Nazionale di Fisica Nucleare,by thePolish NationalScienceCentreunderCon- tractNo.2014/14/M/ST2/00738,2013/08/M/ST2/00257,andbyGer- manBMBFundergrantNo.05P19RDFN1andDFGgrantSFB1245.

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