Multi-quasiparticle sub-nanosecond isomers in $^{178}$W

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Multi-quasiparticle sub-nanosecond isomers in

178

_W

M. Rudigier, P.M. Walker, R.L. Canavan, Zs. Podolyák, P.H. Regan, P.-A.

Söderström, M. Lebois, J.N. Wilson, N. Jovancevic, A. Blazhev, et al.

To cite this version:

M. Rudigier, P.M. Walker, R.L. Canavan, Zs.

Podolyák, P.H. Regan, et al..

Multi-quasiparticle sub-nanosecond isomers in

178

_{W. Physics Letters B, Elsevier, 2020, 801, pp.135140.}

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Multi-quasiparticle

sub-nanosecond

isomers

in

178

W

M. Rudigier

a

,

∗

,

P.M. Walker

a

,

∗∗

,

R.L. Canavan

a

,

b

,

Zs. Podolyák

a

,

P.H. Regan

a

,

b

,

P.-A. Söderström

c

,

d

,

M. Lebois

e

,

f

,

J.N. Wilson

e

,

f

,

N. Jovancevic

e

,

f

,

A. Blazhev

g

,

J. Benito

h

,

S. Bottoni

i

,

M. Brunet

a

,

N. Cieplicka-Orynczak

j

,

S. Courtin

k

,

D.T. Doherty

a

,

L.M. Fraile

h

,

K. Hadynska-Klek

a

,

M. Heine

k

,

Ł.W. Iskra

i

,

j

,

J. Jolie

g

,

V. Karayonchev

g

,

A. Kennington

a

,

P. Koseoglou

c

,

d

,

G. Lotay

a

,

G. Lorusso

a

,

b

,

M. Nakhostin

a

,

C.R. Nita

l

,

S. Oberstedt

m

,

L. Qi

e

,

f

,

J.-M. Régis

g

,

V. Sánchez-Tembleque

h

,

R. Shearman

a

,

b

,

W. Witt

c

,

d

,

V. Vedia

h

,

K.O. Zell

g a_{DepartmentofPhysics,UniversityofSurrey,Guildford,GU27XH,UK}

b_{NationalPhysicalLaboratory,Teddington,Middlesex,TW110LW,UK}

c_{InstitutfürKernphysik,TechnischeUniversitätDarmstadt,Schlossgartenstrasse9,64289,Darmstadt,Germany} d_{GSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany}

e_{InstitutdePhysiqueNucléaire,CNRS-IN2P3,Univ.Paris-Sud,UniversitéParis-Saclay,91406OrsayCedex,France} f_{UniversitéParis-Saclay,15RueG.Clémenceau,91406OrsayCedex,France}

g_{InstitutfürKernphysikderUniversitätzuKöln,ZülpicherStrasse77,D-50937Köln,Germany} h_{UniversidadComplutense,GrupodeFísicaNuclearandUPARCOS,CEIMoncloa,E-28040Madrid,Spain} i_{DipartimentodiFisica,UniversitàdegliStudidiMilanoandINFNsez.Milano,I-20133,Milano,Italy} j_{InstituteofNuclearPhysics,PolishAcademyofSciences,PL-31-342Kraków,Poland}

k_{IPHCandCNRS,UniversitedeStrasbourg,F-67037Strasbourg,France}

l_{HoriaHulubeiNationalInstituteofPhysicsandNuclearEngineering(IFIN-HH),R-077125Bucharest,Romania} m_{EuropeanCommission,JointResearchCentre,DirectorateG,Retieseweg111,2440Geel,Belgium}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received4July2019

Receivedinrevisedform30September 2019

Accepted2December2019 Availableonline11December2019 Editor:D.F.Geesaman

We report onthe firstmeasurement ofthe half-livesof Kπ =11− and 12+ four-quasiparticle states intheeven-evennucleus178_{W.Thesub-nanosecondhalf-livesweremeasuredbyapplyingthecentroid} shiftmethodtodatatakenwithLaBr3(Ce)scintillatordetectorsoftheNuBallarrayattheALTOfacility inOrsay,France.Thehalf-livesofthesestatesonlybecameexperimentallyaccessiblebythecombination ofseveralexperimentaltechniques- scintillator fasttiming,isomer spectroscopywith apulsed beam, and theevent-by-eventcalorimetryinformation providedbytheNuBallarray.Themeasuredhalf-lives are476(44)ps and275(65)ps fortheIπ=11−and12+states,respectively.Thedecaytransitionsinclude weaklyhinderedE1 andE2 branchesdirectlytotheground-stateband,bypassingthetwo-quasiparticle states.Thisisthefirstsuchobservationforan E1 transition.Theinterpretationofthesmallhindrance hingesonmixingbetweentheground-statebandandthet-band.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The A

≈

180 region ofdeformed nuclei exemplifies the com-petitionbetweenindividual-particleandcollectivedegreesof free-dom[1].Akeyaspectisthattheprojectionoftheangular momen-tum,K ,onthenuclearsymmetryaxisisapproximatelyconserved, andthisgivesriseto K isomerswhenthechangein K -value,



K ,

*

Principalcorrespondingauthor.

**

Correspondingauthor.

E-mailaddresses:[email protected](M. Rudigier),[email protected]

(P.M. Walker).

exceeds themultipoleorder ofthedecayradiation,

λ

.Such tran-sitions are called“K -forbidden”,andthe degreeof forbiddenness is defined as

ν

= 

K

− λ

. An extreme case is the T1/2

=

31 y,

K π

=

16+isomerin178Hfatanexcitationenergyof2446keV[2], which is 989 keV below the K

=

0, Iπ

=

16+ collective rotation of theground-state band (GSB).The 31-y isomer hasa structure based on two broken nucleon pairs, i.e. it isa four-quasiparticle (4qp)state.

However, thecompetitionbetweenindividual-particle and col-lectiveexcitationschangesquicklywithnucleonnumber.In178W, forexample,withtwomoreprotonsandtwofewerneutrons,the longest-lived4qpstate(K π

=

15+)observedtodatehasahalf-life https://doi.org/10.1016/j.physletb.2019.135140

2 M. Rudigier et al. / Physics Letters B 801 (2020) 135140

ofjust30ns, andthere areother 4qp states(e.g. K π

=

11− and 12+)withhalf-livesthathavebeentooshorttomeasurein previ-ousstudies(T1/2

≤

2 ns and

≤

1 ns,respectively)[3].Furthermore,

thesetwo stateslie atexcitation energiesconsiderably abovethe yrastline(the 12+ stateis991keVabove the12+ GSBmember) andthey havehighly K -forbidden decaybranchesdirectly tothe GSB,bypassing the 2qpstates. The bypassingtransitions demon-strate an apparent collapse of the goodness of the K quantum

number, thus providing extreme examples of so-called “anoma-lous”decaysthatwerefirstidentifiedfromthe6qp,T1/2

=

130 ns

isomerin182Os[4],andthe4qp,T1/2

=

3

.

7 μs isomerin174Hf[5].

Ithasbeenalong-standingexperimentalchallengetomeasure the shorthalf-livesof the K π

=

11− and12+ states in178_W,so

that theextremenature oftheir anomalous decayscan be quan-tified. Hence, it wouldbe possible to understand better the way in whichthe K quantum number is brokendown. However, the level structure of 178W and its

γ

-ray spectra are complex, and thenon-yrastlocationofthe4qpstatesleads toweakpopulation. Nevertheless,aswe nowreport,byexploitingapulsedbeamand a reaction that populates higher-lying isomers, together with an arrayofLaBr3(Ce)detectorscombinedwithGedetectors,and

ad-vanced analysis techniques, it has been possible to measure the half-livesofthesestates.

2. Experimentalconditions

TheexperimentwasperformedattheALTOacceleratorfacility attheIPN Orsay,France.Abeamof18Oionswas impinged ona 6.3mg/cm2 target of enriched 164Dy witha 1 mg/cm2 Au back-ing.Thebeamconsistedofbunched2nslongpulseswith400ns repetitionperiod.Thestrongestchannelswere164_Dy(18_O,4n)178_W

andCoulomb excitation ofthetarget nucleus. During thesix-day measurementaboutequaltimewasusedforthreedifferentbeam energies,71MeV,76MeV,and80MeV.TheCoulomb barrierlies at72MeV.Thedatatakenwiththebeamenergyat71MeVwere notincludedinthecurrentanalysis.

Decay

γ

radiationwasdetectedwiththeNuBallarray[6] which wassetupforalongcampaignatOrsaythatlastedfrom Novem-ber 2017 until late summer of 2018. The array consisted of 24 Cloverdetectorscloseto90degreeswithrespecttothebeamaxis. Therewere10co-axialHPGedetectorsatbackwardangles,and20 LaBr3(Ce)detectorsatforwardangles.

Data acquisition was fully digital and implemented with the “FASTER”system[7].The

γ

-

γ

time resolution(FWHM) oftheGe andLaBr3 detectors,measuredwitha60Cosource,was20nsand

320 ps respectively. This was the first experiment of the NuBall campaign.Thedetectorandelectronicssetupwasslightlydifferent with respect to the later measurements with the LICORNE neu-tron source [8]. The differences shallbriefly be highlighted here. There were two categories of LaBr3(Ce) crystals,10 of truncated

cone shape, 1.5” in length and 1” and 1.5” at the bases [9] and 10oftheUKFATIMA typewithcylindricalshapeanddimensions 1.5”

×

2” [10], both using the same R9779 photo multiplier tube (PMT)fromHamamatsu.Theconicaldetectorshada1mmlayerof leadshielding around thecrystal. Noother shielding was present betweentheLaBr3 detectors.OnlytheLaBr3 detectorchannelsin

thedataacquisitionhada digitalCFDfortimewalk minimisation andsub-nanosecondtimepick-off.Thismeansthatwalkcorrection forGeandBGOdetectorswasperformedoffline.FortheLaBr3

de-tectorsa residual time walk correction (on thepicosecond scale) was applied offline (see below). In contrast to later experiments inthe campaigna global triggerwas used.The trigger condition was (one LaBr3 AND one Ge) OR (twoLaBr3) detectors within a

windowof2 μs.

In generalconditionsduring the experimentwere verystable. In particular we did not observe a significant gain drift in the LaBr3 energyspectraduringthemeasurementswitheach

individ-ual beamenergy. However, we observedgain shiftsbetween the differentenergyruns,whichweattributetodifferent

γ

rayrates.

3. Dataanalysisandresults

The aim of thisanalysis was to obtain the lifetimesof short-lived sub-nanosecond isomers in 178_{W. From previous}

measure-ments using Ge detectors some of these levels were known to have lifetimes shorter than a couple of nanoseconds [3,11]. The better time resolutionof LaBr3(Ce) scintillator detectorsmakes a

delayed

γ

-

γ

coincidencelifetimemeasurementusingthecentroid shift method [12] possible. This method is well established and based onthefact that thecentroid C ofadelayedtime distribu-tionisshiftedwithrespecttothatofacorrespondingprompttime distribution CPrompt by the mean lifetime

τ

of the intermediate

state:

C∗

=

C

−

CPrompt

=

τ

.

Measurementswith60Coand152Eusourceswereusedforenergy, efficiency,andtimingcalibration.Theprecisedeterminationofthe residualpromptresponsetimewalkfortheLaBr3 detectorsis

cru-cial forsub-nanosecondlifetime measurementswiththe centroid shift method [13]. By measuring previously reported lifetimes in

164_{Dy it was demonstrated that the calibration taken with the} 152_{Eusourceholdsunderin-beamconditions[14].Thesame}

pub-lication [14] contains a figure of the prompt response timewalk

CPrompt

(

Eγ

)

whichwasusedinthiswork.

Coincidencesbetweenneighbouringdetectors,whichare domi-natedbyComptonscatteringbetweencrystals,wereexcludedfrom theanalysis.

The studyofthe decayoflong-livedisomers in178Wis facili-tatedthroughthepulsedbeam.Thisallowstheselectionof

γ

rays that are emitted afterpopulation oflong-lived isomers,of which there are several atenergies above 3 MeV in178W,e.g. the 15+ state at3654keVwithT1/2 =30nsorthe21−stateat5314keV

withT1/2 = 64 ns [3].

By selecting

γ

rays that were emitted outside of the prompt time regionaround abeampulse,the coincidencespectracan be cleanedupsignificantly.Inthiswayitispossibletoperform

γ

-

γ

delayed coincidence measurements out ofbeam. Doing thiswith the LaBr3 detectors enables us to measure the lifetime of short

livedisomersintheseverycomplexexcitationspectraforthefirst time. Statistics was not sufficient to allow an additional energy gateontheGedetectors.

One significantfeature oftheNuBall array isthefact that the BGO crystals surroundingthe Gedetectors were not shielded to-wardsthetargetposition.Theintentionofthiswastousethemas an additionalsource ofinformationforcalorimetry studies.Inan analysislikethepresentoneitcanbeusedasapowerfulchannel selection tool,asit providesuswithahigh-efficiencymultiplicity filter.Bysettingconditionsonthenumberofdetected

γ

-raysfor both the prompt and delayedpart of an event, we were able to improvethepeak-to-backgroundratioofourtransitionsofinterest by afactorofup to3.5, whileatthesametime reducing the to-talnumberofcountsinthecoincidencespectraonlybyafactorof about2.Thedelayedtime windowwasset from40nsto270ns afterthebeampulse.

Fig. 1. Partialdecayschemeof178_Waroundthe12+_and11− _{isomersstudiedin} thiswork;someweaktransitionswereomitted.Datatakenfrom[3].

With these conditions we identified two isomers whose life-timeswewereabletomeasure.Attemptstomeasurethelifetimes ofotherhigh-lyingstates,likethe18− stateat4878 keV,orthose ofthestatesinthebandofthe13−levelat3523 keV were unfor-tunatelynotsuccessfulduetolowstatisticsorcontaminations.

We were able to set clean LaBr3 energy gates on transitions

populatingandde-populatingthe11−isomerat3053 keV,namely the

γ

cascades 181 keV - 921 keV and181 keV - 1090 keV. See Fig.1forapartiallevelschemeof178W.

The lifetimeof the 12+ isomer at3235 keV was not accessi-bleinthisdirectway.Gating onthe290 keV transition, thepeak ofthecoincident transitionat181 keV–connecting thestate at 3235 keV with the state at 3053 keV – is contaminated signif-icantly with a

γ

ray at energy 184 keV. These two transitions cannot be resolved in the LaBr3 spectrum, which renders a

di-rectcoincidencemeasurementofthisstate’slifetimeimpossiblein thiscase.Therefore,wetook advantageofageneralfeatureofthe centroidshiftmethodthat hasmainlybeenexploitedin

β

-

γ

fast timingmeasurementsbefore[12].Ifthetime differencespectrum of two transitions in a direct cascade going through states with lifetimes

τ

1,

τ

2,etc.,ismeasured,thenthecentroidC∗ ofthis

co-incidenceisactuallyshiftedbyjustthesumofthelifetimesofthe intermediatestates

C∗

=

C

−

CPrompt

=

τ

1

+

τ

2

+ ....

(1)

Thecoincidence cascade 290keV - 921keV isclean, andthe same is true for 290 keV - 1090 keV. As we have already de-terminedthe lifetime of the 11− state directly we can infer the lifetimeof the 12+ state using thesecoincidences via the above mentionedrelation.

Ascan beseen fromFigs.2 and3 thereisstill significant co-incidence background–stemmingmostly fromComptonscattered coincident

γ

rays–whichhastobetreatedaccordingly.The peak-to-backgroundratiois0.63forFig.2b),and0.76forFig.3b).In alllifetimemeasurements inthisworkwe applied theprocedure described in ref. [15], where the backgroundcontribution to the centroidofthe totaltime spectrum isseparatedinto threeparts. Thesearethenindividuallyestimatedbysettingenergygates out-side ofthe coincidence regionand interpolatingthe value atthe peak position. Polynomial functions were used for interpolation, and the uncertainty was in each case estimated from the stan-dard deviation of the fit residual. The centroid position for the full energypeak coincidence isthen obtained by subtracting the backgroundcentroidswiththeappropriateweights fromthetotal distribution. One advantage of this approach is that no assump-tionsabouttheshapeofthebackgroundtimedistributionshaveto bemade.

Fig. 2. (a)Centroidinterpolationforthedeterminationofonebackground compo-nentforthemeasurementofthelifetimeoftheKπ=11−isomerat3053keV.The positionsofthetwocoincidenttransitionsofinterestaremarkedwitharrows.A gatedLaBr3spectrumisshowningrey.(b)Rawtimedifferencespectrumobtained

with aLaBr3 coincidencegate onthe 181 keV and1090 keV transitions(black).

Thecentroidofthetotaldistributionisshownasaredbar.Thecentroidsofthe threebackgroundcomponents,determinedviainterpolation(seetext)areshown ingreen,blueandpurple.Thetotalbackgroundcentroidisshowninyellow.The deducedcentroidforthebackground-correcteddelayedcoincidenceisshownin or-ange.

Withthisbackgroundcorrectedcentroidvaluethelifetimecan then be determined by applyingthe prompt responsecorrection, which was obtained fromthe 152Eu calibration [14]. The results fortheindividual measurementsare giveninTable 1.The contri-butionofthepromptresponsecorrectiontotheuncertaintyofthe lifetimeisoftheorderof10ps(7psforthehalf-life).

FromtheresultsinTable1we calculatedaweightedmeanfor bothlifetimes.Thehalf-livesare476(44) ps and275(65) ps forthe 11−and12+isomers(Table2),respectively.Whiletheseareshort comparedtotypicalKisomers,theyatleastindicatethatintrinsic (quasiparticle) states are involved, and it is reasonable to assign theKvaluesasbeingequaltothespinvalues.Relative

γ

intensi-tiesweremeasuredusingtheGedetectors.Conversioncoefficients were calculated using the BrIcc code [16]. The obtained reduced hindrancefactors fν forthetransitionsdepopulatingthe3235keV and3053keVlevelsareshowninTables3and4.Here, fν is de-finedasthe

ν

th rootoftheWeisskopfhindrancefactor[1,2].Note alsothat theassumptionofpuremultipoles isforthepurposeof evaluatingconversioncoefficientsand fν values.InthecaseofM1

transitions,significant E2 admixturesare possible,butthesehave not been measured. In fact, for the present data, the fν values

4 M. Rudigier et al. / Physics Letters B 801 (2020) 135140

Fig. 3. (a)Centroidinterpolationforthe determinationofonetimingbackground componentforthe290 keV - 921 keV cascade.Thepositionofthecoincident tran-sitionat290keVismarkedwithanarrow.Theuncertaintywasdeterminedfrom thestandarddeviationofthefitresidual.AgatedLaBr3spectrumisshowningrey.

(b)Rawtimedifferencespectrumobtainedwithacoincidencegateonthe290 keV and921 keV transitions(black).Thecentroidofthetotaldistributionisshownasa redbar.Thecentroidsofthethreebackgroundcomponents,determinedvia interpo-lation,areshowningreen,blueandpurple.Thetotalbackgroundcentroidisshown inyellow.Thededucedcentroidforthebackground-correcteddelayedcoincidence isshowninorange.

Table 1

CentroidvaluesC∗fortheindicatedγ-γ coin-cidences.ThemeasuredvaluesCarecorrected for background contribution and the corre-spondingpromptcentroidposition.

Eγ ,1(keV) Eγ ,2(keV) C∗(ps) 290 921 1094(84) 290 1090 1067(121) 181 921 651(95) 181 1090 718(84) Table 2

Finalresultsofmeasuredlifetimes.For11−:weighted averageoftwomeasurements.For12+:differenceof weightedaveragesaccordingtoEq. (1).

Iπ ELevel(keV) τ(ps) T1/2(ps)

12+ 3235 397(93) 275(65)

11− 3053 687(63) 476(44)

4. Discussion

4.1. ThelowE2 hindrancefromthe12+isomertotheGSB

The variation of reduced hindrance with proton number is shown in Fig. 4. The figure includes all E1 and E2 “bypassing”

Table 3

Reducedhindrancefactors fνmeasuredinthisworkfor tran-sitionsdepopulatingthe11−stateat3053keVin178_W.Pure

multipolesσλareassumed.Theγ branchingratiob isbased on measured relative γ ray intensitiesand theoretical con-versioncoefficientsforthestatedmultipoleorders.Transition strengthsofE1characterwerecorrectedbyafactorof104_for

comparability(seediscussionfordetails). Decay to Iπ final Efinal (keV) Eγ (keV) σλ ν b (%) fν 10+ 1665 1389 E1 10 1.9(4) 2.80(8) 9− 1964 1090 E2 2 33(4) 15(1) 9− 2041 1012 E2 7 2.0(4) 3.1(1) 10− 2133 921 M1 3 29(3) 39(2) 11− 2328 727 M1 3 3.6(7) 61(4) 11− 2490 564 M1 8 2.9(6) 4.4(1) 12− 2546 508 M1 3 8(1) 33(2) 10− 2578 476 M1 2 11(1) 148(11) 13− 2784 269 E2 2 1.0(6) 2.6(8) 11− 2842 212 M1 2 4.1(5) 71(5) Table 4

SameasTable3butforthe12+stateat3235keVin178_W.

TheK valueofthe12+stateat2845keVwasassumedtobe 8,basedonthediscussionin[3] (seetext).

Decay to Iπ final Efinal (keV) Eγ (keV) σL ν b (%) fν 10+ 1664 1571 E2 10 6.9(12) 2.30(7) 12+ 2244 991 M1 11 4.8(9) 3.09(9) 11− 2327 908 E1 4 1.1(3) 9.6(10) 10+ 2444 791 E2 4 3.8(9) 3.9(3) 12− 2546 689 E1 4 1.0(4) 8.0(11) 11+ 2671 564 M1 5 3.7(9) 9.0(6) 10+ 2683 552 E2 2 8.1(15) 4.3(7) 12+ 2804 431 M1 11 3.1(8) 2.57(8) 12+ 2845 390 M1 (3) 2.4(6) 31(4) 11− 3053 181 E1 0 59(10)

-transitionsfrom4qpisomersineven-evennuclides,directlytothe GSB,i.e.bypassingthe2qpstates.Thegeneraltrendofdecreasing

fν withincreasing Zcould be due toincreasing gamma softness [1,2].Nevertheless,itisevidentthatallthevaluesarelow( fν

<

6). Here the focus is on the 178W value, which is even lower than mightbe expectedfromthetrendof thedata,butfirstwe recall thesituationfor174Hf.

The 174_{Hfvaluewas discussed[5] in termsofmixingwithan}

isolated

(

i13/2

)

2 s-bandstate at I

=

12,though now it would be

moreappropriatetogiveat-bandinterpretation(wherethe Fermi-aligned i13/2 neutrons have significant K projections – see [17]

forarecentsummaryoft-bandstructures).Eitherway,whenthe high-K structure of the

(

i13/2

)

2 admixtureis not explicitlytaken

intoaccount,thereistheappearanceoflowreducedhindrancefor the E2 decaytotheGSB.

In a similar way, there is t-band mixing in 178W [3]. Impor-tantly, in this casethe yrare (energetically unfavoured) band for

I

≥

12 has been identified as a t-band with K

≈

8. The high-K value wasextractedbyPurryetal. [3] fromananalysisofthe E2

branchingratiosinthecrossingregionwiththeGSB,anda GSB/t-bandmixingmatrixelementof68keVwasobtained.Althoughthe

I

=

10 memberofthet-bandwasnot assigned,thiscould plausi-blybethe Iπ =10+state at2682keV,whichisfedfromthe K π

= 12+ isomerby a 552 keV, E2 transition.Ifthe 2682keVstate has K

=

8 fromthe

(

i13/2

)

2,{7₂+

[

633

],

9₂+

[

624

]

} t-bandcoupling,

thenthe552keVtransitionhas

ν

=2,and fν =4.3.Thisisalready a low value, but we note that the configuration of the 12+ iso-meritselfinvolvestwoi13/2neutrons{72

+

_[

Fig. 4. ReducedhindrancevaluesforE2 (filledsymbols)andE1 (opensymbol) tran-sitionswhichgo directly from4qpisomers,with the givenKπ _{values,totheir} respectiveGSB,bypassingthe2qpstates.FortheE1 transition,theWeisskopf hin-drancehasbeendividedby104_{(seetext).Error-barsaresmallerthansymbols.The}

dataarefrom[2–5,19,20] andthepresentwork.Notethatthereducedhindrance dependenceontheenergyrelativetoarigidrotor[1,21],andaγ-tunnelingmodel interpretation[20,22],providealternativeperspectives.

to K

=

8 [3,18],which isjustthet-configuration,so thatthe de-caytothe2682keVlevelwouldrequireonlyasimplerecoupling ofthetwootherneutronsinthe4qpconfiguration.

Usingthe68keVmixingmatrixelementobtainedbyPurry et al.[3], the10+ GSB memberat1665keVcan be calculatedin a two-level-mixingscenariotohavea0.5%t-band,

<

K

>

≈

8 admix-ture. Ifthat0.5% componentaccountsforthe observed1571 keV transitionfromthe12+ isomer totheGSB, butthereduced hin-dranceiscalculatedwith K

=

0 fortheGSB(aswouldusually be done)thenanapparentreducedhindranceof fν =2.3ispredicted, whichisexactlytheobservedvalue.Whilethereareuncertainties intheassumptionsused,thegeneralunderstandingappearstobe good: there is a small t-band admixture in the GSB, which en-ables the direct transition to proceed fromthe 12+ isomer, and thistransitionmaybefacilitatedbytheparticularstructureofthe 4qp isomer, which includes the 2qp, t-band configuration. Note that inthe 174Hf case, thereis noexperimental evidence forthe

K valueofthe I

=

12 mixingstate.Therefore thepresentcaseof

178_W,withK

_≈

_{8 forthet-bandconsistentwithE2 branching}

ra-tios [3], hasspecial significance forunderstanding the nature of bypassingtransitions.

It would be desirable to apply the same procedure with the other4qpisomersthathavebypassingdecays,i.e.thoseillustrated inFig.4. However,for 164Er [19],174W [20] and 182Os[4],there are no observed E2 decay branches to the corresponding yrare states,sothat a differentkindof analysiswouldbe required, in-volving differentassumptions. From an experimental perspective, itwouldbevaluabletoidentifythesemissingtransitions.

Notealsothatthe991keV,



I

=

0 transitiontothe12+ mem-ber ofthe 178_{W GSB also hasa very low reducedhindrance, fν}

=3.1, assuming M1 character. This isslightly larger than forthe competing E2 transitiontothe 10+ GSB member,with fν = 2.3. SuchadifferencebetweencompetingM1 andE2 K -forbidden de-caysistypical[2],butaquantitativediscussionofthedifferenceis inhibitedby thelackof knowledgeofthe E2/M1 mixingratioof the



I

=

0 transition.

4.2.ThelowE1 hindrancefromthe11−isomertotheGSB

TheE1 reducedhindrance,fromthe11−isomerdirectlytothe 10+ memberoftheGSB, fν

=

2

.

8,isverysmall–indeed,itisthe smallestvalueyetobservedforanyK -forbiddenE1 transition,and itistheonlyexampleofabypassingE1 transitiontotheGSBinan

even-even nuclide. With the commonly employed 104 _reduction

applied to the E1 Weisskopf hindrance factor [23,24],similar E2

and(effective)E1 reducedhindrancesaretypicallyfound,andthis iscertainlysupportedbythepresentlyobtainedvaluesof fν =2.3 and2.8,respectively.

The11− isomerconfigurationinvolvesthe 9₂+

[

624

]

,i13/2

neu-tron[3,18],butnot boththei13/2 neutronsofthet-configuration,

as is evident for the 12+ isomer. Nevertheless, the same t-band mixingatI

=

10 introduceshigh-K componentsintotheGSB10+ state, whichcan account forthe smallapparent fν valuefor the

E1 transition(thoughaquantitativeevaluationofthereduced hin-drancewouldrequireadditionalassumptions).

Finally, it is appropriate to consider whether there could be chance near-degeneracies involved, with states having the same spinandparity,butdifferent K values.Sufficetosaythat,atleast forthe12+ and11− isomers,andthe10+GSBstate,nosuch ac-cidentaldegeneraciesare knownwithinanenergyintervalof100 keV. However, with the two isomers being well above the yrast line, it remains a possibility that mixingwith as-yet unobserved statescouldplayarole.

5. Conclusion

With

γ

-ray fast-timing techniques, short half-lives have been obtained for K π

=

11− (0.48 ns) and 12+ (0.28 ns) 4qp states in 178W, at excitation energies close to 3 MeV. Their highly

K -forbidden decaysdirectly to the 10+ memberof the GSB, by-passingthe2qpstates,haveverysmallreducedhindrancefactors. These are interpreted as beingat least partlydue to mixing be-tween the 10+ GSB member and the 10+ t-band state, which hasahigh-K structurebasedontwoi13/2 Fermi-alignedneutrons.

The E2 result ( fν

=

2

.

3) can be understood in a similar wayto thelong-standingvalue in174Hf,whiletheremarkablysimilar E1

result( fν

=

2

.

8)isauniqueobservationofitskind.Further exper-imentalinformationisneededtoenableaquantitativecomparison of the K -mixing mechanism forbypassingdecays in 164_Er, 174_W

and 182_{Os. In the meantime, the presentwork provides some of}

the bestevidence todate that high-K admixturesinthe GSBare key to understandingthe apparent breakdownof theKquantum number.

Acknowledgements

Funding support is acknowledged from the UK Science and Technology Facilities Council under grant numbers ST/L005743/1 andST/P005314/1, as well asthe BMBF undergrants NuSTAR.DA 05P15RDFN1,and05P19PKFNA. Thiswork was alsosupported by theSpanishgouvernmentprojectsFPA2015-65035-Pand RTI2018-098868-B-I00, as well as the project B2017/BMD-3888 PRONTO-CM. P.H. Regan acknowledges support from the UK Department ofBusiness,EnergyandIndustrialStrategy(BEIS)viatheNatioanl Measurement System(NMS). R.L. Canavan acknowledges support fromtheBEIS,andENSAR2transnationalaccessfundingfromthe EuropeanCommission.

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