= Physics Letters B

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Physics Letters B

www.elsevier.com/locate/physletb

New isomers in 125 Pd 79 and 127 Pd 81 : Competing proton and neutron excitations in neutron-rich palladium nuclides towards the N = 82 shell closure

H. Watanabe

^a^,^b^,^c^,∗

, H.K. Wang

^d

, G. Lorusso

^c

, S. Nishimura

^c

, Z.Y. Xu

^f

, T. Sumikama

^g

, P.-A. Söderström

^c

, P. Doornenbal

^c

, F. Browne

^c^,^h

, G. Gey

^c^,ⁱ

, H.S. Jung

^j

, J. Taprogge

^c^,^k^,^l

, Zs. Vajta

^c^,^m

, J. Wu

^c^,ⁿ

, A. Yagi

^o

, H. Baba

^c

, G. Benzoni

^p

, K.Y. Chae

^q

, F.C.L. Crespi

^p^,^r

, N. Fukuda

^c

, R. Gernhäuser

^s

, N. Inabe

^c

, T. Isobe

^c

, A. Jungclaus

^l

, D. Kameda

^c

, G.D. Kim

^t

, Y.K. Kim

^t^,^u

, I. Kojouharov

^v

, F.G. Kondev

^w

, T. Kubo

^c

, N. Kurz

^v

, Y.K. Kwon

^t

, G.J. Lane

^x

, Z. Li

ⁿ

, C.-B. Moon

^y

, A. Montaner-Pizá

^z

, K. Moschner

^aa

, F. Naqvi

^ab

, M. Niikura

^f

, H. Nishibata

^o

, D. Nishimura

^ac

, A. Odahara

^o

, R. Orlandi

^ad

, Z. Patel

^e

, Zs. Podolyák

^e

,

H. Sakurai

^c

, H. Schaffner

^v

, G.S. Simpson

ⁱ

, K. Steiger

^s

, Y. Sun

^ae^,^af

, H. Suzuki

^c

, H. Takeda

^c

, A. Wendt

^aa

, K. Yoshinaga

^ag

aSchoolofPhysicsandNuclearEnergyEngineering,BeihangUniversity,Beijing100191,China

bInternationalResearchCenterforNucleiandParticlesintheCosmos,BeihangUniversity,Beijing100191,China cRIKENNishinaCenter,2-1Hirosawa,Wako,Saitama351-0198,Japan

dCollegeofPhysicsandTelecommunicationEngineering,ZhoukouNormalUniversity,Henan466000,China eDepartmentofPhysics,UniversityofSurrey,GuildfordGU27XH,UnitedKingdom

fDepartmentofPhysics,UniversityofTokyo,Hongo,Bunkyo-ku,Tokyo113-0033,Japan gDepartmentofPhysics,TohokuUniversity,Aoba,Sendai,Miyagi980-8578,Japan

hSchoolofComputing,EngineeringandMathematics,UniversityofBrighton,Brighton,BN24GJ,UnitedKingdom

iLPSC,UniversitéJosephFourierGrenoble1,CNRS/IN2P3,InstitutNationalPolytechniquedeGrenoble,F-38026GrenobleCedex,France jDepartmentofPhysics,Chung-AngUniversity,Seoul156-756,RepublicofKorea

kDepartamentodeFísicaTeórica,UniversidadAutónomadeMadrid,E-28049Madrid,Spain lInstitutodeEstructuradelaMateria,CSIC,E-28006Madrid,Spain

mMTAAtomki,O.Box51,Debrecen,H-4001,Hungary

nSchoolofPhysicsandStateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,China oDepartmentofPhysics,OsakaUniversity,Machikaneyama-machi1-1,Osaka560-0043Toyonaka,Japan

pINFN,SezionediMilano,viaCeloria16,I-20133Milano,Italy

qDepartmentofPhysics,SungkyunkwanUniversity,Suwon440-746,RepublicofKorea rDipartimentodiFisica,UniversitádiMilano,viaCeloria16,I-20133Milano,Italy sPhysikDepartment,TechnischeUniversitätMünchen,D-85748Garching,Germany tRareIsotopeScienceProject,InstituteforBasicScience,Daejeon305-811,RepublicofKorea uDepartmentofNuclearEngineering,HanyangUniversity,Seoul133-791,RepublicofKorea vGSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany wPhysicsDivision,ArgonneNationalLaboratory,Argonne,IL60439,USA

xDepartmentofNuclearPhysics,R.S.P.E.,AustralianNationalUniversity,Canberra,A.C.T2601,Australia yDepartmentofDisplayEngineering,HoseoUniversity,Chung-Nam336-795,RepublicofKorea zIFIC,CSIC-UniversidaddeValencia,A.C.22085,E46071,Valencia,Spain

aaInstitutfürKernphysik,UniversitätzuKöln,ZülpicherStrasse77,D-50937Köln,Germany abWrightNuclearStructureLaboratory,YaleUniversity,NewHaven,CT06520-8120,USA acDepartmentofPhysics,TokyoCityUniversity,Setagaya-ku,Tokyo158-8557,Japan

adInstituutvoorKernenStralingsfysica,KULeuven,UniversityofLeuven,B-3001Leuven,Belgium aeSchoolofPhysicsandAstronomy,ShanghaiJiaoTongUniversity,Shanghai200240,China afCollaborativeInnovationCenterofIFSA,ShanghaiJiaoTongUniversity,Shanghai200240,China

agDepartmentofPhysics,FacultyofScienceandTechnology,TokyoUniversityofScience,2641Yamazaki,Noda,Chiba,Japan

*

Correspondingauthorat:SchoolofPhysicsandNuclearEnergyEngineering,BeihangUniversity,Beijing100191,China.

E-mailaddress:[email protected](H. Watanabe).

https://doi.org/10.1016/j.physletb.2019.03.053

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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(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP .

Atomic nuclei are self-bound, quantum many-body systems consisting of two types of constituents (nucleons), protons and neutrons,which interactstronglywitheach other in afinite vol- ume. The protons andneutrons respectivelyoccupy their single- particle orbits in a mean-field potential, givingrise to a distinct patternof theenergy spacingbetween theorbits, so-calledshell structure.Inashell-modelapproach,individualenergy/spineigen- states are described as the combination of proton and neutron configurations formed within the available model space assum- ing a doubly closed-shell nucleus as an inert core; therefore, a main difficulty isascribed to an increasing numberof configura- tionsthathavetobedealtwithinthecalculation,whenincreasing the proton/neutron valency moving away fromthe closed shells.

Nowadays,theshellstructuresareknowntobechangedwiththe variationoftheprotonorneutronnumber,aswellaswithspeciﬁc particle-hole excitations within the same nucleus, due predominantly to the monopole part of the proton-neutron interaction thatincludesthecentralandtensorforces [1,2].Suchashellevo- lutionary behavior is expected to become pronounced when the proton-neutron imbalance is very large, leading to lost or new magicnumbers(see,forinstance,Ref. [3] andreferencestherein).

As such, spectroscopicstudies ofshort-lived rareisotopes (exotic nuclides) around proton/neutron shellclosures are ofcrucial sig- niﬁcance incorroboratingthe shellevolution faroffstability.The available spectroscopic data of excitation spectra can serve as a goodtestinggroundfordevelopingnuclearshellmodels.

The advent of the new generation in-flight-separator facility, the RI-BeamFactory (RIBF) in RIKEN Nishina Center [4], has en- abled us to explore previously inaccessible nuclear regions with a highly unbalanced ratioof neutrons toprotons [5]. Concerning neutron-richpalladium(₄₆Pd)isotopes,thosewith A=¹²⁵−¹³¹ (N=⁷⁹−⁸⁵⁾ ^have^beenîdentifiedâs^newîsotopesâtRIBF [6–8], followed by spectroscopic studies by means of β- and isomeric- decaymeasurements [9–11] andin-beam

γ

-rayspectroscopy [12]

inthelastdecade.Especiallyemphasizedisthatthedelayed

γ

-ray measurements following isomeric decayscan providea powerful toolforinvestigatingtheexcitedlevelstructure,inparticular,when the nucleus of interest lies at the boundaries of availability for spectroscopicstudies. For ¹²⁸Pd82, whichis a presumed waiting- pointnucleusthatcontributessigniﬁcantlytotheformationofthe secondpeakinther-processsolarabundancedistribution [13,14], aseniorityisomerwithaspinandparityof(8⁺)hadbeenidenti- ﬁed,servingasanindirectevidencefortherobustnessofthe N= 82 shell closure [10]. In the two-neutron-hole neighbor ¹²⁶Pd₈₀, itturnedout thattheproton-neutronmonopolepropertiesofthe centralandtensorforcesplayanimportantroleintheemergence ofthelong-lived(10⁺) isomer [11]. Comparedto sucheven-even systems, neighboring odd-mass nuclei exhibit more complicated excitationspectra,whichprovidecrucialinformationontheeffect

of unpaired nucleons on the level structure. This Letter presents previously unreported isomeric states and their decay properties in ¹²⁵Pd₇₉and ¹²⁷Pd₈₁,which havethreeandone neutron holes relative totheN=^{82 shell}^closure,respectively.Theobtainedre- sultsarecomparedtoashell-modelcalculation,whichpredictsthe competitionbetweenprotonandneutronexcitationsintheproton- holeandneutron-holesystemsinthesouth-westquadrantofthe doublymagicnucleus¹³²Sn.

The neutron-rich odd-A palladium isotopes, ¹²⁵Pd and ¹²⁷Pd, were separated through the BigRIPS in-flight separator [15], following productionvia in-flight fissionof a ²³⁸U⁸⁶⁺ beam at345 MeV/u incident ona berylliumtarget with athickness of3 mm.

The primary beamintensityrangedfrom7 to12pnA during the experiments.About3.1×¹⁰⁵ ⁽¹²⁵^Pd⁴⁶⁺⁾^and⁸.7×¹⁰³ ⁽¹²⁷^Pd⁴⁶⁺⁾ ionsweretransportedthroughtheBigRIPS-ZeroDegreespectrome- terandﬁnally implantedintotheWAS3ABi active stopper,which consisted of eight layers of double-sided silicon-strip detectors (DSSSDs) stacked compactly [16]. Each DSSSDhad a thicknessof 1 mm with an active area segmented intosixty andforty strips (1-mm pitch) oneach side in thehorizontal andvertical dimen- sions, respectively. Gamma rays emitted following the heavy-ion implantation and their subsequent radioactive decay were de- tected by the EURICA

γ

-ray spectrometer [16,17], consisting of 12 Cluster-type detectors, each of which contained seven HPGe crystals packed closely. The methodology of how to analyze the experimentaldatatakenwiththeEURICAsetupisdescribedinde- tailinarecentreviewarticle [18].

Since ¹²⁵Pd and ¹²⁷Pd were discovered as new isotopes at RIBF [6,7], their spectroscopic information has so far been lim- itedonlytotheground-stateβ-decayhalf-lives [9].Inthepresent work,

γ

raysemittedfromtheexcitedstatesintheseneutron-rich odd-A nuclei havebeen observed forthe ﬁrst time.Detailed ex- perimentalresultsofeachisotopearedescribedasfollows:

For¹²⁵Pd,four

γ

raysatenergiesof108,115,757,and825keV areclearlyvisiblewithinatimeintervalof250−^{1250 ns}^after^the ionimplantation,asexhibitedinFig.1(a).Theyareunambiguously assignedasthe transitionsforming asingle cascadefroman isomericstate, whichcanbe conﬁrmedby their mutualcoincidence as demonstrated inFig. 1(b), aswell as by their consistent time behaviorassummarizedinthelastcolumnofTable1.Anexample ofthetime spectrumobtainedwitha gateonthe757-keV

γ

ray isshowninFig.2(a).Aweighted averageoftherespectiveﬁts to thedecaycurvesresultsinanisomerichalf-lifeof144(4)ns.

According to the β-decay studies of ¹²⁵Pd [21] carried out in parallel with the present analysis, there are two β-decaying states withsimilar half-lives, assystematically found in neutron- rich odd-A isotopes of50Snand48Cdwith N82 [23,24]. Either aspin-parityof11/2⁻or3/2⁺isassignedfortheβ-decayingiso- mer, andthecounterpart forthegroundstate. Theβ decayfrom

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Fig. 1.Gamma-rayenergyspectrameasuredinthepresentwork.Thecoincidencegateconditionsareasfollows.(a)and(b):Withinatimerangeof250−^{1250 ns}^after implantationof¹²⁵Pdions.Contaminantsaremarkedwithasterisks.Anadditionalgateissetonthe757-keVγraytomakethecoincidencespectrumshowninthepanel (b).(c)and(d):Withinatimeintervalof0−200 msfollowingimplantationof¹²⁵Pdionscorrelatedwithβrays.Long-livedactivitieshavebeensubtracted.Inthepanel(c), γraysassignedpreviouslyinthedecayschemefromanisomericstateat1501keVtowardsthe(9/2⁺)statein¹²⁵Ag [19,20] arelabeledwiththeirenergyvalues,while transitionsreportedasfeedingthe(1/2⁻)state [21] aremarkedwithdiamonds.Thecoincidencespectrumshowninthepanel(d)isobtainedwithasumofadditionalgates onthe108-,115-,757-,and825-keVγ rays,whichareobservedwithina900-nstimewindowopened100nsaftertheionimplantation.(e)and(f):Withinatimerange of0.25−^{100 μs}^afterimplantationof¹²⁷Pdions.Anadditionalgateissetonthe422-keVγraytomakethecoincidencespectrumshowninthepanel(f).

Table 1

Summaryoftransitionsfromtheisomericstatesin¹²⁵Pdand¹²⁷Pd.EachcolumnshowstheinitiallevelenergyEi,spinandparityoftheinitial(final)state J^π_i (J^π_f),γ-ray energyE_γ,electromagnetictransitionmultipolarityσλ,totalconversioncoefficientα^cal_T calculatedbytheBrIcccode [22],relativeγ-rayintensityI_γ,totaltransitionintensity Itot=(1+α^calT )Iγ,andhalf-lifeT1/2derivedfromafittotheγ-raytimedistribution.

Nucleus Eia[keV] J^π_i → J^π_f Eγ [keV] σλ α^cal_T Iγ^b[relative] Itot[relative] T1/2(γ)

125Pd79 1805.2 (23/2⁺)→(¹⁹/2⁺) 108.4(1) E2 1.05 48(6) 99(13) 138(11) ns

1696.8 (19/2⁺)→(19/2⁻) 115.32(6) E1 1.02×10⁻¹ 100(11) 110(12) 151(9) ns

756.6 (15/2⁻)→(11/2⁻) 756.56(9) E2 1.95×10⁻³ 100(11) 100(11) 153(7) ns

1581.5 (19/2⁻)→(15/2⁻) 824.94(9) E2 1.58×10⁻³ 93(11) 93(11) 134(7) ns

127Pd81 1717.9 (19/2⁺)→(15/2⁻) 422.4(1) M2 3.01×10⁻² 100(21) 103(21) 41(8) μs

1295.5 (15/2⁻)→(11/2⁻) 1295.5(2) E2 6.00×¹⁰⁻⁴ ^105(24) ^105(24) ^{36(9) μs}

a Relativetotherespective(11/2⁻)states.

b Relativetothe757-,and422-keVγ-rayintensitiesfor¹²⁵Pdand¹²⁷Pd,respectively.

the11/2⁻state islikelytofeed J=⁹/2,11/2,and13/2levelsin thedaughternucleus,whilecomparatively low-spinstatescan be populatedintheβ decayfromthe 3/2⁺ state. Asan exampleof the¹²⁵Pd→¹²⁵^Ag^decay,^a β-delayed

γ

-ray spectrummeasured within 200 ms after implantation of the ¹²⁵Pd ions is shownin Fig.1(c). The 670-, 684-, 714-, and 728-keV

γ

rays, which were reportedpreviouslyasthe transitionsinvolvedinthe cascadese- quencesfrom the (17/2⁻) isomer at1501 keV to the presumed (9/2⁺)groundstatein¹²⁵Ag [19,20],areunambiguouslyobserved, supportingthepresenceofthe(11/2⁻)statein¹²⁵Pdthatunder- goesβ decayto ¹²⁵Ag. Inaddition totheseknown transitions,it wasfoundthatseveralnew

γ

raysemerge,beingassignedasfeed- ingthelow-spinstatesin¹²⁵Ag.Furtherdetailsoftheβ-

γ

analysis willbepresentedelsewhere [21].

In order to clarify on which β-decaying state (Jπ =³/2⁺ or 11/2⁻) the aforementioned 144-ns isomer is built in ¹²⁵Pd, thecorrelation betweenthe β-delayed

γ

rays andthepreceding isomeric-decaytransitions hasbeen conﬁrmed. Fig. 1(d) showsa

γ

-rayenergyspectrumcreatedunderthesamegateconditionfor theimplant-β-

γ

correlation asthat usedfor Fig. 1(c), andaddi- tionally,witha sumofenergygatesonthe108-, 115-, 757-,and 825-keV

γ

raysobservedwithina0.1−¹.0 μstimeintervalafter implantationofthe¹²⁵Pdions.Withthisconstraintonthe“isomer implantation”events,itisexpectedthatdelayed

γ

raysfollowing theβ decayfromthestatetowhichthe144-nsisomerﬁnallyde- cayscanbeenhanced,comparedtothetransitionspopulatedfrom theother β-decaying state.It canbe seen inFig.1(d)that

γ

-ray peaksat670and714keV,whichwerepreviouslyassignedasthe (11/2⁺)→(9/2⁺)and(13/2⁺)→(9/2⁺)transitionsin¹²⁵Ag,respectively [19,20],areclearlyvisible,whiletheother

γ

raysreduce

theirpeakcountsaslowasthebackgroundﬂuctuations.Therefore, the144-nsisomerturned outtobe builtonthe β-decayingstate with Jπ=(11/2⁻) in ¹²⁵Pd, though it is still unclear whether this level is the groundstate or the long-lived isomer from the presentexperimentalresult.Notethatwhicheverthe(11/2⁻)level is,the groundstateor thelong-livedisomer, thediscussions and conclusions regardinghigher-lyinglevels presentedbelowarenot changed. The excitation energy of the 144-ns isomer was deter- minedtobe1805keVrelativetothe(11/2⁻)state.

The level scheme of ¹²⁵Pd established in the presentwork is exhibitedinFig. 3(left).The orderofthe 757- and825-keVcas- cade transitionswasdeterminedincomparisonwiththe693-keV [(2⁺)→⁰⁺^] ^and^788-keV ^[(4⁺)→(2⁺)]transitionsintheneigh- boringN=^{80 isotope}¹²⁶^{Pd [11].}^However,^thepossibilityofinver- sionofthesetransitionscan not beentirelyruled outdueto the closeness of their energies. The levels at757 (or 825) and 1582 keVrelative to the (11/2⁻) state were tentatively assignedspins and parities of 15/2⁻ and 19/2⁻, respectively, which are inter- pretedasaneutron(hole)intheh11/2 orbitalcoupledtothe(2⁺) and (4⁺) states in ¹²⁶Pd. Meanwhile, the 15/2⁺ assignment for the1582-keVstate,theanalogoftheoneobservedinthe N=⁷⁹ isotone ¹²⁹Sn [25], canbe ruled out becauseof theabsence ofa competing E1 branch towards a (presumed) 13/2⁻ state, which arises predominantlyfrom the

ν

h⁻₁₁¹_/₂⊗²⁺ ^multiplet, ^and ^therefore,isexpectedtoappearintheproximityofthe(15/2⁻)state.

Thetransitionsof108and115keVareplacedincascadeabove the 1582-keV level. For the 108-keV transition, a total internal conversioncoeﬃcient

α

T of1.1(3) canbededucedfromits

γ

-ray intensitybeingcomparedtothetotalintensityofthe757-keV, E2 transition,seeTable1.This

α

T valueisingoodagreementwiththe

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Fig. 2.(a):Timespectrum(tγ)ofthe757-keVγ rayin¹²⁵Pd.(b):Timedifference spectrum( tγ γ)ofthe115-keVγrayrelativetothe108-keVtransitionin¹²⁵Pd.

(c)and(d):Sumof tγ γ ofthe757- and825-keVγ raysrelativetothe115- and 108-keVtransitionsin¹²⁵Pd,respectively.(e):tγ ofthe422-keVγrayin¹²⁷Pd.In thepanels(a)and(e),theredsolidlinesrepresenttheresultsofalog-likelihood ﬁt.

Fig. 3.Levelschemesof¹²⁵Pdand¹²⁷Pdestablishedinthepresentwork.Eachlevel islabeledwiththespin-parity(J^π)andenergy(relativetothe11/2⁻state)values.

Themeasured(isomeric)half-livesareindicatedinbold.Thewidthsofsolidarrows areproportionaltotheγ-rayrelativeintensitiessummarizedinTable1.

theoreticalvalueof1.05foranE2 multipolarity [22].Similarly,the valueobtainedfromtheintensitybalanceanalysisforthe115-keV transition,

α

T=⁰.0(1),isconsistentonlywithanE1 multipolarity within themargin oferror.The orderingof thesetransitions was determinedbasedontheargumentsontransitionstrengths.Ifthe 108-keV(E2)transitionwereplacedbelowthe115-keV(E1)transition, an intermediate state presumed at 1690 keVshould have a half-life ofthe orderof afew or severalhundreds ofnanosec- onds [e.g. T1/2≈^{500 ns} ^given^the ^reduced ^transitionprobability B(E2)=^{1 W.u.} ^for ^the ^108-keV transition]. This is at variance withwhat was observed from time difference spectra havingal-

sition strengths, either a spin-parity assignment of 23/2⁺→ 19/2⁺→¹⁹/2⁻ or 25/2⁺→²¹/2⁺→¹⁹/2⁻ can be proposed forthe108−^115-keV^cascade^between^the^144-ns^isomer^and^the 1582-keV state in ¹²⁵Pd. In the following discussion, the former sequenceisadoptedwiththehelpofshell-modelcalculations.The reduced transition probability, B(E2)=¹²⁹(4) e²fm⁴ =³.47(9) W.u., can be obtainedfor the 108-keV transitionfrom the mea- suredhalf-lifeofthe1805-keVisomericstate,takingintoaccount theinternalconversionprocesswiththecalculated

α

T value [22].

This B(E2) value is comparable to the corresponding 23/2⁺→ 19/2⁺ transitionobservedinthe N=^{79 isotone}¹²⁹^{Sn [25].}

For ¹²⁷Pd, two

γ

-ray peaks at 422 and 1296 keV have been prominently observed within a long time window ranging from 0.25 to 100 μs after the ion implantation, and their coincidence relationshipconﬁrmedby

γ

-

γ

coincidenceanalyses,seeFigs.1(e) and1(f).Theisomerichalf-lifewasdeterminedtobe39(6) μsfrom a weightedaverageoftherespectiveﬁtstothetime distributions ofthe422- and1296-keV

γ

rays,theformerofwhichisshownin Fig.2(e)asanexemplarycase.

The level scheme of ¹²⁷Pd is proposed as exhibited in Fig. 3 (right). The39- μsisomericstate hasbeenidentiﬁedatan excita- tionenergyof1718keVwithrespecttothe(11/2⁻)level,which isassumedtobethelowest-lyingstateintheisomeric-decaycas- cadeinanalogywith¹²⁵Pd.The1296-keVtransitionwasassigned as feeding the (11/2⁻) state from the (15/2⁻) level owing to a closeresemblanceoftheenergytothe(2⁺)→⁰⁺^transition⁽¹³¹¹ keV) in the neighboring N=^{82 nucleus} ¹²⁸^{Pd [10].} ^Concerning the 422-keV transitionthat de-excitesthe isomeric state, E3 and higher-multipole possibilities can be virtually ruled out because theirstrengthswouldbeunlikelyenhancedcomparedtothetran- sitionsknowninthisregion(seeTable2inRef. [18]).Meanwhile, asingle de-excitationof422keVwithan E1,M1,or E2 multipolarity wouldnot resultinsucha long-livedisomeric state.Conse- quently, the422-keV transitionisexpectedto have M2 character witha reducedtransitionprobability of9.6(15)×¹⁰⁻²

μ

²_Nfm²= 2.3(4)×¹⁰⁻³ ^W.u., ^which ^is ^emitted ^from^the (19/2⁺) isomeric statetothe(15/2⁻)state.

Here, it is to be noted that the possible existence of a low- energy (unobserved) transition above the 1718-keV level as de- excitingthe39- μsisomericstatecanbeexcludedforthefollowing reasons:Inthisscenario,thepresumednon-isomeric stateat1718 keVisexpectedtohave19/2⁻,whichdecaystothe(15/2⁻)state at 1296 keVvia an E2 transition, similar to the decay sequence observedfor¹²⁵Pd.Assuminganobservationlimitof20countsfor anexpected

γ

-raypeakintheion-

γ

correlatedspectrumshownin Fig.1(e),dependingonconversion,limitsonthetransitionenergy canbedeterminedfordifferentmultipolaritiesλ.Regardlessofthe transitionenergy, the39- μs isomeric-decaytransitionis unlikely toproceedwithλ≥^{3 and}λ=^{1 on}âccountôf^the^same^reasonâs the one concerningthe transitionstrengths discussedinthe previous paragraph.Provided thatthe unobserved transitionhasM2 multipolarity, the transitionenergywould haveto be lower than 90 keVwith the reducedtransitionprobability ofthe orderof 1

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Fig. 4.Comparisonbetweenexperimentalandcalculatedlevelenergiesinneutron-richPdisotopes.Theexperimentalvaluesforthe¹²⁶PdlevelsaretakenfromRefs. [10,11], whilethosefor¹²⁵^,¹²⁷Pdarefromthepresentwork.SMrepresentsashell-modelcalculationperformedwithconsideringaneutroncross-shellexcitation(seetext).

Table 2

ExperimentalandtheoreticalB(σλ)valuesfortheselectedtransitionsin^APdiso- topes.

A Transition σλ B(σλ)[W.u.]

Exp. SM

125 23/2⁺→¹⁹/2⁺₂ E2 3.47(9) 5.2

23/2⁺→19/2⁺₁ E2 – 1.1×10⁻⁷

126 7⁻→5⁻₂ E2 2.13(14) 5.7

7⁻→⁵⁻1 E2 – 3.9×¹⁰⁻⁹

127 19/2⁺→¹⁵/2⁻ M2 2.3(4)×¹⁰⁻³ ⁷.6×¹⁰⁻³

W.u.orlarger. Suchan unhindered M2 transition,which exceeds arecommendedupperlimitofthetransitionstrength [27],hardly occursintheregionofinterest.IftheisomericdecayisofE2 char- acterfroma 23/2⁻ state, anupperlimit ofthetransitionenergy wouldbe75keVforitnottohavebeenobserved.Forsuchalow- energytransition, the B(E2)value fromthe39- μsisomeric state is estimatedto be in the order of 0.01−⁰.1 W.u., which could be possible as observed for the (8⁺)→(6⁺) isomeric transition in¹²⁸Pd [10].However, if a 23/2⁻ state were isomeric, itwould prefer to decay via a fast E1 transition to a lower-lying 21/2⁺ level,which is predicted by a shell-model calculation as will be discussedlater,ratherthanthenearby19/2⁻state.Thus,thepos- sibilityofalow-energyisomeric-decaytransitioncanberuledout foranymultipolarities,supportingthe(19/2⁺)assignmentforthe 39- μsisomericstateat1718keVrelativetothe(11/2⁻)level.

In order to understand systematically the level properties of theneutron-richPdisotopestowards N=^82,shell-modelcalculations basedon the extended pairing plus quadrupole-quadrupole forces combined with monopole corrections (EPQQM) [28] have beenperformedfor¹²⁵^,¹²⁶^,¹²⁷Pd. Withthedoubly magic nucleus 78Niastheclosedcore,themodelspaceconsideredincludesfour orbits in the Z =²⁸−^{50 major} ^shell ând ^the ^g7/2, d₅_/₂ orbits above the Z =^{50 shell} ^gap ^for ^protons, ând ^five ôrbits ⁱⁿ ^the N=⁵⁰−^{82 major}^shellând^the ^f7/2,p3/2orbitsabovetheN=⁸² shellgapforneutrons.Theproton/neutronsingle-particleenergies, effectivechargesandg-factors,andtheparametersoftheEPQQM Hamiltonian employed in the presentcalculations are consistent withthoseadopted inthe previous works [29–32].The observed andcalculated level energies are compared in Fig. 4, where the columnsmarkedwithSMexhibit theresultsofalarge-scaleshell modelthatallowstheexcitationofaneutronacrosstheshellgap of N=^82. ^The ^measured ând ^calculated ^values ôf ^the ^reduced transitionprobabilitiesfortheselectedtransitionsaresummarized inTable2.

As mentioned earlier,experimentally there remains a possible spin-parityassignmentof23/2⁺→¹⁹/2⁺ or25/2⁺→²¹/2⁺ for the108-keVtransitiondeexcitingtheisomericstatein¹²⁵Pd.How- ever,theyrast25/2⁺levelisunlikelytobeisomericincomparison with the shell-modelcalculation, which predicts that the energy difference between the 25/2⁺ and 21/2⁺ states is much larger than the observed transition energy, as shown in Fig. 4. Conse- quently, the excited states at 1697 and 1805 keV in ¹²⁵Pd are assignedspinsandparitiesof(19/2⁺)and(23/2⁺),respectively.

Forthehigher-lyinglevelsin¹²⁵Pd,theshell-modelcalculation predicts that thereare two 19/2⁺ statesbelowan excitation energy of 2 MeV, as indicated with different colors in Fig. 4. The ﬁrst 19/2⁺ (hereinafter denoted by 19/2⁺₁) state is predicted to involve predominantly a two-proton-hole excitation

π

(g⁻₉_/¹₂p⁻₁_/¹₂) together with an inactive proton-holepair

π

(g₉⁻_/²₂)₀+, coupled to an active neutron hole in the h₁₁_/₂ orbit (and a neutron-hole pair coupled tospin zero).Meanwhile, the 19/2⁺₂ state is domi- natedby neutron-holeexcitationsofthetype (

ν

⁻³)₁₉_/₂+,suchas

ν

(h⁻₁₁²_/₂d⁻₃_/¹₂),

ν

(h⁻₁₁²_/₂s⁻₁_/¹₂),and

ν

(h⁻₁₁²_/₂g⁻₇_/¹₂),coupledtoaninactive protoncomponent,

π

(g⁻₉_/⁴₂)0⁺ or

π

(g₉⁻_/²₂p⁻₁_/²₂)0⁺. Thus,the proton andneutronexcitationswithintherespectivemajorshellsaresug- gestedtocompetewitheachotherin¹²⁵Pd.

Accordingtothepresentshell-modelcalculationfor¹²⁵Pd,the majorcomponentsofthe23/2⁺ wavefunctiondiffersigniﬁcantly fromthoseofthe19/2⁺₁ state,resultinginastronglyhinderedE2 transition,seeTable2.Ontheotherhand,verysimilarwavefunc- tions arepredictedforthe23/2⁺ and19/2⁺₂ statesof¹²⁵Pd.The factthatthemeasuredB(E2)valuefortheisomericdeexcitationis fairly consistentwiththecalculated B(E2;²³/2⁺→¹⁹/2⁺₂)value indicates that both theexperimental (23/2⁺) and (19/2⁺) levels are dominated by the neutron excitations, as argued in the last paragraph.A candidateforthe19/2⁺₁ shell-modelstate,which is dominatedbytheprotonexcitations,hasnotbeenidentiﬁedinthe currentexperiment.

Similardecaypatterns aresuggestedtotake placeintheone- neutronneighbor¹²⁶Pd.AscomparedinTable2,theexperimental B(E2) value for the (7⁻)→(5⁻) transition [10] is well repro- ducedby SM giventhe E2 transition towards the 5⁻₂ level,thus suggesting that the calculated 5⁻₂ level corresponds to the (5⁻) state observed at 2023 keV [10]. In contrast, the 7⁻→⁵⁻₁ ^de- excitation is calculated to be extremely hindered,similar to the aforementioned23/2⁺→¹⁹/2⁺₁ transitionin¹²⁵Pd.Analyzingthe shell-modelwavefunctions,itcanbefoundthatthemainconﬁgu- rationsofthe5⁻₁_,₂and7⁻ statesin¹²⁶Pdarealmostequivalent to

(6)

Fig.4.The21/2⁺shell-modelstatehasalmostthesameconﬁgura- tionasthe19/2⁺isomericstatein¹²⁷Pd.Thewavefunctionofthe 15/2⁻state,towhichthe19/2⁺ isomerdecays,consistspredom- inantlyofthe

π

(g⁻₉_/⁴₂)⊗

ν

(h⁻₁₁¹_/₂)component.Hence,an M2 decay can not proceed between their main conﬁgurations. Within the Z=²⁸−^{50 major}^shell,^an ^{M2 decay}^can^take ^place^through^the

π

f5/2→

π

g9/2 transition. It is therefore expectedthat the large hindrance of theorder of 10⁻³ W.u.(see Table 2) is ascribed to thesmall admixture ofthe

π

(g⁻₉_/³₂f₅⁻_/¹₂)⊗

ν

(h⁻₁₁¹_/₂)component in the19/2⁺ isomericstate.

It is worth mentioning finally about the evolution of single- particle levels in thisneutron-rich region and its impact on the N=^{82 shell}^closure,^whichîsâlso^crucial^forâ^betterunderstand- ing of the r-process nucleosynthesis [13,14]. In Ref. [31], large- scaleshell-modelcalculations, whichhavebeendoneinthesame framework as that adopted in the present work, suggested that thesizeoftheN=^{82 shell}^gap^decreases^gradually^with^decreas- ingprotonnumberfrom48(¹³⁰Cd)to36(¹¹⁸Kr)onaccountofthe dynamiceffectofthemonopoleinteractionbetweenthe

π

g₉_/₂and

ν

h11/2 orbitals. Since the¹²⁵^,¹²⁷Pd statesdiscussedabove consist of these high-j orbits, the experimental results obtained in this work can serve asa stringent benchmark for testingshell mod- els toforeseea possible N=^{82 shell} ^quenchingⁱⁿ ^exotic^nuclei, whicharestillinaccessibleforspectroscopicstudy.

Toconclude,spectroscopicstudiesof¹²⁵Pdand¹²⁷Pdhavebeen performedatRIBF,andaccordingly,wehaveprovidedfortheﬁrst time experimental information on the excited level structure of these neutron-rich nuclei, which have triple- and single-neutron vacancies relative to the N =82 closed-shell nucleus ¹²⁸Pd. In 125Pd, a previously unreported isomeric state with a half-life of 144(4) ns was assigned tentatively a spin and parity of 23/2⁺ based on the results ofthe

γ

-ray intensitybalance analysis and the measured transitionstrengths with the aid of a shell-model calculation. This isomerand the lower-lying (19/2⁺) states were interpretedasbeingascribedpredominantlytothree-neutron-hole excitations within the N=⁵⁰−^{82 major} ^shell. ^Meanwhile, ^the (19/2⁺) isomer identiﬁed withT1/2=³⁹(6) μs in ¹²⁷Pd was ex- pectedto involvethe proton-holeexcitation

π

(g⁻₉_/³₂p⁻₁_/¹₂) coupled toa neutron holeinthe h₁₁_/₂ orbit. Thus,it turned out thatthe (19/2⁺) states observed atalmost the same excitation energy in

NRF-2016R1A5A1013277andNRF-2013M7A1A1075764,theSpan- ish Ministerio de Economía y Competitividad under contract FPA2017-84756-C4-2-P, the European Commission through the Marie Curie Actions call FP7-PEOPLE-2011-IEF (Contract No.

300096), German BMBF under Contract No: 05P12PKFNE, JSPS KAKENHI GrantNo. 24740188 and 25247045,the NationalNatu- ral Science Foundation of China (Nos. 11505302, 11575112), the National Key Program for S&T Research and Development (No.

2016YFA0400501),andSTFC(UK).

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