γ Physics Letters B

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Physics Letters B

www.elsevier.com/locate/physletb

Observation of a γ -decaying millisecond isomeric state in 128 Cd 80

A. Jungclaus

^a,∗

, H. Grawe

^b

, S. Nishimura

^c

, P. Doornenbal

^c

, G. Lorusso

^c

, G.S. Simpson

^d

, P.-A. Söderström

^c

, T. Sumikama

^e

, J. Taprogge

^a,f,c

, Z.Y. Xu

^c

, H. Baba

^c

, F. Browne

^h,c

, N. Fukuda

^c

, R. Gernhäuser

ⁱ

, G. Gey

^d,j,c

, N. Inabe

^c

, T. Isobe

^c

, H.S. Jung

^k,1

, D. Kameda

^c

, G.D. Kim

^l

, Y.-K. Kim

^l,m

, I. Kojouharov

^b

, T. Kubo

^c

, N. Kurz

^b

, Y.K. Kwon

^l

, Z. Li

ⁿ

,

H. Sakurai

^c,g

, H. Schaffner

^b

, Y. Shimizu

^c

, K. Steiger

ⁱ

, H. Suzuki

^c

, H. Takeda

^c

, Zs. Vajta

^o,c

, H. Watanabe

^c

, J. Wu

^n,c

, A. Yagi

^p

, K. Yoshinaga

^q

, G. Benzoni

^r

, S. Bönig

^s

, K.Y. Chae

^t

, L. Coraggio

^u

, J.-M. Daugas

^v

, F. Drouet

^d

, A. Gadea

^w

, A. Gargano

^u

, S. Ilieva

^s

, N. Itaco

^u,x

, F.G. Kondev

^y

, T. Kröll

^s

, G.J. Lane

^z

, A. Montaner-Pizá

^w

, K. Moschner

^aa

, D. Mücher

^s

, F. Naqvi

^ab

, M. Niikura

^g

, H. Nishibata

^p

, A. Odahara

^p

, R. Orlandi

^ac,ad

, Z. Patel

^ae

, Zs. Podolyák

^ae

, A. Wendt

^aa

aInstitutodeEstructuradelaMateria,CSIC,E-28006Madrid,Spain

bGSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany cRIKENNishinaCenter,RIKEN,2-1Hirosawa,Wako-shi,Saitama351-0198,Japan

dLPSC,UniversitéJosephFourierGrenoble1,CNRS/IN2P3,InstitutNationalPolytechniquedeGrenoble,F-38026GrenobleCedex,France eDepartmentofPhysics,TohokuUniversity,Aoba,Sendai,Miyagi980-8578,Japan

fDepartamentodeFísicaTeórica,UniversidadAutónomadeMadrid,E-28049Madrid,Spain gDepartmentofPhysics,UniversityofTokyo,Hongo7-3-1,Bunkyo-ku,113-0033Tokyo,Japan

hSchoolofComputing,EngineeringandMathematics,UniversityofBrighton,BrightonBN24GJ,UnitedKingdom iPhysikDepartmentE12,TechnischeUniversitätMünchen,D-85748Garching,Germany

jInstitutLaue-Langevin,B.P.156,F-38042GrenobleCedex9,France

kDepartmentofPhysics,Chung-AngUniversity,Seoul156-756,RepublicofKorea lRareIsotopeScienceProject,InstituteforBasicScience,Daejeon305-811,RepublicofKorea mDepartmentofNuclearEngineering,HanyangUniversity,Seoul133-791,RepublicofKorea

nSchoolofPhysicsandStateKey LaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,China oMTAAtomki,P.O.Box51,DebrecenH-4001,Hungary

pDepartmentofPhysics,OsakaUniversity,Machikaneyama-machi1-1,Osaka560-0043Toyonaka,Japan

qDepartmentofPhysics,FacultyofScienceandTechnology,TokyoUniversityofScience,2641Yamazaki,Noda,Chiba,Japan rINFN,SezionediMilano,viaCeloria16,I-20133Milano,Italy

sInstitutfürKernphysik,TechnischeUniversitätDarmstadt,D-64289Darmstadt,Germany tDepartmentofPhysics,SungkyunkwanUniversity,Suwon440-746,RepublicofKorea

uIstitutoNazionalediFisicaNucleare,ComplessoUniversitariodiMonteS.Angelo,I-80126Napoli,Italy vCEA,DAM,DIF,91297Arpajoncedex,France

wInstitutodeF’sicaCorpuscular,CSIC-Univ.ofValencia,E-46980Paterna,Spain xSecondaUniversitadiNapoli,DipartimentodiMatematicaeFisica,2-81100Caserta,Italy yNuclearEngineeringDivision,ArgonneNationalLaboratory,Argonne,IL 60439,USA

zDepartmentofNuclearPhysics,ResearchSchoolofPhysicalSciencesandEngineering,AustralianNationalUniversity,Canberra,ACT 0200,Australia aaIKP,UniversityofCologne,D-50937Cologne,Germany

abWrightNuclearStructureLaboratory,YaleUniversity,NewHaven,CT 06520-8120,USA acInstituutvoorKern- enStralingsFysica,K.U.Leuven,B-3001Heverlee,Belgium

adAdvancedScienceResearchCenter,JapanAtomicEnergyAgency,Tokai,Ibaraki,319-1195,Japan aeDepartmentofPhysics,UniversityofSurrey,GuildfordGU27XH,UnitedKingdom

*

Correspondingauthor.

E-mailaddress:andrea.jungclaus@csic.es(A. Jungclaus).

1 Presentaddress:DepartmentofPhysics,UniversityofNotreDame,NotreDame,Indiana46556,USA.

http://dx.doi.org/10.1016/j.physletb.2017.07.006

0370-2693/©^{2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Receivedinrevisedform3July2017 Accepted4July2017

Availableonline12July2017 Editor:V.Metag

Keywords:

Isomericdecays Shellmodelcalculations Transitionstrengths

a U beamat the Radioactive Isotope Beam Factory atRIKEN. A half-life of T1/2=⁶.3(8)ms was measured for the newstate whichwas tentatively assignedaspin/parity of (15⁻). The experimental results are compared to shell model calculations performed using state-of-the-art realistic effective interactionsand totheneighbouringnucleus¹²⁹Cd. Inthepresentexperimentnoevidencewasfound forthedecayofa18⁺ E6 spin-trapisomer,basedonthecompletealignmentofthetwo-neutronand two-protonholesinthe0h11/2andthe0g9/2orbit,respectively,whichispredictedtoexistbytheshell model.

©^{2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

The regions in the nuclear chart around doubly-magic nuclei such as¹⁰⁰Snand¹³²Snoffera rich testinggroundforthe study of isomeric states of different types. Seniority isomers are ob- served due to the properties of the isovector pairing interaction which lead to a decreasing energy spacing between the excited states formed by the successive alignment of two identical nu- cleons occupying the same orbital. As a consequence the fully aligned state of such a two-nucleon configuration is often long- lived due to the small transition energy for the electromagnetic decay.Examplesofsuchseniorityisomerswithhalf-livesintheμs rangearethe8⁺statesinthesemi-magictwo-protonholenuclei 98Cd50and¹³⁰Cd82[1,2].Ananalogousisomerbasedonthefully- aligned

ν

(0h⁻₁₁²_/2), 10⁺ neutron configuration is observed in the semi-magic two-neutron hole nucleus¹³⁰Sn[3]. Anothertype of isomerfrequentlyobservedintheregionsaround¹⁰⁰Snand¹³²Sn are spin-gapisomers. Inthese casesthe decaytostates atlower excitationenergyrequiresalargechangeinnuclearspinandthere- fore the emission of

γ

rays with high multipolarity. In cases of largehindrancesadecaymediatedby theweakinteraction,i.e.β decay,isfavoured ascompared tothe electromagneticdecay.Ex- amplesare low-lying β-decaying statesin oddnucleiaround the doubly-magicSncoresduetothecloselylying0g9/2–1p1/2 proton and1d_3/2–0h_11/2 neutronsingle-particleorbitalswhichwouldre- quireelectromagneticdecayswithamultipolarityofM4.Another example ofa spin-gap isomerhas recently been reportedin the two-protonholeandtwo-neutronholenucleus⁹⁶Cd[4,5].Theob- served β-decayingstate withahalf-life ofT_1/2=⁰.45⁺₋⁰₀^._.⁰⁵₀₄ s was interpretedasbeingbasedontheconfigurationinwhichthetwo neutronholes and thetwo proton holes,all occupying the 0g9/2 orbit,coupletothemaximumpossiblespinofI=^16.Shell-model (SM) calculationssuggest that this16⁺ state liesbelow the 12⁺ and14⁺levelssothata

γ

decaywouldhavetoproceedviaan E6 transitiontothe 10⁺ state. Instead,β decayto the15⁺ isomeric state in ⁹⁶Ag as well as β-delayed proton emission populating high-spinstatesin⁹⁵Pdhavebeenobserved[4,5].

In ¹²⁸Cd, containing two neutron holes andtwo proton holes with respect to ¹³²Sn, the observation of a 10⁺ isomer (T_1/2= 3.56(6)μs)atanexcitation energyof2.714 MeVwas reportedin Ref.[6]andassignedtohaveapredominant0h⁻₁₁²_/2neutroncharac- ter.SMcalculationspredictinadditiontheexistenceofaspin-gap isomer based on the fully aligned

π

(0g⁻_9/²₂)

ν

(0h⁻₁₁²_/2) configura- tion with a spin of 18⁺, in analogy to the 16⁺ isomer in ⁹⁶Cd.

Furthermore, the recent identification of a (21/2⁺)

γ

-decaying ms isomer in the neighbouring nucleus ¹²⁹Cd with a dominant

π

(0g₉⁻_/¹₂(1p,0f5/2)⁻¹)

ν

(0h⁻₁₁¹_/2)configuration[7]maysuggestthe existence of an analogous 15⁻ isomer in the even–even ¹²⁸Cd builtonthe

π

(0g⁻_9/¹₂(1p,0f_5/2)⁻¹)

ν

(0h⁻₁₁²_/2)configuration.Itwas thereforetheaimofthepresentworktosearch foradditionalβ- or

γ

-decayingisomersathigherangularmomentumin¹²⁸Cd.

TheexperimentwasperformedattheRadioactiveIsotopeBeam Factory(RIBF)oftheRIKENNishinaCenterwithintheEURICAcam- paign. Theneutron-rich¹²⁸Cdnucleiwereproducedfollowingthe projectile fissionofa 345 MeV/u ²³⁸Ubeamwithan averagein- tensity of about 8 pnA, impinging on a 3 mm thick Be target.

The ions of interest were separated from other reaction prod- uctsandidentified onan ion-by-ionbasisbytheBigRIPS in-flight separator [8].The particleidentificationwas performedusingthe E-TOF-B

ρ

methodinwhichtheenergyloss(E),timeofflight (TOF) and magnetic rigidity (B

ρ

) are measured andused to de- terminetheatomicnumber, Z,andthemass-to-chargeratio,A/q, ofthefragments.Detailsabouttheidentificationprocedurecanbe foundinRef.[9].Intotalabout6×^{105 128Cdionswereidentified,} transportedthroughtheZeroDegreespectrometer(ZDS)andfinally implantedintotheWAS3ABi(Wide-rangeActiveSiliconStripStop- per Arrayforβ andiondetection)Siarraypositionedatthefocal plane ofthe ZDS. TheWAS3ABi detector[10,11] consistsofeight closelypackedDSSSDwithanareaof60×^{40 mm2,athicknessof} 1 mm andasegmentation of40horizontaland60verticalstrips each. All decay events detected in WAS3ABi during the first five secondsfollowingavalidimplantationsignalwerestoredandcor- relatedoffline inspaceandtimewiththeimplantedions.Todetect

γ

radiationemittedinthedecayoftheimplantedradioactivenu- clei 12 large-volume Ge Cluster detectors [12] from the former EUROBALL spectrometer [13] were arranged in a close geometry aroundtheWAS3ABidetector.

Inafirststep,spectraof

γ

raysobservedinpromptcoincidence withthefirstdecayeventaftertheimplantationofa¹²⁸Cdionin WAS3ABi were studiedapplying differenttime windowsbetween the implantation and the decay as well as different conditions withrespecttothespatialcorrelation.Nonew

γ

transitionswere observed besides the onesalreadyknown to occur following the decay ofthe groundstate of¹²⁸Cd [14]. Furthermore,during the analysisofthetime distributionofthedecayeventswithrespect totheimplantation,bothwithandwithoutrequiringacoincidence withoneoftheobserved

γ

raysinthedaughternucleus,noindi- cation fortheexistence ofa second β-decaying statebesides the groundstate(T1/2=²⁴⁵(5)respectively246.2(21) ms[15,16])was obtained.Tosearchfora

γ

-decayingisomerwithahalf-lifeinthe ms rangewe followed theprocedure alreadysuccessfullyapplied intheidentificationofa(21/2⁺),T_1/2=³.6(2)ms isomerin¹²⁹Cd [7]. Fig. 1showsthe spectrum of

γ

rays detected inthe Ge de- tectorsin thetime intervalof −^4μs< (tγ−^tdecay)<20 μs with respect tothe firstdecayeventafter theimplantation ofa ¹²⁸Cd ion. Onlydecayeventsregisteredduring thefirst20 msafterthe implantation were considered and furthermorethey hadto fulfil the conditionthat energywas depositedexclusively intheSi de- tector inwhichtheionwasimplanted.Thiscondition wasshown in Ref. [7] to significantly suppress the β-decay events and en- hancethoseinwhichtheemissionofconversionelectronsoccurs.

Fig. 1.Spectrumofγ raysdetectedinthetimeintervalof−4μs< (tγ−tdecay)<

20μs withrespecttothefirstdecayeventregisteredduringthefirst20 msafter theimplantationofa¹²⁸Cdion.Onlythosedecayeventsareconsideredinwhich energywasdepositedexclusivelyintheSidetectorinwhichtheionwasimplanted withanupperlimitof360 keV.Lineslabelledwithanasteriskcorrespondtoknown transitionsin¹²⁸Inpopulatedintheβ decayof¹²⁸Cd[14].Theinset showsthe low-energyregionwiththestrictestconditionthatenergywasdepositedexclusively intheimplantationpixel.

Inaddition,anupperlimitof360 keVfortheenergydepositedin theSidetectorwasapplied.Inspectionofthisspectrumshowsthat the

γ

rayswithenergiesof68,248,463,857,and925 keV,which are known[14] to be emitted following theβ decayof ¹²⁸Cd to 128In,arestill present.However,thestrongestlinesatenergiesof 69(part ofthe doublet), 238,440,538,646, and785keV corre- spondto the

γ

rays whichformthemain decaysequenceofthe known(10⁺) isomeric state atan excitation energyof 2714 keV in¹²⁸Cd which hasa half-lifeof T1/2=³.56(6)μs [6].Thishalf- life inthe microsecond rangeis muchtoo shortto allow forthe observationofthese

γ

rays followinga direct population ofthis statesincethedeadtimeaftereachimplantationamounts toone totwomilliseconds. Itcanthereforebe concludedthatthe(10⁺) statemustbepopulatedfromanewisomericstatewithahalf-life ofatleastacoupleofmilliseconds.InFig. 1fouradditionaltran- sitionswithenergiesof203,309,1060,and1263 keVare clearly visible.It can be assumed that these transitions are involved in thedecayofthenewisomericstatetotheknown(10⁺)microsec- ondisomer.TheinsetofFig. 1showsthelow-energyregionofthe spectrumapplyingtheadditionalconditionthatinthedecayevent energywas releasedexclusively inthe pixelofthe Sidetectorin whichtheionwasimplantedbefore.Thisconditionisthestrictest onewhichcanbeappliedinordertoreducecontaminationsandis usedtodemonstratethatnoadditionallow-energytransitionscan beunequivocally assignedtothedecayofthenewisomericstate in¹²⁸Cd.

Todetermine the half-life ofthe new isomer the distribution ofthetimedifferencesbetweentheionimplantation,tion,andthe detectionofthedecay,tdecay,wasexaminedforallthosedecays,in whichoneofthe

γ

rayswithenergiesof203,238,309,440,538, 646,785,1060,and1263 keVwasdetectedintheGearrayinthe timerange−^4μs< (tγ−^tdecay)<20μs withrespecttothedecay.

Sucha wide timewindow ratherthan aprompt coincidence had tobeconsideredduetotheμs half-lifeofthe(10⁺)state(T_1/2= 3.56(6)μs).Thesummedtimedifferencedistribution(t_decay−^tion) isshowninFig. 2a).A fitto theexperimental points assuming a singleexponentialdecayresultsinahalf-lifeofT1/2=⁶.3(8)ms.

In the next step, the Si energy spectrum observed in coin- cidence with the detection of one of the above listed

γ

rays was constructed for all decay events which occurredin the first 20 msafterthe ionimplantation. Againa time rangeof−^4μs<

(tγ−^tdecay)<20μs wasconsidered forthe

γ

rays.Theresulting

Fig. 2.a)Summedtimedifferencedistribution(tdecay−^tion)forthosedecayevents, inwhichoneoftheγrayswithenergiesof203,238,309,440,538,646,785,1060 and1263 keVwasdetectedinEURICAinthetimerange−4 μs< (tγ−tdecay)<

20 μs withrespecttothedecay,b)energyspectrumofdecayeventsregisteredin theSidetectorsinthefirst20 msaftertheimplantationofa¹²⁸Cdionincoinci- dencewithoneoftheγ rayslistedaboveandc)proposeddecayschemeofthe newlyestablishedmsisomerin¹²⁸Cd.Thelevelandhalf-lifeinformationuptothe (10⁺)stateistakenfromRef.[6].Additionalweakdecaybranchesreportedin[6]

areomittedforsimplicity.

spectrum,whichisdisplayedinFig. 2b),reflectsthedistributionof energiesreleasedinthedecayofthenewmsisomer.Threepeaks atenergies around65,205,and290 keVare visibleinthisspec- trum. Based onthe experience gained in the studyof the decay ofthe ms isomer in¹²⁹Cd [7]we interpret thesepeaksasorigi- natingfromthedetectionofconversionelectronscorrespondingto the partiallyconverted 69,203, 238, and309 keV transitions.As discussedindetailinourpreviouswork,insomecasestheXrays followingtheemissionoftheinternalconversionelectrons escape detectionleadingtoshiftsinthepositionofthepeaksobservedin theSienergyspectrum.Furthermoretheenergycalibrationofthe individualstripsoftheSidetectors,whichhasbeenperformedus- ingComptonscatteringofthe1173and1333 keV

γ

raysemitted from a ⁶⁰Co calibrationsource, is lessreliable in the low-energy regime. The 69 keV (10⁺) → ^{(8+) E}2 transitionhas an internal conversion coefficient of

α

(69 keV)=⁵.9 and thus proceeds in 85% of all cases via the emission of a conversion electron (CE).

However, the detection of this CE is strongly suppressed by the thresholdsoftheindividual Sistripswhichinthecurrentexperi- mentscatter inthe range50–150 keV. Consequentlyonly asmall fractionofall69 keV CEs,roughlyone-tenth,isdetected.

The sum ofthe newly observed 203 and 1060 keV

γ

rays is equal to the energy of another new transition, namely the one with1263 keV.Thisobservationsuggeststhattheformertwotran- sitions form a cascade parallel to the 1263 keV

γ

ray. In this case the multipolarity ofthe 203 keV

γ

ray can be assumedto be rather low, most probably M1, which wouldimply a conver- sioncoefficientof

α

(203 keV)=⁰.066 forthistransition.Thepeak areas observed in Fig. 2b) seem to indicate a larger conversion coefficient for the 309 keV transition and thus multipolarity E3 or higher. Inthe case of E3 the conversioncoefficient wouldbe

α

(309 keV)=⁰.111.Thehighermultipolarityofthe309 keV tran- sition suggeststhat this transitionis the primary isomeric decay leadingtoatentativedecaysequenceforthenewmsisomeratan excitation energyof4286 keVassketchedinFig. 2c). Anindirect

Appendixfordetails).

Eγ (keV) Ei(keV) Irel(%) Iest(%)

203 3977 40(7) 35

238 2108 85(10) 81

309 4286 38(7) 37

440 1871 87(12) 100

538 2646 78(12) 100

646 646 100(14) 100

785 1430 105(15) 100

1060 3774 52(12) 47

1263 3977 28(9) 28

Fig. 3.Comparisonbetween theexperimentalexcitation energies(red dots)and thoseobtainedbythe SMcalculationsusingthe NA-0(dashed line)and NA-14 (solidline)interactions.(Forinterpretationofthereferencestocolourinthisfig- urelegend,thereaderisreferredtothewebversionofthisarticle.)

check ofthescenario proposed inFig. 2c)is providedby a com- parison ofthe

γ

-ray intensities followingthe decayofthe (15⁻) isomer expected on the basis of the experimental trigger condi- tionstotheexperimentallyobservedones.Thiscomparison,which issummarizedinTable 1anddiscussedindetailintheAppendix, showsthattheproposeddecaysequenceisinfullagreementwith theexperimentalobservations.

In the following we will compare the excited states of ¹²⁸Cd showninFig. 2c)totwodifferentSMcalculations.Thefirst,named NA-0 in the following, employs a two-body effective interaction derivedfromtheCD-Bonnnucleon–nucleonpotentialrenormalized by way of the V_low−k approach [17]. Specifically, the interaction is constructed by assuming ¹³²Sn as closed core and consider- ing the full N=50–82 major shell for neutrons (i.e. the 0g7/2, 1d5/2, 1d3/2, 2s1/2 and 0h11/2 orbitals) and the Z =28–50 shell forprotons(i.e.the0f_5/2,1p_3/2,1p_1/2and0g_9/2orbits).Theneu- tronsingle-particleenergies(SPE)weretakenfromRef.[18],while forthe protons energies of 0.365 (1p_1/2) and1.353 MeV(1p_3/2) relativetothe0g9/2 orbitalwereemployed[19,20].Fortheexper- imentallystillunknownenergyofthe0f_5/2 protonorbitalavalue of2.6 MeVrelative to 0g9/2 was adopted.Notethat thesecalcu- lations are similar to the ones presented for ¹²⁸Cd in Refs. [21, 22]inwhich,however,slightlydifferentSPEhavebeenemployed.

Thisandallfollowingcalculationswere performedwiththecode OXBASH[23].

An inspection of Fig. 3 shows that with the NA-0 interaction the2⁺,4⁺,and6⁺ statesare calculatedtoohighinenergy. This isparticularlytrueforthe2⁺state,whoseanomalouslylow exci- tationenergywastracedbackinRef.[24]tospecialcharacteristics of the Cd isotopes which favour prolate configurations close to theN=^{82 shellclosure.}Furthermore,the15⁻levelispositioned

Fig. 4.Comparisonbetweenthelevelstructuresontopofthe(10⁺)isomerin¹²⁸Cd and abovethe(11/2⁻)levelin¹²⁹Cd withthecorrespondingshell-modelcalcu- lationsemployingtheNA-14interaction.Thestatesin¹²⁸Cdhavebeenshiftedto alignthe(10⁺)levelwiththe(11/2⁻)statein¹²⁹Cd(x=^{2714 keV,x}=^{2686 keV).}

Notethatit is presentlyexperimentallyunknownwhichofthe twoβ-decaying statesof¹²⁹Cd,3/2⁺or11/2⁻,isthegroundstate(i.e.yisunknown).

above the 13⁻ and14⁻ statesand consequently the experimen- tally observed isomeric character of thisstate is not reproduced bytheNA-0calculations.Inourrecentstudiesofseveralneutron- rich Cd andInisotopes amodified interaction namedNA-14was proposed which was shown to cure some of the shortcomings of NA-0 and to provide a consistent description of 46≤^Z ≤^50, N≤^{82 nuclei[7,25–27].The}modifications concernedthe pairing andmultipolepartsoftheinteraction,inparticularthe

π π

pairing wasreducedto88%andthe

νν

and

π ν

multipoleswereincreased by factorsof1.6and1.5inthedominantconfigurations

ν

(0h⁻₁₁²_/2) and

ν

(0h11/2)

π

(0g9/2). As shownin Fig. 3, the calculations em- ploying NA-14describemuchbetter thelevelsequenceup tothe (10⁺)isomerandalsoreproducetheisomericcharacterofthe15⁻ state.However,incontrasttotheNA-0calculations,theyexhibita clear overbinding of all states above the 10⁺ isomer and in ad- ditiontheexperimental E2/M1 branchingratioofroughly 40/60%

forthedecayofthe(12⁺)stateisbadlyreproducedbytheNA-14 calculations(84/16%).Asalast commentonFig. 3,wewouldlike to pointout that a18⁺ E6 spin-gapisomer isrobustlypredicted by bothcalculationsanditsobservationthereforeremainsachal- lengeforfutureexperiments.

As mentioned in the introduction, recently the decay of a (21/2⁺)

γ

-decaying ms isomer with the dominant

π

(0g⁻_9/¹₂(1p, 0f_5/2)⁻¹)

ν

(0h⁻₁₁¹_/2)configurationwasobservedintheneighbour- ing nucleus ¹²⁹Cd [7] and interpreted as stretched coupling be- tween the neutron hole in the 0h11/2 orbit and the 5⁻ proton state in semi-magic ¹³⁰Cd. One obvious possibility would there- fore bethat the (15⁻) statein ¹²⁸Cd isformed by theanalogous fullyaligned

π

(0g⁻_9/¹₂(1p,0f_5/2)⁻¹)

ν

(0h⁻₁₁²_/2)configuration(inthe followingabbreviated

π

5⁻

ν

10⁺).AsillustratedinFig. 4,thelevel structuresobservedinthedecaysofthe(15⁻)levelin¹²⁸Cdand the (21/2⁺) state in¹²⁹Cd are indeedvery similar. Both isomers decayvia an E3 transitionfollowed byparallel M1 and E2 decay branches.Note,however,thatthelevelsequencein¹²⁹Cdismuch more stretched ascompared tothe one above the(10⁺) levelin 128Cd,leading toa differenceofmore than350 keVbetweenthe (15⁻)and (21/2⁺) levels relative tothe (10⁺) and(11/2⁻) neu- tronstates,respectively(compareFig. 4).Since¹²⁸Cdhasbothtwo proton and two neutron holes with respect to ¹³²Sn, there is of courseanaturalalternativetothe

π

5⁻

ν

10⁺ configurationforthe 15⁻ state, namely the stretched coupling between the

π

(0g⁻_9/²₂)

Table 2

Experimentalandcalculated(NA-14)B(E3)valuesinW.u.for transitionsin^128,129Cdand¹²⁹In.

Nucleus I^π_i I^π_f B(E3)exp (W.u.)

B(E3)S M (W.u.) 128Cd (15⁻) (12⁺) 0.66(8) 0.42 129Cd (21/2⁺) (15/2⁻) 0.47(3)¹ 0.46 129In (29/2⁺) (23/2⁻) 0.069(10) 0.042 1 NotethatinRef.[7],bymistake,aslightlylargervalueof B(E3)=⁰.50(3)W.u. wasquotedduetotheomissionoftak- ingintoaccounttheinternalconversioncoefficientα=⁰.0665 [29]ofthe353 keVE3 transition.

andthe

ν

(0h⁻₁₁¹_/21d⁻_3/¹₂) configurations (

π

8⁺

ν

7⁻), i.e. the known 8⁺and7⁻ isomersintherespectivetwo-protonandtwo-neutron holenuclei¹³⁰Cdand¹³⁰Sn.

An inspection of the wave functions obtained using the NA- typeinteractionsshowsthattheleadingconfigurationoftheyrast 15⁻ stateisindeedrobustly

π

8⁺

ν

7⁻,whilethesecond15⁻state, which is predicted 330–530 keV higher in energy, is dominated by the

π

5⁻

ν

10⁺ configuration. Note that the calculated energy of this second 15⁻ relative to the 10⁺ state nicely agrees with the energy of the

π

5⁻

ν

(0h⁻₁₁¹_/2), 21/2⁺ state in ¹²⁹Cd. In the odd-Z,two-neutronholenucleus¹²⁹Inisomeric stateswithspins of(23/2⁻)and(29/2⁺)havebeenobservedatexcitationenergies of1630(56) and 1911(56) keV,respectively [28]. The energies of thesestates,which are basedon the stretched

π

(0g₉⁻_/¹₂)

ν

7⁻ and

π

(0g⁻_9/¹₂)

ν

10⁺configurations,arecalculatedonlyabout∼^{100 keV} lowerby theshell modelemployingthe NA-14interaction.Turn- ingnowtothetransitionprobabilitiesitisworthmentioningthat the strength of all three E3 transitions discussed above, namely the(15⁻)→(12⁺)in¹²⁸Cd,the(21/2⁺)→(15/2⁻)in¹²⁹Cdand the(29/2⁺)→(23/2⁻) in¹²⁹In,are well reproducedby thecur- rentcalculations(seeTable 2)usingeffectivechargesofeπ=¹.5e andeν=⁰.7e.

Finally,we can now use the NA-14 interaction to predict the positions of the remaining excited states in ^128–130Cd which are basedonfullyalignedconfigurationsandhavenot yetbeenfixed experimentally.The

π

8⁺

ν

(0h⁻₁₁¹_/2),27/2⁻ state in¹²⁹Cd iscalcu- latedatan energyof1695 keV,whilethe

π

(0g₉⁻_/¹₂(1p,0f_5/2)⁻¹), 5⁻ level in¹³⁰Cdis predictedatan energyof2075 keV,27keV belowthe calculatedenergyofthe8⁺ state.Finally,theseniority

υ

=⁴,18⁺ spin-gapisomerin¹²⁸Cdispredictedtohavean exci- tationenergyof3995 keV.

To conclude we reported on the identification of a new iso- meric state with a half-life of T1/2=⁶.3(8) ms in the nucleus 128Cdwhichdecaysviatheemissionofa

γ

raywithanenergyof 309 keVandamultipolarity E3.Thedecaywasidentified viathe observationofknown

γ

rays emitted following thedecay ofthe (10⁺)isomeric stateincoincidencewiththedetectionofinternal conversionelectrons in an active stopper. Based onthe observed

γ

-ray intensities andstate-of-the-art shellmodel calculationswe tentativelyassigned a spin/parity of15⁻ to thisstate. The shell- model study of ¹²⁸Cd presented here reinforces the conclusions fromourpreviouswork thatadjustmentsofthepairingandmul- tipolepartsofthe effectiveinteraction derivedfromtheCD-Bonn nucleon–nucleon potential are required in order to describe the propertiesofnucleiintheregionaround¹³²Sn.Finally,predictions aremadefortheexcitationenergiesofthestillunobserved27/2⁻ statein¹²⁹Cd,the5⁻levelin¹³⁰Cd,andthe18⁺ spin-gapisomer in¹²⁸Cd.

Acknowledgements

We thank the staff of the RIKEN Nishina Center acceler- ator complex for providing stable beams with high intensi- ties to the experiment. We acknowledge the EUROBALL Own- ers Committee for the loan of germanium detectors and the PreSpec Collaboration for the readout electronics of the clus- ter detectors. This work was supported by the Spanish Ministe- rio de Ciencia e Innovación under contract FPA2011-29854-C04 and the Spanish Ministerio de Economía y Competitividad un- der contract FPA2014-57196-C5-4-P, the Generalitat Valenciana (Spain) under grant PROMETEO/2010/101, the National Research Foundation of Korea (NRF) grant funded by the Korea govern- ment (MEST) (NRF-2014S1A2A2028636, 2016K1A3A7A09005579, 2016R1A5A1013277),thePriorityCentersResearchPrograminKo- rea (2009-0093817), OTKA contract numberK-100835, JSPS KAK- ENHI (Grant No. 25247045), the European Commission through the Marie Curie Actions call FP7-PEOPLE-2011-IEF under Con- tractNo.300096,theU.S.DepartmentofEnergy,OfficeofNuclear Physics, under Contract No. DE-AC02-06CH11357, the STFC (UK), the “RIKEN foreign research program”, the German BMBF (No.

05P12RDCIA, 05P12RDNUP and 05P12PKFNE), HIC for FAIR, the DFG cluster of excellence “Origin andStructure of the Universe”

andDFG(ContractNo. KR2326/2-1).

Appendix A. Considerationsof

γ

-rayintensitiesandtrigger conditions

To examine the plausibility of the structure proposed above the (10⁺) state in ¹²⁸Cd (see Fig. 2c)) we estimate the intensi- tieswithwhich thedifferent

γ

rays emitted inthe decayof the (15⁻) isomerareexpectedtobeobservedconsideringtheexperi- mentalconditionssuchascoincidencetimewindowsanddetector thresholdsaswellasthehalf-livesofintermediatestatesandmul- tipolaritiesoftheinvolvedtransitions.Theresultofthisestimation is compared to the experimentally determined intensities in Ta- ble 1. We start with an assessment of the probabilities for the differentconversion electrons (CE), whichare emitted in thede- cayofthemsisomer,totriggerthedataacquisitionbasedontheir conversioncoefficients. Totake intoaccountthetime structureof thedecaysequencewewillapplythefollowingtwoassumptions:

i)Inallcasesinwhicheithera309ora203 keVCEisdetectedany further energy deposition relatedto transitions below the (10⁺) isomer escapesobservation duetothe longhalf-life ofthe inter- mediate (10⁺) state and the dead time of the data acquisition and ii)in casethat two conversionelectrons are emitted within a periodof nanoseconds their energies are summed. Onthisba- sis weestimate probabilities of9.7%forthe309 keVCE, 3.1%for the203 keV CE,69% forthe69 keVCE, 0.9%forthe238 keV CE and 4.9% for the sum of the 69 and 238 keV CEs, which corre- spondsto307 keV.Asmentionedbeforethedetectionprobability forthe69 keV CEisdrasticallyreducedduetotheenergythresh- oldsoftheSidetectorsleadingtoaneffectivetriggerprobabilityof 7.8%forthe69 keVCE.Notethathencethepeakaround290 keV observedintheSi energyspectrum ofFig. 2b)contains contribu- tions of both the 309 keV CE above and thesum of the69 and 238 keV CEsbelowthe(10⁺)state.Inthisestimatethecontribu- tion of Compton electrons is neglected. Simulations in line with the ones presented in Ref. [7] estimate their contribution to be well below5%.Summingall individualtriggerprobabilitiesshows that only every fourth decay of the newly identified ms isomer isobserved atall. Anillustrationof thetwo main triggermodes, namelythe69 keVCEandthetwocomponentscontributingtothe peakaround290 keV,isgiveninFig. 5.Thisfigureshowsthedis- tributions ofthetimedifferencesbetweenthedetectionofthe

γ

Fig. 5.Summedtimedifferencedistributions(tγ−tdecay)fora)the203,309,1060, and1263 keVγ raysandadecayenergyintherangelabelledIinFig. 2a),b)the sameγ raysandadecayenergyintherangelabelledI IinFig. 2a),c)the238,440, 538,646,and785 keVγ raysandadecayenergyinrangeIandd)thesameγ raysasinc)andadecayenergyinrangeI I.

ray,tγ,andtheenergydepositionintheSidetector,t_decay,forthe twoSienergygates, I andI I,indicatedinFig. 2b)andeitherthe

γ

rays aboveorbelowthe(10⁺) isomer. Clearlythe

γ

rays with 203,309,1060,and1263 keVareemittedbefore thedetectionof a69 keV CEintheSi detector(compare Fig. 5a)),whilethey are emittedinpromptcoincidencewiththe309 keV CE(seeFig. 5b)).

Forthe 238,440,538,646,and 785 keV

γ

rays observed inthe decayofthe (10⁺) isomer, onthe other hand,the time distribu- tion withrespect to the 69 keV CE nicelyreflects the 270(7) ns half-lifeofthe (5⁻) state.Finally, Fig. 5d)showsthat besidesthe short-livedcomponentobservedinFig. 5c),the

γ

rays belowthe (10⁺) isomer are also observed microsecondsafter the detection ofan energyaround 290 keV inthe Si detector. Thislatter con- tribution stems fromthe309 keV CE andreflects the half-life of T1/2=³.56(6)μs of the(10⁺)state.Notethat thetimerangefor

thedataacquisition.

Combiningallthesepiecesofinformationwithrespecttotrig- ger probabilities andtime constraintsthe expected intensities of the

γ

rays observed inFig. 1can now be estimated. The results of this estimate are compared to the experimentally determined valuesinTable 1.Agoodgeneralagreementisobservedproviding indirectsupport fortheassumptions madeconcerning themulti- polaritiesofthe203 keV (M1)and309 keV (E3)transitions.

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