Betadecaystudiesofthemostexoticnuclei

GiovannaBenzoniINFNsezione diMilano(Italy)

Outlineofthelessons:PARTI:Generalconcepts

Howtomeasureb decayinexoticnucleiPARTII:b decaygrosspropertiesT1/2 andPnPARTIII:HighresolutionvsTAS

Intr

oduc

tion

NZ

~3000knownnuclei,bothnatural(288)andartificial7000+/- 500currentestimatesforboundnucleiBoundariesofthe nuclei(driplines)arenotdefinedyet

b decaydominatedbyweakinteractionanditspropertiesdirectlyrelatetofundamentalquestions:• Propertiesoftheneutrinosè energyspectrum,double-b decay,sterileneutrinos• Abundancesofelementsinuniverseè halflivesandcompetingdecaymodes

andapplications:• PETscanners• Radioactivesources(scienceandmedicine)• Homelandsecurity• Nuclearwaste

Introd

uctio

na decay:

b- decay:

b+ decay:

EC:

SpontaneousFission

Exoticdecaymodes:ndecaypdecayclusteremission

b-mediateddecays:b-delayedn/pemissionb-delayedfission

Decaymodes

−

82

proton-rich nuclei

p n

neutron-rich nuclei

p n

stable nuclei

p n

b- decay:en p e n-® + +

b+ decay:ep n e n+® + +

a decay:4 42 2 2 2

A AZ N Z NX Y He-

- -® +

Spontaneous fission

Usefuldefinitionsfordecays:

Lawofradioactivedecay:

l decayratet=2p/l meanlifeT1/2 =ln2*t half-life

Qvalue =Minitial – Mfinal

Branchingratio:decayprobabilityoftwoormorecompetingprocessesIntr

oduc

tion

𝑁 𝑡 = 𝑁%𝑒'()

Daughter/Successorè Finalnucleus

Mother/Precursorè Initial/Emittingnucleus

t

Batemanequations:mathematicalmodeldescribingabundancesandactivitiesina decaychain asafunctionoftime,basedonthe decayratesandinitialabundances.Ifatatimet,thereareNi(t)atomsofthei-th isotopewhichdecaysintothei+1onewithadecayrateli,theamountsofisotopesinthek-th stepofthedecaychainevolvesas:

𝑑𝑁+(𝑡)𝑑𝑡 = −𝜆+𝑁+ 𝑡

𝑑𝑁/(𝑡)𝑑𝑡 = −𝜆/𝑁/ 𝑡 + 𝜆/'+𝑁/'+ 𝑡𝑑𝑁1(𝑡)𝑑𝑡 = 𝜆1'+𝑁1'+(𝑡)

Thiscanbewritteninanexplicitformas:

𝑁2 𝑡 =3𝜆455𝑁/(0)𝑒'(7 )

∏ (𝜆9 − 𝜆4)29:+,9<4

2

4:+

2

/:+

2'+

4:+

Intr

oduc

tion

Thiscanbeextendedtocasesinwhichwehavemanybranches

H. Bateman. "Solution of a System of Differential Equations Occurring in the Theory of Radio-active Transformations," Proc. Cambridge Phil. Soc. IS, 423 (1910) https://archive.org/details/cbarchive_122715_solutionofasystemofdifferentia1843

Intr

oduc

tion • Eachmemberofthefamilyisadewar.They

areconnectedandthefilleachotherinchain

• Therateofemptying(-dN/dt)arefunctionofthelevelinthedewar Nandthedecayratel

• Atequilibriumtherateofevacuationineachdewar isequal

• InnuclearphysicsrateofdecayistheActivityanddependonthedecayconstantl

• Atequilibriumallactivitiesareequal

Secularequilibrium:TherateofproductionanddecayofanelementisconstantItcanbeachievedinadecaychainifthedaughterBhasamuchshorterhalf-lifethanthemotherAThedecayrateofA,whichistranslatedintotheproductionrateofBisconstantThequantityofBaccumulatessincethenumberofnucleiwhichdecayin1sifequaltothatproducedin1s.

ThisdependsonNA(t=0),lA and lB

Intr

oduc

tion

Detectinga b g nparticles:reminderofbasicproperties

a particle:massive,chargedè interestedinenergy,angulardistributionè spectrometers,Si,plasticdetectors

b particles:light,chargedè interestedinenergyandcorrelationsè e+ annihilatesintotwo511-keVg raysè spectrometers,Si,plasticdetectors

g particles:massless,neutralè interestedinenergyandangulardistributionsè HPGe detectors,inorganicscintillators

Neutrons:massive,neutralè interestedinenergyandcorrelationsèmeasuredindirectlyviacapturereactionsè liquidscintillators,inorganicscintillators

Incoming radiation

Bremsstrahlung

Main e- track

Compton

photoelectricPair

Intr

oduc

tion

Exampleofdetailedstudyofadecay:

ZAN

Z+1AN-1

β- decays

1)ProduceandIdentifyPARENTnucleus:reactions/ISOL/fragmentation

2)Detectthedecay:identifytheemittedparticlea/bidentifycompetingmechanismsidentifydecayingstate,g.s.orexcitedisomericstatemeasurehalf-life

3)StudypropertiesofDAUGHTERnucleus:whichlevelsarepopulatedBranchingRatiobtwlevelssubsequentdecays

T1/2Qvalue%b, %a … Ib logft

bdecayisaweakinteraction“semi-leptonic”decay

ThequarklevelFeynmandiagramforβ- decayisshownhere:

b- decay

b+ decay

EC

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• TheQvalueinb decayiseffectivelysharedbetweentheelectronandantineutrino.

• Thisisthecaseofgs->gs decay

( ) ( )( )

( ) ( )( )( ) ( )( ) ( ) 2

maxmax

1,1,

2

21,,

since

1,, isdecay for value

cmZAMZAMQ

TTQ

keVTTTTTTQQ

cZAMZAMQQ

e

e

ZAMeeZAM

---=

==

<+»++=

+-=

+

-

++-

-

++

-

b

nb

nnb

b

b

b

Notetheseareatomicmasses

Sumoftheenergyoftheelectron(positron)andantineutrino(neutrino)

Iftheothertermisnull

Forelectroncapture:𝑄>? = 𝑀 𝐴, 𝑍 − 𝑀C 𝐴, 𝑍 − 1 𝑐F − 𝐵2

𝐵2𝑏𝑖𝑛𝑑𝑖𝑛𝑔𝑒𝑛𝑒𝑟𝑔𝑦𝑜𝑓𝑛 − 𝑠ℎ𝑒𝑙𝑙𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛

NB:ECandb+arenotalwayscompeting:ifb+,ECispossible,thecontraryisnotguaranteed

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Eb

Iipi

Ifpf

ββfi SLII ++=

bpp Lfi )1(-=

)(~)( nnbbb llL += +-

{ ­¯­­¯¯+- =+= or

01(ννν~)(βββ ssS

allowed

whentheangularmomentumconservationrequiresthatLb=n >0

andpipf=(-1)Lb

1,0º-=D fi III

whenLb=n=0

andpipf=+1

Electronandneutrinodonotcarryangularmomentum

Lb = n definesthedegreeofforbiddenness (n)

forbidden

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Selectionrulesforpossibledecays

Type of transition Order of forbiddenness

DI pipf

Allowed 0,+1 +1

Forbidden unique1234.

!2!3!4!5

.

-1+1-1+1.

Forbidden1234.

0, !1!2!3!4

.

-1+1-1+1.

)1( +=fippClassificationofalloweddecaysFermi

¯­= 0bS0=bL

0º-=D fi III

0+Eb

0+0+

Eb1+

Gamow-Teller

0=bL ­­=1bS ¯¯or1º-=D fi IIIGe

nera

l Pro

pert

ies

of b

deca

y

Thefifthpowerbetadecayrule: thespeedofab transitionincreasesapproximatelyinproportiontothefifthpowerofthetotaltransitionenergy

q dependsonspinandparitychangesbetweentheinitialandfinalstate

q additionalhindranceduetonuclearstructureeffects:

isospin,“l-forbidden”,“K-forbidden”,etc.

( ) 52])1()([1 cZMZM ±-µtEbIf

Ii

Usefulempiricalrules

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• Treatbetadecayasatransitionthatdependsuponthestrengthofcouplingbetweentheinitialandfinalstates

• DecayconstantisgivenbyFermi'sGoldenRule

• èElectronandneutrinodonotpre-existinatombutareformedatthetimeofdecay

• èThedecayistheresultoftheinteractionbtwthenucleonandthefieldproducedbytheelectron-antineutrinocoupleè weakinteraction

• Perturbationtheorycanbeappliedsincetheinteractionis“weak”• Mmatrixelementwhichcouplestheinitialandfinalstates• Rateproportionaltothestrengthofthecouplingbetweentheinitialandfinalstates

factoredbythedensityoffinalstatesavailabletothesystemelectron-antineutrino

dvVMEM iff ò== yyrplb );(2 2

!

FermiGoldenRule

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iPTTt i

b

bexp2/1

2/1 =º

ò -=W

eneeeen dWCWZFWWWpgT 1

203

2

2/1

),()(2

2lnp

partialhalf-lifeofagivenb- (b+,EC)decaybranch(i)

g – weakinteractioncouplingconstantpe – momentumoftheb particleWe – totalenergyoftheb particleW0 – maximumenergyoftheb particle

F(Z,We)– Fermifunction– distortionoftheb particlewavefunctionbythenuclearcharge

Cn – shapefactorZ– atomicnumber

ò --=

=

oW

oo

o

dWWWWWWZFf

hgcmK

1

22/12

72454

)()1(),(

/64p

oif fMKt

2

2/1

2ln==l

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• BasedonprobabilityofelectronenergyemissioncoupledwithspectrumandtheCoulombcorrectionfot1/2 iscalledthecomparativehalflifeofatransition

• Assumesmatrixelementisindependentofenergy (trueforallowedtransitions)Yieldsft (orfot1/2),comparativehalf-lifemaybethoughtofasthehalflifecorrectedfordifferencesinZandenergy

• ALLOWEDtransitionssecondtermisindependentonnucleus,

• è ft hasthesamevalueforallallowedtransitions

• Forforbiddendecaysft increaseswithdegreeofforbiddenness

ComparativeHalfLives

𝑓𝜏 =2𝜋WℏY𝑐W

𝑔F 𝑀/Z 2

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Logft <6.0

Logft >6.0

100SnN=Z=50HeaviestN=Znucleus

~260100Snnucleiproduced(0.75/h)~126fullyreconstructeddecaychains

2.62

Measurin

glogft

Nature48

6,341

(201

2)RelativisticFragmentationreaction124Xebeamon9Betarget

Hig

hly

forb

idde

n de

cays

A.Giaz

etal.EPL11

0(201

5)420

02

b Decay of138LaLantanum has two isotopes• 139La, stable• 138La, radioactive:

• T1/2= 1.05*10 11 years• abundance 0.09%.

138La has two decay branches• b- towards 138Ce, BR= 33.6%• EC towards 138Ba BR=66%

Both decays are second forbidden decays5+è 2+

Experiment:measuringtheBRandtheelectronspectraUsingLaBr3(Ce)detectorsassourceANDasdetectors

b-

e

gg

e-

XLaBr3:Ce

LaBr3:Ce

• b- decay: e- in the det. which b decays, 789 keV g ray in the other;

• EC: X ray in the det. which decays, 1436 keV g ray in the other

A.Giaz

etal.EPL11

0(201

5)420

02

Background subtraction to get e- spectrum:• Coincidence with 789 keV (black box) total spectrum• Compton bg from 1436 keV (red box)• Bg subtraction cancel peaks at 37.44 and 5.6 keV in

coincidence with 1436 keV.

Hig

hly

forb

idde

n de

cays

Theoryhashardtimereproducinglow-energyshapeofb-electronspectrum

InteractionbtwCoulombfieldofthenucleusandelectron

Quantitiesthatcanbeextractedinab decayexperiment

ZAN

Z+1AN-1

β- decays

T1/2Pn/p%b, %a …

g transitions

Possibleexistenceofmanydecayingstates

g-g coincidencesè levelschemesRelativeintensitiesIblogft

Selectionrulesallowtosuggest/defineIp inbothmotheranddaughter

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“pandemoniumeffect” – exoticnuclei– log ft isajustupperlimit

68Mn

68Fe

68Co

67Fe

67Co

b

b

bn

b

Producingradioactivebeamsi.e.exoticnuclei

relativisticfragmentation/fission ofheavynucleionthintargets• >50MeV/uè productionof

cocktailbeamsofmanynuclei• Useofspectrometersto

transport/separatenucleiofinterestè RelativelylongdecaypathsDt>150-300ns

• Nucleiarebroughttorestinfinalfocalplaneandletdecay

+cocktailbeam:manynucleiatonce+bothshortandlong-livingspecies+getinformationalreadywithfewions

- Lowcrosssections- Limitationonratetodistinguish

contributionfromeachspecies

spallation/fission/fragmentation onthicktargets,followedbychemical/physicalprocessestoextractdesirednuclei• beamsproducedatverylowenergies(~60keV)• Mono-isotopicbeamssometimesachieved.

Impuritiesduetofewcontaminantspeciesèusuallylong-livingthough

+highcrosssection+noneedtore-acceleratebeams+highratesaccepted

- short-livingspeciesmightnotbeaccessedeasily

- Refractoryelements- Presenceoflong-livingimpurities(isobariccontamination)

Intr

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tion

Intr

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tion

IN-FLIGHT ISOLmethod

RIKEN

NSCL-FRIB

SPIRAL2

SPES

HIE-ISOLDE

GSI-FAIR

Examplesoffacilitiesallovertheworld…in-flightandisol

ALTO

Measuringb decay

Implantationpoint

Decaypoint

Tapedecaystations

BeamPlasticbdetector

HPGeLaBr3 ta

petape

IN-Flight facility

ISOLfacility IDS@CERN

Eurica@RIKEN

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Ion-betacorrelationtechniques:distinguishimplantationanddecaywithinsamedetector

Implantation-decaycorrelationswithlargebackground(halflifessimilartotheimplantationrate):

ü implant-decaytimecorrelation:activecatcherü implant-decaypositioncorrelation:granularityü implantofseveralions:thicknessandareaü energyoftheimplantedionandtheemittedb

*Dualgainpre-ampsonDSSSDtogetenergiesofimplantedionandb-particle*AlleventstimestampedwithMHzclock.

GSIRIKEN

*Lowgainbranchforimplantedions*High-gainbranchforb anda decays

TAPE Station systems

Principleofoperation

• Implantationanddecayinthesamemeasuringpoint• Equippedwithegs.GedetectorsandPlastic(orSidetectors)forb particles• Triggergivenbyprotonarrivalandb signal• Long-livingactivityisremovedbymovingawaythetape• NB:nodirectsignalofimplantation

BEDO@ALTO

IDS@ISOLDE

b

Realsituation

ZAN

Z+1AN-1

g1

g2

2

1

f2 = Ig 2f1 = 0(Ig 2 = Ig 1 )

Pandemoniumeffect

ZAN

Z+1AN-1

g1

2

1

f2 = 0f1 = Ig 1

Apparentsituation

b

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ZAN

Z+1AN-1

β- decays

ZAN

Z+1AN-1

β- decays

• HPGedetectorsareconventionallyusedtoconstructthelevelschemepopulatedinthedecay

èHigherQvalue higherpossibilityofmissing feeding owing tohigh-energy gray emission or emission oflarge number ofg rays

•Fromtheg intensitybalancewededucetheβ-feeding

Pandemoniumeffectimplies

èWrongdefinitionofgammafeedingandbranching ratiosIb andlogft

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Since the gamma detection is the only reasonableway to solve the problem, we need a highly efficientdevice:

ATOTALABSORTIONSPECTROMETER

Instead of detecting the individual gamma rays wesum the energy deposited by the gamma cascades inthe detector.

A TAS is a calorimeter!

Big crystal, 4π (BaF2/NaI/HPGe)

TotalAbsorption GammaSpectrometer measurements

Ge det.

TAS det (NaI(tl))

(Det 1 & det 2).

Tape station

Rad. beam .

Si det.

TASexperimentalsetup

• A large NaI cylindrical crystal 38 cm Ø, 38cm length

• An X-ray detector (Ge)• A β detector• Possibility of collection

point inside the crystal

Lucrecia:theTASatISOLDE(CERN)(Madrid-Strasbourg-Surrey-Valencia)

å ×==j

jiji orfRd fRd

R is the response function of the spectrometer, Rijmeans the probability that feeding at a level j gives counts in data channel i of the spectrumThe response matrix R can be constructed by recursive convolution:

kjkj RgR å-

=

Ä=1

0

j

kjkb

gjk: γ-response for j è k transitionRk: response for level kbjk: branching ratio for j è k transition

0

1

2

3

Mathematical formalization by Tain, Cano, et al.

TAGSanalysis

β-decay

bD

ecay

in E

xoti

c N

ucle

i§ Shorteningofhalf-lives§ IncreasingQvalue§ DecreasingSn (onn-richside)§ Higherpossibilitiesofcompeting

mechanisms§ GTunfavoured owingtolargemismatchin

wavefunctionsbtwmother/daughter§ Increasingroleofforbiddendecays

neutron-rich nuclei

p n

Qb-

Sn

ZAN

Z+1AN-1

β- decays

ZAN

Z+1AN-1

β- decays

§ Pandemoniumeffect

Goingawayfromstability