Evidence of octupole-phonons at high spin in $^{207}$Pb

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Evidence of octupole-phonons at high spin in

207

_Pb

D. Ralet, E. Clément, G. Georgiev, A.E. Stuchbery, M. Rejmund, P. van

Isacker, G. de France, A. Lemasson, J. Ljungvall, C. Michelagnoli, et al.

To cite this version:

D. Ralet, E. Clément, G. Georgiev, A.E. Stuchbery, M. Rejmund, et al..

Evidence of

octupole-phonons at high spin in

207

_Pb.

_{Physics Letters B, Elsevier, 2019, 797, pp.134797.}

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Evidence

of

octupole-phonons

at

high

spin

in

207

Pb

D. Ralet

a

,

b

,

E. Clément

b

,

∗

,

G. Georgiev

a

, A.E. Stuchbery

c

,

M. Rejmund

b

,

P. Van Isacker

b

,

G. de France

b

,

A. Lemasson

b

,

J. Ljungvall

a

,

C. Michelagnoli

b

, A. Navin

b

,

D.L. Balabanski

d

,

L. Atanasova

u

, A. Blazhev

g

,

G. Bocchi

e

,

ab

,

R. Carroll

f

,

J. Dudouet

h

,

E. Dupont

a

,

B. Fornal

i

,

S. Franchoo

aa

, C. Fransen

g

,

C. Müller-Gatermann

g

, A. Goasduff

k

,

A. Gadea

j

, P.R. John

t

,

k

,

D. Kocheva

v

,

T. Konstantinopoulos

a

,

A. Korichi

a

,

A. Kusoglu

l

,

S.M. Lenzi

k

,

S. Leoni

e

,

ab

,

R. Lozeva

a

,

m

,

A. Maj

i

,

R. Perez

j

, N. Pietralla

t

,

C. Shand

f

,

O. Stezowski

h

, D. Wilmsen

b

,

D. Yordanov

aa

,

D. Barrientos

o

,

P. Bednarczyk

i

,

B. Birkenbach

g

,

A.J. Boston

p

,

H.C. Boston

p

,

I. Burrows

q

,

B. Cederwall

n

, M. Ciemala

i

,

J. Collado

r

, F. Crespi

e

,

D. Cullen

s

,

H.J. Eberth

g

,

J. Goupil

b

, L. Harkness

p

,

H. Hess

g

,

A. Jungclaus

x

, W. Korten

w

,

M. Labiche

q

,

R. Menegazzo

k

,

D. Mengoni

k

,

B. Million

e

,

J. Nyberg

y

,

Zs. Podolyák

f

,

A. Pullia

e

,

B. Quintana Arnés

z

,

F. Recchia

k

,

P. Reiter

g

,

F. Saillant

b

,

M.D. Salsac

w

,

E. Sanchis

r

,

C. Theisen

w

, J.J. Valiente Dobon

o

,

O. Wieland

e

a_{CSNSM,Univ.Paris-Sud,CNRS/IN2P3,UniversitéParis-Saclay,F-91405Orsay,France} b_{GANIL,CEA/DRF-CNRS/IN2P3,Bd.HenriBecquerel,BP55027,F-14076Caen,France} c_{DepartmentofNuclearPhysics,AustralianNationalUniversity,Canberra, ACT2601,Australia}

d_{ELI-NP,HoriaHulubeiNationalInstitute forR&DinPhysicsandNuclearEngineering,077125Magurele,Romania} e_{InstitutoNazionalediFisicaNucleare,Milano,I-20133Milano,Italy}

f_{DepartmentofPhysics,UniversityofSurrey,Guildford,GU27XH,UnitedKingdom} g_{InstitutfürKernphysik,UniversitätzuKöln,D-50937Cologne,Germany}

h_{UniversitédeLyon,UniversitéLyon-1,CNRS/IN2P3,UMR5822,IPNL,F-69622VilleurbanneCedex,France} i_{InstituteofNuclearPhysics(IFJ),PAN,31-342Krakow,Poland}

j_{InstitutodeFísicaCorpuscular,CSIC-UniversidaddeValencia,E-46071Valencia,Spain}

k_{DipartimentodiFisicaeAstronomia,UniversitàdegliStudidiPadovaandINFN,SezionediPadova,I-35131Padova,Italy} l_{DepartmentofPhysics,FacultyofScience,IstanbulUniversity,Vezneciler/Fatih,34134,Istanbul,Turkey}

m_{IPHC/CNRS-UniversityofStrasbourg,F-67037Strasbourg,France} n_{KTHRoyalInstituteofTechnology,10691Stockholm,Sweden}

o_{INFN,LaboratoriNazionalidiLegnaro,ViaRomea4,I-35020Legnaro,Italy}

p_{OliverLodgeLaboratory,TheUniversityofLiverpool,OxfordStreet,LiverpoolL697ZE,UnitedKingdom} q_{STFCDaresburyLaboratory,Daresbury,WarringtonWA44AD,UnitedKingdom}

r_{DepartmentofElectronicEngineering,UniversityofValencia,E-46100Burjassot(Valencia),Spain}

s_{SchusterBuilding,SchoolofPhysicsandAstronomy,TheUniversityofManchester,ManchesterM139PL,UnitedKingdom} t_{InstitutfürKernphysik,TechnischeUniversitätDarmstadt,D-64289Darmstadt,Germany}

u_{DepartmentofMedicalPhysicsandBiophysics,MedicalUniversity-Sofia,1431Sofia,Bulgaria} v_{UniversityofSofia,Sofia,Bulgaria}

w_{IRFU,CEA/DRF,CentreCEAdeSaclay,F-91191Gif-sur-YvetteCedex,France} x_{InstitutodeEstructuradelaMateria,CSIC,E-28006Madrid,Spain} y_{DepartmentofPhysicsandAstronomy,UppsalaUniversity,Uppsala,Sweden}

z_{LaboratoriodeRadiacionesIonizantes,UniversidaddeSalamanca,E-37008Salamanca,Spain} aa_{InstitutdePhysiqueNucléaire,CNRS/IN2P3-UniversitéParis-Sud,F-91406Orsay,France} ab_{DipartimentodiFisica,UniversitadegliStudidiMilano,I-20133Milano,Italy}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received2July2019 Accepted19July2019 Availableonline24July2019

A lifetime measurement ofthe 19/2− state in 207_{Pb has been performed using the Recoil Distance}

Doppler-Shift(RDDS)method.Thenucleiofinterestwereproducedinmulti-nucleontransferreactions inducedby a208_{Pbbeamimpingingona}100_{Mo enrichedtarget. Thebeam-likenuclei weredetected}

*

Correspondingauthor.

E-mailaddress:clement@ganil.fr(E. Clément).

https://doi.org/10.1016/j.physletb.2019.134797

2 D. Ralet et al. / Physics Letters B 797 (2019) 134797 Editor:D.F.Geesaman Keywords: AGATAspectrometer γ-Raytracking VAMOS++spectrometer Plungerdevice Nucleardeformation Octupolephonon

and identifiedintermsoftheiratomicmassnumberintheVAMOS++spectrometerwhiletheprompt

γ

rays weredetectedbytheAGATAtracking array.The measuredlarge reducedtransition probability

B(E3,19/2−→13/2+)=40(8)W.u.isthefirstindicationoftheoctupolephononathighspinin207Pb. Ananalysisintermsofaparticle-octupole-vibrationcouplingmodelindicatesthatthemeasuredB(E3)

value in207_{Pbiscompatiblewiththecontributionsfromsingle-phononandsingleparticle E3 aswell}

as E3 strengtharisingfromthedouble-octupole-phonon6+state,alladdingcoherently.Acrucialaspect of thecoupling model,namelythe strongmixing betweensingle-hole andthe phonon-hole states,is confirmedinarealisticshell-modelcalculation.

CrownCopyright©2019PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY license(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

Theoccurrenceofcollectivevibrations,whenalatticeofatoms ormoleculesoscillatesuniformly atasingle frequency forminga quantum-mechanicalphonon, isa well-knownphenomenon.Such vibrationscorrespond,inclassicalmechanics,towave-likenormal modes. Quantum-mechanical phonons,however, exhibit particle-like properties, too. The excitation spectra of several different many-body systems can be described as a superposition of ele-mentary excitation modes that are (approximately independent) fluctuationsabout equilibrium. There is a close relation between theinternalstructureofthesystemandthenatureofthese fluctu-ations,whichmayleadtodensityvibrationsorshapeoscillations. Innucleithecharacterofcollectivevibrationsfollowsfromthe ob-servationthatsome arespherical,likedoubly-magicnuclei,while others are deformed, like mostrare-earth nuclei. In an interme-diatesituationtheshapecanundergolargefluctuationsaboutone oftheequilibriumshapes.Incontrasttomolecules,thenuclear en-ergyscalesrelatedtovibrationalandsingle-particleexcitationsare ofthesameorder,andthustheir interweavinghasprofound con-sequences.

Doubly-magicnucleihaveasphericalequilibriumshape.Among them,the 208Pbisotope, with Z

=

82 protons and N

=

126 neu-trons,istheheaviestknowndoubly-magicnucleus.Itsfirst-excited state has been established to be of natural-parity octupole type,

J π

=

3−_c, at an excitation energy of Ex

(

3−c

)

=

2615 keV, about

800 keV lower than the neutron shell-gap energy at N

=

126, the index c stands for collective. The highly enhanced and col-lectivetransition connectingthe 3−c levelto the 0+ groundstate

has been measured to have a reduced transition probability of

B

(

E3

,

3−c

→

0+

)

=

34

.

0

(

5

)

W.u. [1],thatis,itexceedsby34times

theWeisskopfunitorsingle-particle estimate.The3−_c state is in-terpreted as a one-phononexcitation corresponding to a nuclear surfacevibrationofoctupolecharacterwhileitsmicroscopic struc-tureisunderstoodasthecoherentandcollectivesuperpositionof one-particle-one-hole (1p–1h) excitationsacross the neutron and protonshellgaps.

Providedthat this3−_c state representsthefirst phonon ofthe octupole vibration, it is expected that the double-octupole quar-tet

(

0+_c

,

2+_c

,

4+_c

,

6+_c

)

of two-phonon states exists at an energy of abouttwice Ex

(

3−c

)

[2].In thecaseofa fullyharmonicvibration,

allmembers ofthisquartet,andinparticularthe 6+_c level,decay totheone-phononstatewiththecharacteristicreducedtransition probability B

(

E3

,

6+_c

→

3−_c

)

=

2

×

B

(

E3

,

3−_c

→

0+

)

.Manyattempts havebeenundertakentoidentifythemembersofthetwo-phonon octupole quartet [3–11]. Candidates for the lower-spin members have been proposed [10,11] but the 6+_c member has not been identified asyet.Onthe basis ofa large-scale shell-model calcu-lation, including up to 2p–2h excitations, Brown [12] concluded thatthe6+c memberofthedouble-octupolequartetisfragmented.

Furthermore,hefoundthatthereare0+,2+,and4+stateswitha concentrated double-octupolestrength butdecayingvia weak E1

and E2 transitions, which in themselvesare not strongevidence forthespecialdouble-octupolenatureofastate.

In the nuclei neighboring 208Pb, with one valenceparticle or hole, the particle-octupole-phonon model favors strong coupling betweentheorbitals j1

=

l1

±

1

/

2 and j2

=

l2

±

1

/

2 if

|

j1

−

j2

|

=

|

l1

−

l2

|

=

3,preserving therelativeorientationofthespinand

or-bital angular momenta [13, (Vol. II, p. 419)]. In addition to the particle or hole states, several excitations have been found and interpretedasacollectiveoctupolephonon

|

3−c



coupledtoa

par-ticleorhole.Becauseofthestrongcouplingmentionedabove,such states are expected to mix i.e.

|

j(₁−1)



with

|

j(₂−1)

×

3−_c

;

J1

=

j1



and

|

j(₁−1)

×

3_c−

;

J2



with

|

j₂(−1)

×

6+c

;

J2



,the latterbeinga

par-ticle or hole coupled to a double-octupole phonon. Given this mixing, it has been suggested in Ref. [14], in analogy to the case of 147_{Gd [15], that the characteristic enhancement of the}

B

(

E3

,

6+_c

→

3−_c

)

valuein208Pb,shouldbereflectedinanenhanced

B

(

E3

,

J2

→

J1

)

valueintheodd-massnucleus.

The octupoleexcitationscoupled tothe low-spingroundstate in 207_{Pbhavebeeninvestigatedearlier [16,17].The 5}

_/

₂+ _stateat

2624 keV and 7

/

2+ state at 2662 keVhave been interpreted as membersofthelow-spin

ν

p−_1/1₂

× φ

1

(

3−c

)

multipletresultingfrom

weakcoupling.Thecorrespondingreducedtransitionprobabilities have been measured as B

(

E3

,

5

/

2+

→

1

/

2

−)

=

30

(

3

)

W.u. and

B

(

E3

,

7

/

2+

→

1

/

2

−)

=

28

(

2

)

W.u. [17].The smallpositiveenergy shifts,

+

9 keVand

+

47 keVrelativetoEx

(

3−c

)

,canbenoticedthat

couldberelatedtotheblockingofthe

ν

p1/2 orbital.

For207_{Pb,amongtheavailableneutronorbitals, p}

1/2,p3/2, f5/2,

f7/2, h9/2 and i13/2, forming a major shell 82

≤

N

≤

126, only

the j1

=

ν

i13/2 and j2

=

ν

f7/2 satisfy the strong coupling rule,

describedabove.Thecorrespondingstates,13

/

2+ and7

/

2−, dom-inantlyof single-holecharacter, are well studied [18].The 19

/

2− stateandthecorresponding2485keVtransitiontothe13

/

2+state were assignedto207_{Pbby Schrammetal. [6],andthe E3}

charac-terofthetransitionwas recentlydeterminedbyShandetal. [19]. The 13

/

2+, 7

/

2−, and 19

/

2− states were analyzed in terms of particle-octupole-vibration coupling in Ref. [14] using the exper-imentally known level energies and assuming the dominance of theabove-mentionedorbitals.Thiscouplingschemeisdepictedin Fig. 1. In panel (a) the one-phononstate is illustrated for 208Pb. Thecoupledanduncoupledstatesin207_{Pbareshowninpanels(b)}

and(c),respectively.Thewave functionsofthe13

/

2+ and19

/

2− statesare representedassingle-hole statesandsingle-hole states coupledtoasingle ordoubleoctupolephononin208Pb.The coef-ficients

α

i and

β

i,asshowninpanel(d)ofFig.1,dependcrucially

Fig. 1. Illustrationoftheparticle-octupole-vibrationcouplingmodel:(a)Thelowest octupole-vibrationalphononof208_{Pb,(b)selectedstatesresultingfromthe}

particle-octupole-vibrationcouplingin207_{Pb,(c)uncoupled(unperturbed)statesin}207_Pb,

(d)wavefunctionsofthe13/2+and19/2−statesintheparticle-octupole-vibration couplingmodel.TheenergiesoftheknownstatesaregiveninMeV.

ofh

=

0

.

710 MeV.Finally,itcanalsobecalculatedwiththe shell-modelexpression,wheretheparticle-holematrixelementscanbe obtainedfromparticle-particlematrixelements usingthePandya transformation [21] h

=



1 2





kk aν_kk



ν

f7/2

ν

i−131/2

;

3−

| ˆ

Vνν

|

jνkj_ν−k1

;

3−



+



ll aπ_ll



ν

f7/2

ν

i−₁₃1_/2

;

3−

| ˆ

Vνπ

|

jπlj_π−1_l

;

3−





,

which gives the separate contributions of the neutron-neutron (

νν

) and neutron-proton (

νπ

) interactions. The sums are over the neutron and proton particle-hole excitations that constitute the octupole phonon. The amplitudes aν_kk and aπll are obtained

microscopically in a shell-model calculation for 208_{Pb with 24}

single-particle energies takenfrom Ref. [22] andwith the realis-ticnucleon-nucleoninteractionasgiveninRef. [23].Althoughthe off-diagonalmatrixelementsintheexpressionforh generallyare smallandofvaryingsign,multipliedwithamplitudestheyact co-herently, giving rise to a large mixing matrix element with the valueofh

=

0

.

655 MeV.Thisisthehallmarkofcollectivebehavior, whichtherefore is found to be presentin a realistic shell-model description. The consistency of the values forthe mixing matrix elementderivedwiththreetotallydifferentapproacheslends sup-porttothehole-octupole-phononinterpretationofstatesin207Pb. Inthefollowingtheexperimentalvalueofh

=

0

.

725 MeVisused.

Theexperimental value ofh

=

0

.

725 MeVwas determined as-suming the contribution of the collective vibrational-phonons to the 13

/

2+ and19

/

2− states.Due tothe presenceof thespecific orbits, the f7/2 and i13/2 for 207Pb, a strong

particle-octupole-vibrationcouplingisexpectedtoattractanadmixtureofthe dou-ble octupole state to the low-lying yrast 19

/

2− state, that can decaybythecharacteristicenhanced E3 transition.Themainpart of the double octupole state remains however in the higher ly-ing 19

/

2−, which could be fragmented and havedifferent decay modes. The negative energy shiftof

−

130 keV for the2485 keV transition between the 19

/

2− and 13

/

2+, relative to Ex

(

3−c

)

, is

thereforeunderstoodasresultingfromthemixingofone-phonon statewiththetwo-phononstate.ThelargeB

(

E3

,

19

/

2−

→

13

/

2+

)

value, characterizing the contribution of octupole phonons, has howevernot been measured.A predicted B

(

E3

,

19

/

2−

→

13

/

2+

)

valueisobtained(seediscussionbelow)thatisenhancedas com-paredto B

(

E3

,

3−_c

→

0+

)

in 208_{Pb, duetothe strongmixingand}

thecoherentcontributionofthesingle-phononandsingle particle andthe double-octupole-phononstrengths. The aim ofthiswork was toprovidetheexperimentalevidenceofthecollectivenature ofthe E3

(

19

/

2−

→

13

/

2+

)

transitionby meansoflifetime mea-surement. The knowledge of the strength of this transition will allow toprovethe hypothesisofthe strongcouplingschemeand quantifythecontributionsofone-phononandtwo-phononstates; ultimatelyitmayprovetheexistenceofthelatter.

The measurement of sub-nanosecond lifetimes of high spin states in nuclei near 208_{Pb is very challenging. These high spin}

statescanbe efficientlypopulatedinmulti-nucleontransfer reac-tions of heavy ions atthe energies near the Coulomb barrier [6,

14,23]. The excited products of interest are distributed near the grazing angle, far away from the beam axis, in contrast to fu-sionreactions.Multi-nucleontransfer reactionsproducehundreds ofnucleiatthesametime,thereforesomeselectionofthereaction productsisrequired.Itcanbeobtainedusing

γ

−

γ

coincidences orusing a massanalyzeror magneticspectrometer to determine the mass number. The direct measurement of the atomic num-ber at Z

∼

82 for low energy ions is not possible today. Mass analyzers havetypically low acceptanceandare restrictedto op-eration near 0◦. Further, the use of the plunger technique, for measurement of sub-nanosecond lifetimes of states populated in multi-nucleontransferreactions,requiresan event-by-event mea-surementoftherecoilvelocityvector. Inthisworkthe VAMOS++ spectrometer was used to identify, for the first time, the atomic massnumberofthelead-like ejectilesatenergies rangingfrom1 to2 MeV/u.The requiredmassresolutionwas reachedonly fora partof the focalplane setup (

∼

15%),which resultedin reduced statistics.In thisletterwe presenttheresultsofthe firstlifetime measurementofthe J π

=

19

/

2− levelin207Pb, provingthe one-octupolephononnatureofthisstateandsuggestingtheexistence ofadouble-octupole6+_c statein208Pb.

The experimentwas performedattheGrand Accélérateur Na-tional d’Ions Lourds, Caen, France using the RDDS method [24], in combinationwith a multi-nucleontransfer reaction in inverse kinematics.A208Pbbeamat6

.

25 A MeVimpingedonanenriched 1.9 mg/cm2_-thick 100_{Mo target followed by a 2 mg/cm}2_{-thick Ni}

degrader. Beam-likereaction products were detected and identi-fiedonan event-by-eventbasisinthelarge-acceptanceVAMOS++ spectrometer [25,26].Theopticalaxisofthespectrometerwas po-sitionedat26o_{withrespecttothebeamaxis,atthegrazingangle}

ofthebeam-likeproducts.TheVAMOS++spectrometerallowedthe identificationofthereactionproductsinmass-over-charge( A

/

Q )

andatomiccharge( Q ),andprovidedthevelocityvector(V )



nec-essaryfortheDopplercorrection.

mass-4 D. Ralet et al. / Physics Letters B 797 (2019) 134797

Fig. 2. Two-dimensional identificationmatrixobtainedwith the VAMOS++ spec-trometer.Nucleiwithatomicmassnumber A=206 andA=208 arehighlighted forseveralchargestatesmeasuredinthespectrometer.Duetothelowvelocityof therecoils,anelementidentification(Z)isnotpossible.

Fig. 3.γ-Ray spectrumgatedonmassA=207 atthetarget-to-degraderdistanceof 75 μm.ThetransitionsmarkedwithacirclecorrespondtotheCoulombexcitationof the100_{Motarget,Dopplercorrectedusingthevelocityvectoroftheheavypartner.}

over-charge ratio as a function of the atomic-charge state. Mass resolutionof

∼

0

.

9

/

208 (FWHM)was obtained. The analysis pro-cedureisfurtherdetailedinRef. [27].Excited-statehalf-lifes(T1/2)

weremeasuredusingtheRDDStechniquewiththeplungerdevice oftheUniversityofCologne [28].Doppler-correctedprompt

γ

rays, emitted beforeand afterthe Ni degrader foil,were measured by theHPGeAGATAtrackingarray [29,30] placedatbackwardangles inacompactgeometry(target-to-detectordistanceof148.5 mm). The

γ

-rayenergyDopplercorrectionwasperformedusingthe re-coilvelocity(V ),



obtainedfromthe VAMOS++spectrometer, after theNidegrader,andthepositionofthefirst

γ

-rayinteraction ob-tainedfromtheOrsayForwardTrackingalgorithmsusingstandard parameters [31].

Fig. 3shows the Doppler-corrected

γ

-ray spectrum measured in the AGATA spectrometer, selected with mass A

=

207 in the VAMOS++spectrometerforthe75 μmtarget-to-degraderdistance. Transitionsat570 keV,898 keV,1770 keV,and2485 keVbelong to207_{Pb.The2067 keVlinecorrespondstotheshiftedcomponent}

ofthe short-lived (T1/2

=

660 fs [32]) 7

/

2+₁ state decayin 207Pb

tothe 5

/

2−₁ state. The transitionat2615 keVcorresponds tothe 3−_c state decayin208Pb;itisa contaminantfromtherandom co-incidenceresultingfromtheinelasticscatteringofthebeam. The transitions marked with a circle correspond to the 100_{Mo decay}

followingCoulombexcitation,Dopplercorrectedusingthevelocity vectorofthebeam-likeion,measuredafterthedegrader.

Fig.4showsDopplercorrected

γ

-ray spectrameasuredinthe AGATA spectrometer, selected onmass A

=

207 in theVAMOS++ spectrometer,forfivetarget-to-degraderdistances(75 μm,200 μm, 625 μm,1000 μm,and2000 μm)fortherelevanttransitionsused forthe lifetime measurement. Since the Doppler correction used

thevelocitymeasuredafterthedegrader,theunshifted(U) compo-nentcorrespondstotheeventswherethe

γ

-raywasemittedafter thedegrader andshifted (S)totheeventswheregamma-raywas emitted beforethedegrader. Thevelocity ofionsdetected in VA-MOS++rangedfrom14 to22 μm/ps,andthedecreaseofthe veloc-ityinthedegraderwastypicallyabout13%.Eventswitharelative angle greater than 138◦, between the

γ

-ray and the outgoing-particlevelocityvector,wereselectedtoenhancetheclear separa-tionbetweentheshifted(S)andunshifted(U)componentsofthe

γ

-raytransitions.TheparametersrequiredfortheDoppler correc-tionusingtheAGATAandVAMOS++spectrometerswereobtained using the inelastic scatteringof the 208_{Pb in a data set without}

thethick Nidegrader.OntheleftpanelofFig.4,thetwo compo-nents, shifted (S) at2454 keV andunshifted(U) at2485 keV, of the19

/

2−

→

13

/

2+transitionin207Pbareobserved.

Within the RDDS technique, a decay curve was constructed from the intensities of the unshifted (U19/2−) component of the

19

/

2−

→

13

/

2+ transitionnormalizedto the7

/

2−₁

→

5

/

2−₁ tran-sition in 207Pb as a function of the target-to-degrader distance. The7

/

2−₁ state,atanexcitationenergyof2339.9 keV,decaysbya

γ

-raytransitionof1770.2 keVtothefirst-excited5

/

2−₁ state.Only theshiftedcomponent(S7/2−)wasobservedduetotheveryshort

lifetime of the 7

/

2−₁ state (see rightpanel of Fig. 4). The

γ

-ray transition intensities were determined assuming forall distances thesamewidthandcentroidforthepeaks.Thenormalization us-ingthesumoftheshifted(S19/2−)andunshifted(U19/2−)

compo-nentsofthe2485 keVtransitionisinagreement,withinthe statis-ticaluncertainties,withthenormalizationusingthe7

/

2−₁

→

5

/

2−₁ transition.Theformerhasahigherstatisticalerrorduetotheweak intensity of the shifted (S19/2−) component. In the following,all

quotederrorsarestatistical.Inagreementwiththelevelschemeof

207_{Pb [19],}

_γ

_-

_γ

_{-coincidenceanalysisshowedtwotransitionsabove}

the 13

/

2+ statepopulatingthe 19

/

2− state:the 21

/

2−

→

19

/

2− and 23

/

2−

→

19

/

2− transitions with the respective energies of 592 keV and749 keVandfeeding of20

(

6

)

% and37

(

5

)

%, respec-tively.Thesestates,havingaverylongeffectivelifetime,aretaken into account in the analysis, following the method described in Ref. [24].The lifetimewasextractedfromthefirstthreedistances where the RDDS analysis showedmaximum sensitivity. The life-timeanalysisprocedurewasverifiedusingtheknowndecayofthe 2+₁ state in 206_{Pb (T}

1/2

=

8

.

30

(

24

)

ps [33]). The deduced value

from thisexperimentis T1/2

=

12

(

3

)

ps, takinginto account the

feedingsfromthe3+ and4+states,inreasonableagreementwith thepublishedvalue.

The result of the lifetimeanalysis forthe 19

/

2− state decay-ingbythe2485keVtransitionin207PbispresentedinFig.5.The deducedvalue of T1/2

=

20

(

4

)

ps, correspondsto B

(

E3

,

19

/

2−

→

13

/

2+

)

=

40

(

8

)

W.u., assuming a branching ratioof 100%. When compared with the B

(

E3

,

3−_c

→

0+

)

=

34

.

0

(

5

)

W.u. in 208Pb, it isa clearfirstindication thatthe octupole-vibrationsplayan im-portant role inthe natureofthe 19

/

2− state. Further,the differ-entcontributionsto theoctupolestrength canbeevaluated.With the wave functions of the 19

/

2− and 13

/

2+ states as given in Fig. 1(d) and with the two-to-one-phonon strength B

(

E3

,

6+_c

→

3−c

)

=

2

×

B

(

E3

,

3−c

→

0+

)

,thereducedtransitionmatrixelement

Fig. 4. Dopplercorrectedγ-rayspectraformass A=207 asafunctionofthetarget-to-degraderdistance.Left:the19/2−→13/2+transitionin207_{Pb.Right:the7}

/2−1→

5/2−1 transitionin207Pbusedfornormalization.

Fig. 5. Meanlifetime(τ)determinationofthe19/2−stateof207_{Pb.Thecontinuous}

redlinecorrespondstothefittedmeanvalueofτ asthedashedlinescorrespond toits1σerrorbar.

Thecoefficients

α

and

β

can be takenfromthe analysisin [14]. WithWoods-Saxonradial wave functionsandan effectivecharge

eeff

=

1

.

35

(

45

)

e, one obtains the single-hole reduced matrix

el-ement



ν

f₇−_/1₂

E3

ν

i₁₃−1_/2



= −

359

(

119

)

e fm3 _{[14]. The errors}

associated with the effective charge and the reduced transition matrix element follow from the experimental precision of the

B

(

E3

,

15

/

2−

→

9

/

2+

)

in209Pb [34].Thefirsttermintheequation, proportionalto

α

19

α

13multipliedwiththecollectiveE3 matrix

el-ement,providesthedominantcontribution,withcorrections

stem-ming from the two-to-one-phonon 6+_c

→

3−_c transition (second term, proportional to

β

19

β

13) andthesingle-hole

ν

i−131/2

→

ν

f−

1 7/2

transition(thirdterm,proportionalto

α

19

β

13).

Threedifferentscenarioscanbeconsideredalongwiththe cal-culatedreducedtransitionprobability(inparentheses):(i) Neglect-ing the strong coupling and the two-phonon contribution using

α

19

=

α

13

=

1 and

β

19

= β

13

=

0 (34.0(5) W.u.) (ii) Neglecting

the two-phonon contribution using

α

19

=

1,

α

13

=

0

.

98,

β

19

=

0

and

β

13

= −

0

.

19 (37(2) W.u.) (iii) Considering all the

contribu-tions using

α

19

=

0

.

97,

α

13

=

0

.

98,

β

19

= −

0

.

25 and

β

13

= −

0

.

19

(40(2) W.u.). The errorsassociated withthe calculatedvalues re-sultfromthoseofB

(

E3

,

3_c−

→

0+

)

in208_Pbande

eff.Theobserved

strength andacomparisonwiththeabove calculatedvalues sug-gestan enhancementwithrespecttothe known B

(

E3

,

3−_c

→

0+

)

6 D. Ralet et al. / Physics Letters B 797 (2019) 134797

isamainsourceofuncertaintiesinthecalculations,wouldbe re-quired.

In summary, a large B

(

E3

,

19

/

2−

→

13

/

2+

)

=

40

(

8

)

W.u. re-ducedtransitionprobabilityhasbeenmeasuredin207Pbbasedon thelifetimemeasurementofthe19

/

2−stateusingtheRDDS tech-nique.Suchcollective characterindicatesthat thedominant com-ponentofthisstate isa single-holeexcitation coupledto the oc-tupolephononofthe208Pbcore.Theenergyloweringofthe2485 keV transitionin 207Pb, as compared to the 2615 keV transition in 208Pb, is consistent witha mixingwitha state containing the double-octupole-phononexcitation.The measuredreduced transi-tion probability is compatiblewitha contribution fromthe two-to-one-octupole-phonon E3 transition.Furtherinformationonthe double-octupole-phononstate can beobtainedby a moreprecise lifetimemeasurementofthe19

/

2− statein207Pborofthe corre-sponding21

/

2+statein209_{Pb,wherethe B}

₍

_E3

₎

_{waspredictedto}

be50 W.u. [14].Inaddition,amoreaccuratemeasurementofthe lifetimeofthe15

/

2− state in209_{Pbismandatoryto improvethe}

precisionoftheE3 effectivecharge.

TheauthorsaregratefulforthehelpoftheGANILstaffandof theAGATA collaboration. D. R. Chakrabarty isgratefully acknowl-edged forthe careful reading of the manuscript. This work was supportedbytheEuropeanUnionSeventhFrameworkthrough EN-SAR (Contract No. 262010) andpartlyfunded by the P2IO LabEx (ANR-10-LABX-0038) in the framework Investissements dávenir (ANR-11-IDEX-0003-01)managed bytheFrenchNationalResearch Agency (ANR). DLB is supported by the Extreme Light Infras-tructure Nuclear Physics (ELI-NP) Phase II, a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund - the Competitive-ness Operational Programme (1/07.07.2016, COP, ID 1334). This work was supported by the Bundesministerium für Bildung und Forschung under grant No. 05P18RDFN9. A.G and R.P were par-tially supported by Ministry of Science, Spain, under the Grants FPA2017-84756-C4 and SEV-2014-0398, and by the EU FEDER funds. A.E.S was partially supported by the Australian Research CouncilgrantNo.DP0773273.Thisworkwassupportedbythe Na-tionalScienceCenter(NCN),PolandunderHARMONIAcontractNo. 2016/22/M/ST2/00269.

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