a photonuclear study of the halo nucleus 6-he

A PhotonuclearStudyof theHaloNucleus�He

Mark JamesBolandB.Sc.(Hons)

Submittedin total fulfilment of therequirementsof

thedegreeof Doctorof Philosophy

September25,2001

Schoolof Physics

TheUniversityof Melbourne

Victoria,3010,Australia

Abstract

Thephotonuclearreaction� Li �� Hewasstudiedusingtaggedphotonsin

the energy rangeof 50 to 70 MeV at threelab anglesof 30 , 60 and90 . By

measuringthe protonmissing-energy, the low-lying excited statesin � He were

identified.As well astheknow groundstateandfirst excitedstate,evidencewas

foundto supporttheexistenceof anew statewhichhasbeenpredictedby theory.

The � He nucleushasa neutronhalo surroundinga � He core. A soft dipole

resonancebetweenthehaloandthecorehasbeenpredictedto occurat low exci-

tationenergies. This thesiscomparesthenewly foundstatewith thetheoretical

parametersof thesoft dipole.

In thedataanalysisof the presentmeasurement,a well establishedandun-

ambiguousbackgroundremoval processwasused.This techniqueis contrasted

with chargeexchangeexperimentswhichhaveclaimedto observethesoftdipole

resonance.Photonucleartechniquesareshown to bea morereliablemethodof

observingthestatesin � He.

This is to certify that:

1. thethesiscomprisesonly my originalwork towardsthePhD,

2. dueacknowledgementhasbeenmadein thetext to all othermaterialused,

3. thethesisis lessthan100,000wordsin length,exclusiveof tables,maps,bib-

liographiesandappendices.

Acknowledgments

I would like to thank.....

Contents

1 Intr oduction 1

2 Moti vation 5

2.1 Halo Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 BasicPhysicsof Halo Nuclei . . . . . . . . . . . . . . . 6

2.1.2 GeneralPropertiesof Halo Nuclei . . . . . . . . . . . . 10

2.1.3 TheoreticalDescriptionsof Halo Nuclei . . . . . . . . . 14

2.1.4 TheSoftDipoleResonancein Halo Nuclei . . . . . . . 16

2.2 TheHalo Nucleus� He . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 TheRadiusof � He . . . . . . . . . . . . . . . . . . . . 18

2.2.2 New StatesPredictedin � He . . . . . . . . . . . . . . . 19

2.2.3 PreviousMeasurementsof � He . . . . . . . . . . . . . . 22

2.3 Advantagesof the � Li �� HeMeasurement. . . . . . . . . . 28

3 Experimental Method 31

3.1 ProducingPhotons . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.1 Photonsfrom Bremsstrahlung. . . . . . . . . . . . . . 32

3.1.2 PhotonTagging . . . . . . . . . . . . . . . . . . . . . . 33

3.2 TheMAX-lab . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.1 TheMAXINE ElectronAccelerator . . . . . . . . . . . 35

3.2.2 MAX-I BeamPulseStretcher . . . . . . . . . . . . . . 36

vii

viii Contents

3.2.3 TheMAX-lab PhotonTagger . . . . . . . . . . . . . . 37

3.3 DetectingProtons. . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 TheGLUE Chamber . . . . . . . . . . . . . . . . . . . 39

3.3.2 Solid StateDetectorTelescopes . . . . . . . . . . . . . 40

3.3.3 ChargedParticleIdentificationMethod . . . . . . . . . 44

3.3.4 � Li Target . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3.5 NuclearExperimentalHall (Cave) . . . . . . . . . . . . 46

3.4 DataAcquisitionSystem . . . . . . . . . . . . . . . . . . . . . 48

3.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4.2 HardwareCircuit . . . . . . . . . . . . . . . . . . . . . 48

3.4.3 EventTrigger . . . . . . . . . . . . . . . . . . . . . . . 51

3.5 Summaryof ExperimentalParameters. . . . . . . . . . . . . . 52

4 Data Analysis 55

4.1 AnalysisOverview . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 ROOT/CINT Software . . . . . . . . . . . . . . . . . . . . . . 56

4.3 ParticleIdentification . . . . . . . . . . . . . . . . . . . . . . . 58

4.4 PhotonEnergy Measurement. . . . . . . . . . . . . . . . . . . 60

4.5 ProtonEnergy Measurement. . . . . . . . . . . . . . . . . . . 61

4.5.1 Energy LossCorrections . . . . . . . . . . . . . . . . . 61

4.5.2 ReactionKinematics . . . . . . . . . . . . . . . . . . . 63

4.5.3 Missing-Energy . . . . . . . . . . . . . . . . . . . . . . 65

4.6 Correctionfor AccidentalTagging . . . . . . . . . . . . . . . . 67

4.6.1 TDC Timing Spectra . . . . . . . . . . . . . . . . . . . 67

4.6.2 PromptMissing-Energy Spectrum. . . . . . . . . . . . 70

4.6.3 AccidentalMissing-Energy Spectrum . . . . . . . . . . 71

4.7 �� Correction. . . . . . . . . . . . . . . . . . . . . . . . . 73

Contents ix

5 Resultsand Discussion 77

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.2.1 ExcitationEnergy Spectra . . . . . . . . . . . . . . . . 79

5.2.2 StatesIdentified. . . . . . . . . . . . . . . . . . . . . . 84

5.2.3 AngularDistribution . . . . . . . . . . . . . . . . . . . 85

5.3 Interpretations. . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.3.1 Comparisonwith PreviousMeasurements. . . . . . . . 86

5.3.2 TheLow-Lying Region, �� MeV . . . . . . . . . 89

5.3.3 TheHigh Region, �� MeV . . . . . . . . . . . . 93

6 Conclusion 95

A Analysis of TDC Spectra 97

A.1 Structureof UncorrelatedContribution . . . . . . . . . . . . . . 97

A.2 Timing Resolution . . . . . . . . . . . . . . . . . . . . . . . . 99

B Experiments Conductedat the MAX-lab 101

B.1 !�� O ��#"$%!�& N . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.2 !�� O ��'�(�#")*!�& O . . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.3 !�� O ��'��%!�& N . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.4 !�+ C ��%!�, B . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

B.5 � Li �-�.�� He . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

C Papers 105

C.1 ConferencePapers . . . . . . . . . . . . . . . . . . . . . . . . 105

C.2 JournalPapers. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

List of Figures

2.1 Neutronand / componentsof the � Hematterdistribution . . . . 8

2.2 Momentumdistribution from fragmentationof � He . . . . . . . 9

2.3 Comparisonof !0! Li radiusto ,0102 Pband � 2 Ca . . . . . . . . . . . 11

2.4 Neutrondrip line on thetableof isotopes. . . . . . . . . . . . . 13

2.5 Schematicof aneutronhalo . . . . . . . . . . . . . . . . . . . 17

2.6 TheBorromeanrings . . . . . . . . . . . . . . . . . . . . . . . 18

2.7 � Li ��3�� Hecalculationby Danilin et al. . . . . . . . . . . . . 22

2.8 � Li �� Li �4� Be�� Heexperimentby Sakutaet al. . . . . . . . . . . 23

2.9 � Li �� Li �4� Be�� Heexperimentby Janeckeet al. . . . . . . . . . . 25

2.10 � Hefragmentationexperimentby Aumannet al. . . . . . . . . . 26

2.11 � Li �� Li �4� Be�� Heexperimentby Nakayamaet al. . . . . . . . . 28

2.12 � Li �-56�4+ He0� Heexperimentby Nakamuraet al. . . . . . . . . . . 29

3.1 bremsstrahlungenergy spectrum . . . . . . . . . . . . . . . . . 32

3.2 Schematicof photon-taggingprinciple . . . . . . . . . . . . . . 34

3.3 Overview of theMAX-lab . . . . . . . . . . . . . . . . . . . . 35

3.4 TheMAXINE accelerator. . . . . . . . . . . . . . . . . . . . . 36

3.5 TheMAX-lab photontagger . . . . . . . . . . . . . . . . . . . 38

3.6 TheGLUE chambertopview . . . . . . . . . . . . . . . . . . . 39

3.7 Detectortelescope. . . . . . . . . . . . . . . . . . . . . . . . . 41

3.8 TheGLUE chambersideview . . . . . . . . . . . . . . . . . . 42

xi

xii List of Figures

3.9 Energy Spectrumof ,0,02 Th . . . . . . . . . . . . . . . . . . . . 43

3.10 Particleidentificationprinciple . . . . . . . . . . . . . . . . . . 44

3.11 78� - � plot from aspectrometer . . . . . . . . . . . . . . . . . 45

3.12 Experimentalhall layout . . . . . . . . . . . . . . . . . . . . . 47

3.13 78� - � coincidencecircuit . . . . . . . . . . . . . . . . . . . . 49

3.14 Dataacquisitioncircuit diagram . . . . . . . . . . . . . . . . . 50

3.15 X-triggerandtaggertiming . . . . . . . . . . . . . . . . . . . . 52

4.1 Event-by-eventanalysisoverview . . . . . . . . . . . . . . . . 57

4.2 Typicalparticleidentificationplot . . . . . . . . . . . . . . . . 59

4.3 Thetaggercalibration. . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Protonenergy losscorrectionfunction . . . . . . . . . . . . . . 62

4.5 Reactionkinematics. . . . . . . . . . . . . . . . . . . . . . . . 63

4.6 Raw protonmissingenergy spectrum. . . . . . . . . . . . . . . 66

4.7 TypicalTDC spectrum . . . . . . . . . . . . . . . . . . . . . . 68

4.8 Accidentaltaggingremoval . . . . . . . . . . . . . . . . . . . . 69

4.9 Promptmissing-energy spectrum. . . . . . . . . . . . . . . . . 70

4.10 Accidentalmissing-energy spectrum. . . . . . . . . . . . . . . 71

4.11 TDC timing regions . . . . . . . . . . . . . . . . . . . . . . . . 72

4.12 Background-subtractedmissing-energy spectrum . . . . . . . . 73

4.13 �� backgroundspectrum. . . . . . . . . . . . . . . . . . . 75

4.14 Correctedmissing-energy spectrum . . . . . . . . . . . . . . . 76

5.1 Nuclearlevelsin � He . . . . . . . . . . . . . . . . . . . . . . . 77

5.2 Excitation-energy spectra. . . . . . . . . . . . . . . . . . . . . 80

5.3 Integratedspectrum. . . . . . . . . . . . . . . . . . . . . . . . 81

5.4 Fittedexcitation-energy spectra. . . . . . . . . . . . . . . . . . 83

5.5 Angulardistributionof statesin � He . . . . . . . . . . . . . . . 85

List of Figures xiii

5.6 � Heenergy level diagram . . . . . . . . . . . . . . . . . . . . . 88

5.7 Comparisonof �:9 levels . . . . . . . . . . . . . . . . . . . . . 90

5.8 Comparisonof �<; levels . . . . . . . . . . . . . . . . . . . . . 92

5.9 Missing-energy spectrumfrom � Li ��& He. . . . . . . . . . . 94

A.1 A comparisonof taggingrates . . . . . . . . . . . . . . . . . . 98

List of Tables

2.1 A tableof variousradii for He,Li andBe. . . . . . . . . . . . . 19

3.1 List of / -particleenergiesfrom a ,0,02 Th source. . . . . . . . . . 42

3.2 List of experimentalparametersandtheir values. . . . . . . . . 53

5.1 Energy levelsin � He . . . . . . . . . . . . . . . . . . . . . . . 84

5.2 A summaryof statesin � He . . . . . . . . . . . . . . . . . . . . 87

xv

Chapter 1

Intr oduction

Oneof the frontiersof today’s nuclearscienceis the studyof structureat the

limits of stability. Theneutrondrip-line is onesuchlimit, beyondwhichnuclear

binding endsand the strongforce no longerholdsnucleonstogether, they lit-

erally drip out of the nucleus.Interestingphenomenatake placein this region

of large neutronto proton ratio, for examplethe formation of neutron halos;

loosely-boundneutrondistributionsthatextendfaroutsidetheboundsof thesta-

ble nuclearmatterdistribution.

A well establishedexampleof ahalonucleusis thatof � He. Thissystemhas

beensuccessfullymodeledasa � He coresurroundedby a two-neutronhalo[1],

andtheneutrondistributionhasbeenmeasuredto extendfar beyondthenormal

nuclearmatterradiusfor a nucleuswith = = 6 [2, 3]. For thesereasons,� He

hasbeenusedasa testcaseto studythebehaviour of loosely-boundthree-body

systems.As a consequence,� He hasbeenoneof the mostextensively studied

halo nuclei, both theoretically[4–13] andexperimentally[14–20]. The results

of thesestudieshave beenthe predictionandmeasurementof new statein the

excitation spectrumof � He. Theseexciting new results,which have emerged

over the pastdecade,have openedup a whole new areaof research.However,

thecalculationsandexperimentaldataarefar from completeor conclusive,and

1

2 Chapter 1. Intr oduction

they requirecontinuedimprovementsandconfirmation.

Experimentalmeasurementsof new statesreportedin theliteraturehavepre-

dominantlybeenfrom reactionsusinghadronicprobes,for exampleradioactive

beamsor ion beams. In generaltheseexperimentshave involved somenon-

rigorousanalysisprocedures.It is thereforeof particularinterestif theavailable

datacanbeimprovedusingmoretransparentexperimentaltechniques.This the-

sis reportson suchanexperiment;onethatprovidesevidenceof a new statein� Hefollowing areactionwith anelectromagneticprobe.Measuringthemissing-

energy spectrumfollowing the reaction � Li �-�.��0� He revealsthe populationof

statesin theresidualnucleus� He. Significantimprovementsareobtainedin the

backgroundremoval processusingtaggedphotontechniques,comparedwith the

radioactive beamor ion beamexperiments.In themeasurementreportedin this

thesis,well-known andunambiguousdataanalysistechniquesareusedto obtain

high-qualitydatathatshowsclearevidenceof a new statein � He.

Thefollowing chaptersgivea detaileddescriptionof how theseresultswere

obtained.Chapter2 presentsthe motivation for conductingthis research.The

featuresof photonuclearreactionsarediscussed,including thespecificreaction� Li �-�.��0� He andthe informationthatcanbeextractedfrom it. An overview of

the physicsof halo nuclei is given, and the literatureon the recenttheoretical

andexperimentalresultsin this field arereviewed. Previousmeasurementsand

thetechniquesusedto analysethemarecritiqued,followedby acommentonthe

improvementsachievedin thecurrentmeasurement.

Chapter3 outlinestheexperimentalmethod.Considerabletechnicaldetailis

givenof theresearchfacility andthedetectorsystemusedto make themeasure-

ment. The dataacquisitioncircuit anddetectorcalibrationarealsodescribed,

andtheexperimentalparametersaretabulated.

Chapter4 explainshow thedatawasanalysed.Importantly, themethodused

3

to unambiguouslyremove the backgroundis illustrated, highlighting the im-

provementsthataremadeover otherexperimentaltechniques.Thestepstaken

to transformtheraw datainto excitation-energy spectraof � Hearecovered.

Theresultsof thedataanalysisarepresentedin Chapter5 andthier signifi-

canceis discussedin termsof theliteraturereview from Chapter2. Thischapter

arguesthattheknowledgegainedfrom the � Li �-�.��0� Hereactionshowsclearev-

idenceof a new statein � He at an energy level of 5 MeV andwith a width of

3 MeV. In thefinal chapter, concludingremarksaremadeon thesignificanceof

theresearchprojectin theunderstandingof halonuclei.

Chapter 2

Moti vation

It might be said that at this stagethe understandingof the structureof nuclei,

thatthelexicon of excitedstateswaswell established,andostensiblyconsistent

with theunderstandingof thenucleon-nucleonforce.Oneareawherethis is not

the caseis wherenuclei arecloseto the neutrondrip-line. Attemptsto predict

their level structureusingmodelssuchastheShellModel failed to explain the

known structure.Recently, asa resultof particularinterestin theseneutron-rich

nuclei, moreappropriatemodelshave beendeveloped. Theseare reviewed in

this chapter.

However, ontheexperimentalfront, attemptsto verify thesepredictionshave

beenfrustratedby the extremeinstability of the nuclei themselves. The major

reactionmechanismusedto probetheir structureinvolvedchargeexchange.Ion

beamreactionshave playeda majorrole in this research[21,22], sincethey can

resultin productionof nucleiwith extremeneutronexcess.They are,however,

somewhatnon-specific,producinga rangeof residualnuclei. Charge-exchange

via thereaction� Li �-��?>�;�� He hasbeenproposed[23] whenthenew 250-MeV

facility is availableat MAX-lab. Evenmoreexotic reactions,involving theuse

of radioactive ionsasprojectiles,have madesomecontribution [17]. Theshort-

comingsof theseexperimentsareanalysedin latersectionsof thischapter.

5

6 Chapter 2. Moti vation

It is thereforereassuringthat,at leastfor the � Henucleus,examinationof its

level structurecanbe doneusingthe relatively simple,but totally appropriate,

photonuclearreaction � Li �-�.��0� He. A proposalwas madeto make this mea-

surementat theMAX-lab, anda preliminarymeasurementby theGentGroup,

althoughfailing to resolve theissue,did provide sufficient justificationto allow

theexperimentreportedhereto proceed.

2.1 Halo Nuclei

Two classesof nuclearhalosexist; neutronhalosandprotonhalos[21]. Of these,

theneutronhaloshave beenstudiedin moredetail,consequentlythey arebetter

understood.The focusof this research,is a neutron-halonucleus� He, andso

thefollowing discussionwill be limited to neutron-halonuclei. In thenext few

sections,anoverview will begivenof thediscovery andsomephysicalcharac-

teristicsof nuclearhalos,followed by a discussionof somerecenttheoretical

modelsandpredictions.

2.1.1 BasicPhysicsof Halo Nuclei

Halo nuclei do not conformto someof the characteristicsof mail-line nuclei.

For example,thenuclearradius @ of stablenucleiwith mass= is foundto obey

therelationship @ ACB 1 =EDF � (2.1)

where B 1HG �JIK� fm. However, thetwo-neutronhalonucleus!0! Li hasa radiusof

3.2fm, aslargeasthemuchheavier nucleus+0, S.

Similarly thesurfacediffusenessof halosdiffer markedly from thenorm.At

the surfaceof stablenuclei, the nucleardensitydropsfrom about70% to 30%

of its maximumover a rangeof 1 fm. The surfacethicknessof halo nuclei is

2.1. Halo Nuclei 7

far greater, andtheneutrondensitydecreasesgraduallyover a rangeof several

fermi [5]. Oneof the moststriking differencesbetweenhalo nuclei andother

nucleicanbeseenby comparingtheradii of theprotonandneutrondistributions.

In the stableisotope � 2 Ca, for example,the differenceis 0.1 fm, whereasthe

surfaceof !0! Li is composedalmostentirelyof theneutronhalo,which extends

approximately1 fm beyondtheprotondistribution [24].

A qualitative analysisof halosrevealsthat the small separationenergy of

thevalenceneutronsis predominantlyresponsiblefor their extendedspatialdis-

tribution. Theattractive forceexertedby thenuclearcoreon a neutron,canbe

approximatedby asquare-wellpotentialandtheradialwavefunctionof aneutron

in this potential,canbewrittenas[22]

L ��BM3A N O�P>�Q eR6S�*�UT O @� !�V�,XW Q e9 RZYB W � (2.2)

where @ is the radiusof the potentialand B is the distanceto the centreof the

nucleus.Thespatialdistributionof thewavefunctionis determinedby thevalue

ofO, which is given by the separationenergy �H[ andthe reducedmassof the

system\ using �*]^ O , A��:\_�H[ZI (2.3)

CombiningEquations2.2 and2.3 it canbeseenthat thesmallertheseparation

energy, thegreaterthespatialdistribution. In stablenuclei,theseparationenergy�H[ of the last neutronis typically 6–8 MeV, while in halo nuclei it is much

smaller, oftenlessthan1MeV. Consequently, thewavefunctionfor theseweakly-

boundneutronsextendsfar beyond the wavefunctionof a neutronin a stable

nucleusof similar mass.

Figure2.1 shows the resultsfrom a calculationof the propertiesof � He by

Zhukov et al. [5] in which the total densitybeyond B`�a�bIKc fm is duemostly


to the valenceneutrons.The matterdistribution of the / -core, dJe , follows the

Figure 2.1: A calculationof the f andneutroncomponentsof the � He matterdistribution. (Source:M. V. Zhukov et al., Phys.Rep.231,151(1993).)

shapeof thefamiliar nuclearmatterdistributiongivenby theFermiprofile

d#��BXgA d 1�UT eh Y 9 Sji%k)V�l � (2.4)

whereB is theradius,d 1 is thecentraldensity, @ 1 is theradiusathalf densityandm is a measureof thediffusenessof thenuclearsurface.On theotherhand,the

neutrondistribution hasa long tail which cannotbeparameterisedusingEqua-

tion 2.4.

Fromtheapplicationof theHeisenberg uncertaintyprinciple, the largespa-

tial extentof thewavefunctionimplies that themomentumdistribution of these

neutronsmustbewell defined.Themomentumdistribution no�p� is theFourier

2.1. Halo Nuclei 9

transformof thewavefunctionL ��BM , andis givenby

no�p�gA q� , T O , � (2.5)

where � is the momentumof the neutronand q is a constant. This equation

togetherwith Equation2.5 and2.3 indicatesthat as the separationenergy de-

creases,thewidth of themomentumdistributionbecomesnarrower.

This is foundto bethecasefor two-neutronhalonuclei in radioactive beam

experiments.Themomentumdistributionof haloneutronsin � Hewasmeasured

following the fragmentationreactionC � � He�Z�:�� He, and determinedto have

a width rsAut<v MeV/c [14] (seeFigure2.2). In contrast,stablenuclei have

Figure 2.2: The fragment momentumdistribution following the reactionC w � Hex*y{z| � He. (Source:T. Kobayashi,Nucl. Phys.A538, 343c(1992).)

a broaderdistribution closeto 80 MeV/c. For more usualnuclei, this can be

parameterisedin termsof themassesof thesystemas

r , A}r ,1 Q�~ �� ~ ��P W � (2.6)

where � is themassof thebeamparticle, ~ themassof thefragmentand r 1�G�J�MeV/c.

From this qualitative overview it is clearthat halo nuclei have significantly


different spatialpropertiesthan normal nuclearmatter. Investigationof these

propertieshasledto thediscoveryof new modesof nuclearexcitation.Thestudy

of nucleiat theextremesof stability promisesmany new researchopportunities

[25]. Neutron-richnucleioffer apossibilityof studyingessentiallypureneutron

matter, which hasnever beforebeendonein the laboratory. Resultsof this new

areaof researchrangefrom understandingthebarenucleon-nucleoninteraction,

to Big Bangandstellarnucleosynthesis[17,26].

2.1.2 GeneralPropertiesof Halo Nuclei

The original observation of what we now refer to asa halo nucleuswasmade

by Tanihataet al. [2] in experimentsusingradioactive nuclearbeams[14,26].

To make radioactive nuclearbeams,high-energy beamsof stableions undergo

spallationreactionswith heavy targetsto produceawiderangeof nuclei,includ-

ing unstableneutron-richnuclei suchas !0! Li and � He. Thesenuclei are then

separated,andacceleratedto producesecondarybeams,which becomeprojec-

tiles for reactionswith secondarytargets. Using this technique,Tanihataet al.

measuredthe interactioncrosssectionsof neutron-richnuclei. The interaction

crosssection( r�� ) is the total probability that a projectilenucleuswill undergo

transmutationafter interactingwith a targetnucleus.Fromtheinteractioncross

sectionr�� theradiusof theprojectilecanbefoundusingtheexpression

r��A}>��@�� T�@�� , � (2.7)

where@ � � and @ �� aretheinteractionradiiof theprojectileandtarget,respectively.

After they carefullyestablishedthat @ � � isawell definedsizeparameter, theirdata

revealedaconsiderablylargerradiusfor !0! Li and � Hethanfor theirneighbouring

nucleus.Initially theeffectwasthoughtto becuasedby a largedeformationor a

2.1. Halo Nuclei 11

tail in thematterdistribution. Figure2.3 shows just how anomalousthesizeof!0! Li is by comparingit with heavier nuclei.

Pb208

Ca48

Li11

Li9

7 fm

12 fm

Figure 2.3: The large matterradiusof !0! Li comparedwith ,0102 Pb and � 2 Ca.(Source:J.S.Vaagenet al., PhysicaScriptaT88,209(2000).)

After Kobayashiet al. [27] experimentallyconfirmedtheresultsby Tanihata

et al., theoristsbeganto pondertheconsequencesof nuclearhalos.Two papers,

oneby HansenandJonson[28] andtheotherby Ikeda[29], independentlysug-

gestedacollectiveresonancecouldbeexcitedasanoscillationbetweenthecore

andthehalo.They calculatedthatthis so-calledsoftdipoleresonance(soft DR)

wouldoccurat lowerenergiesthanothercollectiveresonances,suchasthegiant

dipole resonance(GDR), dueto the weakrestoringforce of the loosely-bound

halo. Subsequentexperimentalandtheoreticalstudiesenthusiasticallypursued


thesoft dipolein their measurementsandcalculations.However, it provedto be

anelusive featureto observe [27,30,31]. Conflictingcalculationsandinconclu-

sive datahave plaguedtheunequivocalconfirmationof thesoft dipole, leaving

its existenceto remainanopenquestion(seeSection2.1.4).

After the ground-breakingidea of binary halosby Hansenand Jonson(in

theircasethey modeled!0! Li asadi-neutronanda � Li core),developmentsmoved

away from this highly clusteredpictureof the nucleus.Currentinterpretations

favour the imageof a tightly-boundcore with a thin veil of neutrons. These

neutronstunnelinto “forbidden” regionsfarremovedfrom the“normal” nucleus,

forming dilute nuclearmatter. This complicatedco-existenceof normalnuclear

matterand loosely-boundnucleonsrequiresthe inclusionof Pauli-blocking in

thewave-functiondescribingthesystem[32]. Pauli-blockingtakesinto account

thattherearefewer degreesof freedomfor thehaloneutrons,sincethethecore

neutronsalreadyoccupy theinnerstates.

Nucleon-nucleoncorrelationin the nuclearhalo plays a crucial role in its

structure.For example, !�1 Li is unbound,but whena neutronis addedto form!0! Li , thesystembecomesbound. It is thoughtthat the three-bodydynamicsof

thecore+ � + � altersthespatialcorrelationssothat,althoughthecore+ � and� + � interactionpotentialsarenot individually sufficiently strongto bind the

two clusterstogether, the three-bodysystemdoesform a loosely-boundstates.

Interestingly, the theory of this type of three-bodysystemwas developedby

ZehnandMacek[33] in 1988in thefield of atomicphysics,whereasit wasnot

until 1993thatZhukov etal. [34] independentlydevelopedthetheoryfor nuclear

halos.

Halo nuclei areof particularinterestin the studyof nuclei far from stabil-

ity, in theneutrondrip-line region. Figure2.4 shows the region on the tableof

isotopeswherethe light halo-nucleiarefound. Along with theobvious interest

2.1. Halo Nuclei 13

β−−decay

halo candidatenaturally abundantH1 H3

Li12Li11Li9Li8

n1

He5 He6 He8

Be7 Be11Be10

He10

Be12 Be14

B8

H2

He3 He4

Li6 Li7

Be9

B10 B11

proton halo?

neutron drip−line

Figure 2.4: Thelower endof thechartof nuclides,showing theneutrondrip-line andcandidatesfor halonuclei

associatedwith nuclearbinding,nucleon-nucleonpotentialsanddiffusenuclear

matter, thereareapplicationsof the studyof neutronhalosin astrophysics.In

particular, � He playsa role in the theoryof Big Bangandstellarnucleosynthe-

sis[17,26].

Nucleosynthesiscalculationsinvolvessolvingmany coupleddifferential-equations

representingtherate,crosssectionandenergy distributionof numerousreaction

chains. Most heavy elementsaremadefrom hydrogenandhelium in a chain

of nuclearreactionsthat proceedthroughstablenuclei. However, nucleosyn-

thesiscanalsooccurvia a seriesof rapid radiative neutroncaptures,calledthe

r-process, suchas

� He��P�3�?�� He��:�3�?�� 2 He�� 9�� 2 Li ��/U�'�� !0! B I (2.8)

In thecaseof Equation2.8,short-livednucleiareproducedthatarenotstableto

particleemission.In orderto calculatereactionratesandcrosssectionsinvolv-

ing theseneutron-richnuclei, accurateinformation is neededon their nuclear

states.Recentcalculationsshow that if thenewly predictedstatesin � He arein-

cluded,thereis asignificantincreasein thecontributionto thecreationof heavier


elementsfrom the r-processchain[35]. Detailedstudiesarenow underway to

determinewhat importancethenew halostatesin neutron-richnucleiwill play

in nucleosynthesis.

2.1.3 Theoretical Descriptionsof Halo Nuclei

The successfulshell model (SM) of nuclei hasnot beenable to reproducethe

new featuresobserved at the limits of boundnuclearmatter. Clusteringinside

halo nuclei appearsto lend itself betterto a few-body treatment,ratherthana

full multi-nucleoncalculation. For this purposethe clusterorbital shell model

(COSM)[36] wasdeveloped,which treatsthenucleusasaninert corewith va-

lenceneutrons.To calculatethestatesin � He, realisticpotentialswererequired

for the neutron-neutronandthe core-neutroninteractionpotentials,alongwith

experimentallydeterminedvaluesof the core radius[1]. The valence-neutron

wave functionswerealsomodifiedto accountfor thePauli-forbiddenstatesthat

exist dueto thereality of thesubstructureof thecore.

ReasonableagreementwasachievedbetweenCOSMcalculationsandscat-

tering data,including the large electromagneticdissociation(EMD) crosssec-

tions of � He and !0! Li [5]. Nevertheless,a fundamentalproblemwith the SM

wave functionsis that they have incorrectasymptoticbehaviour. Sincehalonu-

clei have a largeextendedtail in their neutrondistribution, theSM is an inade-

quatedescriptionof theseweaklyboundstates.To dealwith theextendedwave

functionsproperly, the methodof hypersphericalharmonics(HH) was devel-

opedby Danilin andZhukov [37]. Thismethodmodifiestheco-ordinatesystem

to calculatethethree-bodydynamicsof halonuclei,by definingthehyperradiusd as d , AC= 9 ! +��$�:�?� ! = � = � B ,�� (2.9)

2.1. Halo Nuclei 15

whereB ,�� aretheinter-particledistancesand = is theparticlemass.Calculations

of this typeuse� Heasatestcase,sincethey areparticularlygoodatreproducing

thewell established� ; groundstateandthe �<; first excitedstate[38].

Severalothermodelshavebeendevelopedto studyspecificreactionsinvolv-

ing halo nuclei. Oneapproachis the four-body distorted-wave method,which

modelsthehalo-nuclearsystemasacore+ � + � projectilenucleusplusa target

nucleus[11]. In this model,theground-statewave-functionof thehalonucleus,L ��dj , is calculatedusing the HH method. The dissociationcrosssection,for

example,is thencalculatedusing� r�b��Z�M3A ~��>g]^ , ,( �¡£¢ � � L ��dj? , � (2.10)

where ~ is an expressioncontainingthe masses,momentaand spectroscopic

factorsof the systemand ¡£¢ � is the transitionamplitudefor the reaction. It

is assumedthat neitherthe target nor the otherthreebodiesform excited state

states,a processreferredto as“dif fractive breakup”[10]. In orderto compute

¡£¢ � , anoptical-modelpotentialis usedfor thetargetnucleus,andcore-neutron

( ¤#¥j¦ ) andneutron-neutron( ¤�¦§¦ ) interactionpotentialsarerequired.Onceagain

the � He systemcanbe modeledwith oneof thesebases,because¤#¥j¦ and ¤�¦§¦arewell establishedfor the � He + � andthe � + � systemsfrom experimental

data(see[1, 38] andreferencestherein). Currenttheoreticalandexperimental

studiesseemto be in goodagreement[13], althoughmorework is requiredto

remove someof the assumptionsin the model, and improve the fundamental

understandingof halonuclei.


2.1.4 The Soft Dipole Resonancein Halo Nuclei

Collectiveexcitationshaveplayedanimportantpartin clarifying thestructureof

theatomicnucleus.In earlyexperimentalwork, thephotonucleareffect revealed

theGDR, anda largebodyof datawasgeneratedon thesubject.Realphotons

with energiesupto 30MeV wereusedto excitearangeof nucleiacrossthetable

of isotopes.Usingtheliquid-dropmodel,theGDRis describedasanoscillation

of the“neutronfluid” ralativeto the“protonfluid”, with acharacteristicresonant

energy of ��¨�© S«ª¬:® = 9 DF MeV [39]. Similarly, thesoft DR is describedasan

oscillationof a core relative to the valenceneutrons,andmay alsobe studied

usingmediumenergy photons.

In principle,theGDRin halonucleicanbesplit into two componentsdueto

theloosely-boundvalenceneutrons.Figure2.5showsschematicallythedifferent

components,andthecorrespondingresonanceenergies. Thesoft DR occursat

a lower energy than the GDR due to the weak binding energy of the valence

neutrons,which producesa weaker restoringforce betweenthe core and the

halo. An estimateof the excitation energy of the soft DR, madeby Suzukiet

al. [1], is givenby

��[�¯ ¢ � A t � =�g��°g±_T�²�±' ]^ ,³µ´ @ ,6¶?· 9¹¸ � (2.11)

where³ themassof thehalonucleus, @o, ¶?· 9¹¸ is ameasureof theneutrondistri-

butionradius,°�± and ²�± arethenumberof coreprotonsandneutronrespectively

and � is thenumberof valenceneutrons,so that =Aº°g±3T}²»±3T¼� . Applying

Equation2.11to � He leadsto anestimateof thesoft DR energy of ��[�¯ ¢ � A½v�I ¬MeV.

In practice,thesoft DR hasbeendifficult to observe experimentallyin halo

nuclei. Systematicstudiesarecurrentlyunderway to characterisethedipolere-

2.2. The Halo Nucleus � He 17

saturationproton and neutron

GRDSoft DR

ρ

low neutron density

Eex

transitionstrength

Figure2.5: A schematicdiagramof aneutronhaloformedin � Heandthethreetypesof collective oscillationspossible.(Source:I. Tanihata,J. Phys. G, 22,157(1996).)

sponsein light neutron-richnuclei(seefor exampleAumannet al. [40] andref-

erencestherein). It is the intentionof the presentmeasurementto prodive an

improvementover the currentlyavailabledata,andpossiblyidentify the pres-

enceof asoft DR in � He.

2.2 The Halo Nucleus�He

Thehalonucleus� He hascapturedtheimaginationof thenuclearphysicscom-

munity. The curiousfeaturethat the nucleusis bound,yet noneof its binary

subsystemsare bound,hasled to it being called a “Borromean”system[34].


Figure 2.6: Theheraldicsymbolof theBorromeanRings.

TheBorromeanringsshown in Figure2.6,aretheheraldicsymbolof thePrinces

of Borromeo,carvedin stoneon their castlelocatedon an islandin LagoMag-

giore, in northernItaly. If any oneof the interlockedringsarebroken,all three

comeapart.So too arethe � He + � andthe � + � systemsunbound,while � He

formsastablehalo-nucleus.

2.2.1 The Radiusof ¾ He

The half life of � He is 806.7ms,decayingby ¿ 9 -emissionto � Li . This makes

it hardto performany directmeasurementof its properties.However, with the

developmentof radioactivebeamsit hasbeenpossibleto performscatteringex-

perimentswith beamsof � He. Thefirst observationof the � Hehalowasmadeby

Tanihataet al. [2] who deducedtheinteractionradius @�� from thecrosssection

(seeSection2.1.2andEquation2.7). Using the interactionradius,it is possi-

ble to calculatedtheroot meansquared(rms)valueof thematterradius( @�Àrms),

thecharge radius( @ ±rms) andtheneutronradius( @ ¦rms). A significantdifference

wasfound in the neutronradius @ ¦rms of � He comparedwith � Li. In itself this

is not surprising,since � He hasonemoreneutronthan � Li. Thesignificanceis

bestillustratedby comparingthe differencebetweenthe � He- � Li radii andthe� Be- � Li . Table2.1shows that the =½A ¬ systemshave essentiallythesame@�� ,


and @ ±rms � � Be G @ ¦rms � � Li , asmight be expected. In contrast,� Li hasidenti-

cal valuesfor its matter( @ Àrms), charge ( @ ±rms) andneutron( @ ¦rms) radii, whereas� He shows clusteringof the charge distribution, anddispersionof the neutron

distribution. Thisprovidedthefirst evidenceof theneutronhaloin � He.

Interaction Matter Charge Neutron@H� @�Àrms @ ±rms @ ¦rms� He 2.18 2.73 2.46 2.87� Li 2.09 2.54 2.54 2.54� Li 2.23 2.50 2.43 2.54� Be 2.22 2.48 2.52 2.41

Table 2.1: A table of root meansquared(rms) radii for variousisotopestohighlight thelargeextentof the � He neutronradius.(All valuesarein unitsoffermi.)

Theextentof the � He neutronhalowasconfirmedmostrecentlyby Shostak

et al. [3] usingthereaction� Li �p��6�Á�(0� He with 70 MeV protons.At this energy,

only thesurfacepropertiesof � He werebeingprobed,asthewavelengthof the

protonsis approximately5 fm. Thedatagave a valueof @ ¦rms = 2.85fm, signif-

icantly larger thantheexperimentallydeducednuclearcharge radiusof @ ±rms �2.50fm [3, andreferencestherein]. Theseresultsimply thepresenceof anex-

tendedneutron-cloudsurroundingachargedcentral-core,i.e. aneutronhalo.

2.2.2 NewStatesPredictedin ¾ He

The mostrecentlisting of the known statesin � He [41] shows the first excited

stateat 1.8 MeV, andthenno statesuntil above the + H + + H thresholdat 12.3

MeV. Resultsfrom calculationsof thenuclearlevelsin � He,usingthetheoretical

methodsdescribedin Section2.1.3,have challengedthis picture,with predic-

tions of new low-lying states. This sectiondiscussesthesetheoreticalpredic-

tions,while Section2.2.3considerstheexperimentalevidencefor new statesin� He.


Thenuclearlevelsin a stablesystemof =ÂA � nucleons,suchas � Li , canbe

accuratelycalculatedusingtraditionalShell-Model(SM) methods.For example

thecalculationsby Karataglididset al. [42] arein goodagreementwith theex-

perimentallydeterminedlevels [41]. However, SM calculationshave not been

successfulatexplainingthelevel structurein � He. Onereasonfor this is thatthe

neutronseparationenergy ( Ã(¦ ) of � He is significantlylower that � Li ( Ã(¦j�� He =1.86MeV and Ã(¦j�� Li = 5.66MeV [43]). To modeltheseloosely-boundneutron

systems,modificationsweremadeto thebasesof theSMcalculations.By specif-

ically takinginto accounttheclusteringin thenucleus,modifiedSM calculations

havebeensuccessfulin modeling� He. Generally, this is doneby consideringthe� Henucleusasthreeclusters:� He+ � + � .Thefirst calculationto producea particle-stableboundstatein the � He + �

+ � system,wasperformedby Suzukiet al. [1] usingthe COSM (seeSection

2.1.3). To accountfor the weak binding energy, and the large spatialexten-

sionof thevalenceneutrons,single-particleorbitswith largeangularmomentum

were includedin the calculation. The modelwasable to calculatethe ground

stateof � He, but thebindingenergy wasunderestimatedby 0.5MeV compared

with experimentalvalues.No attemptwasmadeto calculateexcitedstates.The

electromagneticdissociation(EMD) crosssectionwascalculated,and a large

enhancementwasfound betweenan excitation energiesof 4–7 MeV. This was

doneby assumingthatthe � Hecoreremainedin its groundstate,andcalculating

theelectricdipole transition-probabilities�Ä��: for valenceneutronsto states

with ÅÆ�AÇ� 9 . The largedipolestrengthat low excitationenergy wasin agree-

mentwith thepropertiesof thepredictedsoftDR. However, thecalculatedEMD

crosssectionunderestimatedthe experimentalresult,so it wasconcludedthat

moreinformationwasneededon theunderlyingreactionmechanism.Nonethe-

less,theseresultswereasignificantstepin theunderstandingof thenuclearhalo


in � He.

Aoyamaet al. [44] extendedthe the COSM calculationsof Suzuki et al.

using the complex scalingmethod(CSM) [45] to transformthe wavefunction

of � He. Correctionsof this typeavoid problemsassociatedwith theasymptotic

behaviour of thesystem,which is importantwhencalculatingthenuclearlevels.

Significantimprovementswere achieved with this methodover the resultsby

Suzukiet al. Not only wastheground-stateenergy successfullycalculated(0.2

MeV discrepancy with experiment),but the �<; 1.8 MeV first excitedstatewas

predictedat1.81MeV with awidthof 0.26MeV. Thesecalculationswerelimited

to � -shell configurationsof thevalenceneutronsin orderto focuson the three-

bodyresonances,of which the �<; 1.8MeV statesis one.No signof the � 9 soft

DR could be found below 10 MeV using this model, possiblyindicating that

morecomplicatedorbitsneedto beincludedin themodel.

Predictionsof a low-lying � 9 softDR in � Heweremadeby Danilin etal. [8]

usinga � He+ � + � clustermodel.To calculatethegroundandexcitedstates,the

HH methodwasused(seeSection2.1.3)in the framework of charge-exchange

and inelasticscatteringreactions. The distorted-wave impulseapproximation

(DWIA) reactiontheory, appropriatelymodifiedfor dilute matter, wasapplied

to calculatethereactioncrosssection� r�È � � of thereactions� Li ��.��0� He and� He�)��j"$0� He, with an incidentnucleonenergy of �ÉAÊc � MeV in eachcase.

Theuncertaintysurroundingtheexistenceof a truesoft DR “state” is illustrated

by thecurve labeled � 9 in Figure2.7. Althougha local maximumis predicted

in thecrosssectionto a � 9 configurationin � He, it is broadandpoorly defined

comparedwith the � ; strength.Thelackof adistinctpeakhasledto suggestions

thatthe � 9 enhancementis dueto dynamicaleffectsfrom final-stateinteractions

[8,45].

It hasbeensuggestedthat any calculationwhich treatsa � He clusterasin-


Figure 2.7: Reactioncross-sectionto the � He bound-statesandthethree-bodycontinuumfollowing thecharge exchangereaction� Li wËz_xÍÌ#| � He. (Source:B.V. Danilin etal., Phys.Rev. C 55, R577(1997).)

ert is inadequate,consideringthat realisticgroundstatewave-functionsof � He

containonly a 20%admixtureof the � He + � + � configuration[46]. Further-

more,a muchmoreaccuratecalculationof the ground-statebinding energy of� He wasmadeby Csoto [47] (seealso[48]) usingadmixturesof � He + � + �and 5.TÎ5 configurations.Csoto calculatedthebindingenergy of � He relative to� He to be �ºAÏ� � I ® � � MeV, comparedwith �ºAÏ� � I ®M¬ c MeV obtainedfrom

experimentaldata[41]. Despitetheseflaws in three-body� He + � + � mod-

els,theoristscontinueto usethis framework becauseof its successin calculating

charge-exchangereactionsleadingto � He[9,38].

2.2.3 Previous Measurementsof ¾ He

In the last ten years,experimentalstudiesof the neutronhalo have beendone

predominatelyusinghadronicreactions. With the advent of radioactive beam

facilities,many new andexotic nucleineartheneutrondrip-line have beencre-

ated[21]. Haloshave beenstudiedin !0! Li, 2 Be, ! � Be and � He, but of theseonly


� He canbe studiedsimply andeffectively usingphotonucleartechniques.For

this reason,thediscussionof otherexperimentswith halonuclei,will belimited

to measurementsof � He. What follows is a review of five key experimentson� Heandspecificcritiquesof someof theanalysistechniques.

Figure 2.8: � He excitation energy spectrum following the reaction� Li w � Li x � Be| � He. (Source: S. B. Sakutaet al., Europhys. Lett. 22, 511(1993).)

� Li �� Li �K� Be0� He by Sakuta et al. 1993 Sakutaet al. [15] were the first to

claim to have found experimentalevidencefor the soft DR in � He. Following

thechargeexchangereaction� Li �� Li �4� Be0� He,they measuredtheenergy of the� Be reactionproductsusinga magneticseparator. The excitation-energy spec-

trum of � He that wasmeasuredis shown in Figure2.8. Somenotablefeatures

arethehydrogenpeakscontaminatingthespectrum,andthewell known � ; 1.8

MeV first excitedstate.At a centralenergy of 6 MeV, thereis a broadstructure


thatwasidentifiedby Sakutaet al. asa candidatefor thesoft DR. Theangular

distribution datadid not conclusively determinethespin andparity ( Å Æ ) of the

structure. Significantly, the backgroundin the experimentwasnot measured,

ratherit wasdeducedfrom a phasespacecalculation,andnormalisedto theex-

perimentaldata.Thesmoothcurvelabeled1 in Figure2.8,showsthedistribution

obtainedfrom acalculationof thebackground,whichwasnormalisedto thedata

at an excitation energy of about23 MeV. A fit wasmadeto the background-

subtracteddatausingfour Gaussians(labeledcurve2), andthecentroidenergies

obtainedwere �� G �JI � � � �{��b�{� ® MeV. Despitethe lack of a measuredback-

ground,andthecomplicationsresultingfrom thehydrogencontamination,these

resultsdo indicatea broadstructurethatmight beevidenceof thepredictedsoft

DR. They alsohaveevidencefor broadstatesat higherexcitationeneries.

� Li �� Li �K� Be0� He by Janecke et al. 1996 Janecke et al. [16] usedthe same

reactionasSakutaet al., althougha differenttechniquewasusedto extract the� He excitation energy spectrum. In an attemptto cleanup the spectrum,� Be

ejectilesweremeasuredin coincidencewith 430-keV de-excitation � -raysfrom� Be��ÑÐ � BeÒ6Ó [%ÓÔT�� . Figure2.9shows the � He excitationenergy spectrum(a)

without,and(b) with, ade-excitation � -ray coincidencerequirement.Thestates

identifiedin Figure2.9 areat ��ÕA � I � and �JI � MeV, alongwith broadreso-

nancesat 5.6,14.6and23.3MeV. Theangulardistribution dataof the5.6MeV

resonanceseemsto indicateit is a �:; state,but the fit is far from convincing.

Onceagain,like the Sakutaet al. measurement,the contributionsfrom back-

groundreactionslike p � � Li � � Be n werenot measured,but werecalculated.The

structureat Ö 6 MeV found by Sakutaet al. wasconfirmedby Janecke et al.,

but it couldstill notbefully characterised.


Figure2.9: � Heexcitationenergy spectrumfrom � Li w � Li x � Be| � He(a)withoutand(b) with a coincidentde-excitation × -ray requirement.(Source:J.Janeckeetal., Phys.Rev. C 54, 1070(1996).)

� He Ð � He TØ��TÙ� break-upoff Pb and C by Aumann et al. 1999 Thehalf-

life of � He is only 806.7ms,thereforeit is noteasyto performexperimentswith

this nucleus.Despitethis difficulty, Aumannet al. [17] successfullymeasured

the breakupreaction � He Ð � He To�ÚTC� by scatteringa secondary� He beam

off PbandC targets.A primarybeamof !�2 O wasfragmentedusinga beryllium

target; the � He fragmentswerethenseparatedandtransportedto thesecondary

target.

Figure2.10showstheexcitationenergy spectraof � Hededucedfrom thein-

elasticnuclearscatteringoff PbandC. Thefamiliar �<; 1.8MeV resonancewas

observedwith aresolutionof 0.2MeV. Therewasevidencefor asecond� ; state

at 4.4 MeV thatconflictedwith � ; stateat 5.6 MeV reportedby Janecke et al.:

thestatefoundby Aumannet al. was0.2 MeV wide, whereasthat claimedby


Janecke et al. hada width of 10 MeV. Qualitativeanalysisof thedatasuggested

thepresenceof strengthin thelow-lying continuumfrom amixtureof monopole

and quadrapoleresonances.No indication of the soft DR was reported,and

above thefirst excitedstate,thespectrumappearsrelatively smoothandfeature-

less. This might be dueto restrictionsin the possibletransitionsavailable for

inelasticscatteringbetweenstatesof certainspinandisospin[18].

Figure2.10: � Heexcitationenergy spectrumfrom thefragmentationof � HeoffPbandC targets.(Source:T. Aumannetal., Phys.Rev. C 59, 1252(1999).)

� Li �� Li �K� Be0� He by Nakayama et al. 2000 Like Janecke et al. andSakuta

et al. beforethem,Nakayamaet al. [19] measuredstatesin � He via thecharge

exchangereaction � Li �� Li �K� Be0� He. However, their approachto thedataanal-

ysis wascompletelydifferent to the previous two measurements.Firstly, they

isolatedthespin-flip ( 7ÛÃ�AÜ� ) from thespin-nonflip( 7ÛÃ A � ) excitationsby

measuringde-excitation � -raysin coincidencewith � Be ejectiles[49]. It was


thenassumedthatthe 7ÛÃÝA � spectrumcontainedexclusively GDRexcitations,

andthe 7ÛÃ«A½� spectrumcontainedamixtureof thesoftDR andthespindipole

resonance(spinDR). Citing previousstudiesondipoleresonances,theGDRand

the spin DR wereassumedto have the sameenergy distributionsandthesame

strength. On this basis,the soft DR was observed by simply subtractingthe7�Ã£A � spectrumfrom the 7ÛÃÝA½� spectrum.

The resultingfit to the structurecanbe seenin Figure2.11 asa shaded-in

Lorentziancurve,with anexcitationenergy of ��ACv MeV andawidth of ÞßAv MeV. As with all theothermeasurements,the � ; 1.8 MeV first excitedstate

is observed. Claimsby Nakayamaet al. that the resultsarea candidatefor the

soft DR, maybecompromisedby not having consideredany otherbackground

channelsin their analysis. Consideringthat the spin DR backgroundwasnot

measureddirectly, andthe assumptionsmadeto accountfor it, the spectraare

not totally convincingevidencefor thesoftDR.

� Li ��56�à+ He �� He by Nakamura et al. 2000 Nakamuraet al. [20] measuredthe

reaction� Li ��56�à+ He�� Hewith a secondarytriton beam,usinga methodsimilar to

Aumannet al. A � He beamimpingedon a beryllium target to producea triton

beam,whichin turnimpingedona � Li target.They observedabroadasymmetric

structureat ��Ö�c MeV, alongwith thefamiliargroundandfirst excitedstates.

The � Heexcitation-energyspectrumthey measuredcanbeseenin Figure2.12.A

distributionmomentumtransferwasalsofound,andwhencomparedwith theory

wasin agreementwith a transitionto negative parity stateswith 7Ûá�AÊ� . The

analysisprocedurestill containssomeof theflaws of thepreviousexperiments;

Specifically, thebackgroundwasnotmeasured,but calculationedandnormalised

to thedata.No otherspecificbackgroundchannelswerecorrectedfor. Despite

thesedrawbacks,thesedataprovide goodevidenceof thepresenceof low-lying

dipolestrengthin � He.


Figure 2.11: � He excitation energy spectrum following the reaction� Li w � Li x � Be| � He. The two spectrashown are(a) the â�ã`äså spin-flip spec-trum and(b) the â�ãÙäÎæ spin-nonflipspectrum.(Source:S.Nakayamaet al.,Phys.Rev. Lett. 85, 262(2000).)

2.3 Advantagesof the ¬ Li ç6èêé�ëíì � He Measurement

In theprevioussection,all theexperimentsshowedsomeevidenceof new struc-

turein theexcitation-energy spectrumof � He. They all revealedgroundstateand

known first-excited state:essentialfeaturesthat mustbe seenfor the resultsto

becredible. In theregion of primary interest,from 3 to 10 MeV excitation,the

experimentaldatado not agree.Two of the � Li-beamexperimentsshow broad

overlappingstates,while the othershows a singlenarrow state. Similarly, the

tritium-beamexperimentshowsamixtureof broadstates,andthe � He fragmen-

tation reactionshows a single narrow state. One threadthat runs throughall

the previous experiments,is the lack of an unambiguousbackgroundremoval

process.

2.3. Advantagesof the � Li �-��0� He Measurement 29

Figure 2.12: � He excitation energy spectrum following the reaction� Li wÍîïx + He| � He. (Source:T. Nakamuraetal., Phys.Lett. B493, 209(2000).)

Noneof theexperimentsusinglithium-ionsmeasuredthebackgroundfor the

datathey present.Consequently, they donothaveaconsistentmethodfor dealing

with the backgroundreactionchannels.On the otherhand,the tagged-photon

techniqueusedto measurethe � Li �� He reaction,measurestheuncorrelated

backgroundcontribution aspart of the normalexperimentalprocedure.In the

off-line dataanalysis,theuncorrelatedspectrumis producedandsubtractedfrom

thecorrelatedspectrumto giveabackgroundcorrectedspectrum.Thisprocessis

well-known[50–55],andhasbeenusedsuccessfullyin severalimportantstudies,

for examplethatby Kuzinet al. [55].

The importanceof thenew resultspresentedin this thesisis not strictly re-

lated to the photonuclearreactionmechanism,as they are not explicitly com-

paredwith any photoabsorptionmodels.However, it is serendipitousthatthecur-


rent interestin halonuclei, in particular � He, andotherareasof nuclearphysics

shouldoverlapin the reaction � Li �� He. Indeed, � He is probablythe only

neutron-halonucleusthatcanbestudiedusingphotonucleartechniques:heavier

neutron-richnucleimustbe createdby fragmentationreactionsat a radioactive

beamfacility. Thus,usinga stable� Li targetanda taggedphotonbeam,a very

cleanpictureof the nuclearlevels in � He hasbeenobtained. Importantly, the

groundstateandfirst excitedstateareclearlyobserved,alongwith new structure

abovethesewell known states.Theprecisionof the �-�� measurement,includ-

ing a carefulbackground-subtractionprocess,hasgivenclearandunambiguous

evidenceof theexistenceof at leastonenew statein � He.

The chaptersthat follow, describethe experimentalanddata-analysistech-

niquesusedto obtainthenuclearlevelsin � He.

Chapter 3

Experimental Method

A beamof taggedphotonsin theenergy range�ñðØA 50–70MeV wasusedto in-

ducethereaction� Li �-��0� He. Photontaggingis achievedusingfastcoincidence-

detectionelectronics,whichmeasuresboththerealeventsandtherandomevents.

In thisexperiment,notonly areprotonsproduced,but awholerangeof particles,

for exampleneutrons,deuterons,tritons andhelium isotopes.All the charged

particlesemittedby the photonuclearreactions,weredetectedusingsolid-state

detectortelescopes.A charged-particlespectrometerwith two componentswas

usedto identify the protonsfrom the otherchargedparticles,on the basisthat

particleswith differentmass,charge andenergy, have a differentrangein each

detectorcomponent.Thisallowseachparticletypeto beseparatedfrom theoth-

ersby their energy-losscharacteristics.All thedatacollectedfrom thedetector

systemswererecordedby acomputerandstoredfor off-line analysis.

3.1 ProducingPhotons

In orderto studythe �� photonuclearreactionsit is necessaryto haveaknow

flux of photonswith a known energy. Sourcessuchasnaturalradioactive iso-

topescanbeused,but they arelimited in their useby therelatively low energy

31

32 Chapter 3. Experimental Method

photonsthey emit (of order1–10MeV), and the difficulty in measuringtheir

flux. To producephotonsof higherenergies( � 10 MeV) electronaccelerators

arerequired.Thefirst few sectionswill discussthegeneralprinciplesof thetech-

niqueusedfor theexperimentpresentedin this thesis.Thesubsequentsections

will discussthespecificsof thelaboratorywheretheexperimentwasconducted.

3.1.1 Photonsfr om Bremsstrahlung

Whenan electronis scatteredby the Coulombfield of a nucleus,a photonis

createdto conservemomentum.Photonscreatedthiswayarecalledbremsstrah-

lung, the Germanword for brakingradiation,i.e. decelerationradiation. The

energy spectrumof this type of radiationis continuous[56], ascanbe seenin

Figure3.1.

Eò

γó (MeV)0ô

10 20õ

30ö

40÷

50ø

60ù

70ú

80 90û

100

Nγ

(MeV

-1)

1

10

102ü

103ý

104

105þ

Tagging Range

0ô

10 20õ

30ö

40÷

50ø

60ù

70ú

80 90û

100

1

10

102ü

103ý

104

105þ

Figure 3.1: The Schiff energy spectrumof bremsstrahlungproducedby anelectronbeamof energy ÿ ��

MeV.

If a beamof electronsimpingeson a thin targetof high-° material,for ex-

amplegold, bremsstrahlungphotonsareemittedwith energiesfrom zeroup to

3.1. Producing Photons 33

theincidentenergy of theelectrons�� . Thesehigh-energy photonscanbeused

to inducenuclearreactionsin targetsmadefrom stablenuclear-matter. However,

sucha measurementonly provides an integratedyield, rather than an energy

dependentcrosssection.In orderto performhigh-resolutionenergy dependent

measurementsthat canresolve individual nuclearstates,the interactingphoton

energy mustbeknown. Onetechniquedevisedto achieve this is calledphoton

taggingandis describedin thenext section.

3.1.2 PhotonTagging

The techniqueof photontaggingis designedto indirectly measurethe energy

of bremsstrahlungphotons. A schematicdiagramillustrating the principle of

photontaggingis shown in Figure3.2. If anelectronof energy �� is scattered

by a thin radiator, andits final energy is measuredto be �»"� , the energy of the

photonthatis createdis givenby

�ñð»AC�� "� I (3.1)

Thescatteredelectronis detectedin a positionsensitivespectrometerwhich is

discussedin detail in Section3.2.3.

Assumethat thephotontheninteractswith a targetnucleus,resultingin the

emissionof a reactionproduct-particle. If this particle is detectedin coinci-

dencewith theassociatedscatteredelectron,theenergy of theinteractingphoton

is determinedby Equation3.1. In the resultingexperimentaldata,a complete

measurementof thekinematicsof eachreactioneventis recorded.


e eγE = E − E’

E’e

Ee

Radiator

Electron Beam

Bending Magnet

Photon Beam Target

DetectorDetector

Timer

Coincidence

Electron

ChargedParticle

Figure3.2: Theprincipleof photontagging,showing theelectronspectrometerwhich is usedto detectrecoil-electronsin coincidencewith ejectilesfrom thetarget.

3.2 The MAX-lab

TheMAX-lab is theSwedishNationalElectronAccelerator Laboratory for Nu-

clear Physicsand Synchrotron RadiationResearch and is situatedon campus

at Lund University in Sweden.Amongsttheacceleratorfacilities is an injector

race-trackmicrotron,MAXINE, andan electronstorage/stretcherring, MAX-

I. MAXINE is usedasa sourceof energetic electronsthatareinjectedinto the

storage/stretcherring. MAX-I is primarily usedasa sourcesof high-luminosity

X-ray for synchrotron-lightexperiments.It canalsobeusedasa pulsestretcher

to producea continuouswave (CW) electron-beamfor nuclearphysicsexper-

iments. The taggingfacility at the MAX-lab usesthis CW electronbeamto

producebremsstrahlungwith energiesof up to Ö 95 MeV. A schematicof the

equipmentandthebeamline relevantfor nuclearphysicsis shown in Figure3.3.

The following sectionsgive a descriptionof the MAX-lab taggingfacility

andtheconfigurationwhichwasusedfor theexperimentpresentedin this thesis.

3.2. The MAX-lab 35

e Injector−

e Beam−

γ Beam

MAX−I

GROUND FLOOR

Kicker Magnet

Dipole Magnets

Quadrupole Magnets

Septum Magnet

Undulator

500 MHzCavity

Synchrotron Light Beam Lines

Tagger

Nuclear Physics Beam Line

550 MeV Storage Ring

BASEMENT 100 MeV Microtron

Figure 3.3: A schematicoverview of theMAX-lab showing the taggerin thebasement.(Source:J.-O.Adler etal., Nucl. Instr. andMeth.A294, 15(1990).)

3.2.1 The MAXINE Electron Accelerator

The primary electronacceleratorat the MAX-lab is a 100 MeV race-trackmi-

crotroncalledMAXINE, a detaileddescriptionof which is presentedin Refer-

ence[57]. MAXINE is a pulsedacceleratorand is usedto inject the MAX-I

storage/stretcherring with a beamof energeticelectrons.A pulsedbeamis pro-

ducedbyanelectrongundeliveringa100keVbeamintoabuncher, whichinjects

into the linearaccelerator(linac). The linac consistsof a radio frequency (RF)

cavity that producesa standingwave to accelerateelectronbunches.After the

electronsemergefrom theRF cavity, apair of magnetsguidesthebuncharound

andbackinto thecavity (seeFigure3.4). Eachpassthroughthelinac, increases

thekinetic energy of anelectronby Ö c MeV, up to a maximumof 19 turns.A

small magnetis usedto extract the beamin an evacuatedtransportbeam-line.

Theusualoperatingenergy of MAXINE is Ö ® c MeV at anaveragecurrentofÖ 30 nA.

Theacceleratorcanbeoperatedin two frequency modes;at50Hz in synchrotron-

light mode,and at 100 Hz in photon-taggingmode. For this experimentthe

microtronwassetto anenergy of 92.45MeV in 100Hz mode.


Buncher

ElectronGun

MagnetsDisplacing

BendingMagnet

BunchesElectron

Extraction Magnet MagnetBending

RF Cavity

Linac

Figure 3.4: A simplifiedview of MAXINE, the100MeV microtronat MAX-Lab.

A drawbackof this accelerationmethodis thatbunchesof electronsarede-

liveredin Ö 1 \ s pulsesevery 10 ms,i.e. a duty factorof 0.01%.Thearrival of

sucha largebunchin ashorttimewouldfloodanelectrondetectorsystem,mak-

ing taggingexperimentsvery difficult to conduct.Thesolutionto this problem

is to stretchthe beampulseto several millisecondslong, producingan almost

continuousbeamof electrons.At theMAX-lab this is achievedwith theMAX-I

stretcherring asdiscussedin thenext section.

3.2.2 MAX-I BeamPulseStretcher

The MAX-I ring [58,59] functionsasboth a beam-pulsestretcherfor nuclear

physicsmeasurements,anda storagering for synchrotron-lightexperiments.In

synchrotron-lightmodeit is capableof acceleratinganelectronbeamup to 550

MeV andstoringthis beamfor severalhours.For thepresentexperimentit was

usedasa pulsestretcherto producea CW beam. To achieve this, the ring is

injectedevery 1.3 ms with a 0.4 \ s long pulsefrom the microtron. After the

pulse-stretchingprocess,theduty factorof thebeamis increasedfrom Ö 0.01%

3.2. The MAX-lab 37

to Ö 50%.Theextractionprocessis controlledby theseptummagnet(seeFigure

3.3). As electronsloseenergy in the ring from synchrotronradiation,they fall

into anorbit that theseptummagnetextractsout of the ring. A beam-linethen

transportsthenearcontinuouselectronbeamto the tagginghall, wherebrems-

strahlungphotonsareproduced.

3.2.3 The MAX-lab Photon Tagger

TheMAX-lab photontagger� is capableof taggingphotonsin theenergy range��ð = 20–80MeV. It consistsof a magneticspectrometerthat focuseselectrons

to a point along the focal plane(seeFigure3.5). The photontaggingenergy

is calculatedfrom the positionof the electrondetectorsalong the focal plane.

Thereare64 electrondetectorsmadefrom NE102plasticscintillatorsmaterial

andhave anenergy resolutionof 78�ñð G 300keV. Thetaggerhastwo arraysof

32 detectorswhich canbe moved independently, andcover an energy rangeof

about10 MeV each.Thetaggingenergy rangeis setby sliding thetaggeralong

railsalignedwith thefocalplane.

Thespectrometerhasafixedmagneticfield of approximately0.3T. An elec-

tron passingthroughthis field will bedeflectedin a circularpath,with a radius

proportionalto its energy. Therefore,electronsof a givenenergy will all cross

thefocal planeat thesameposition.Thepositionson thefocal planehave been

calibratedto electronenergy.

Theefficiency with which photonsaretaggedis � � Ö 25%. For somemea-

surementswheretheabsolutecross-sectionof thereactionis required,a special

measurementof thetaggingefficiency is madeto determine� � for eachof the64

detectors.Theoperatingcurrentof thebeamthat is extractedfrom theMAX-I�Thetaggerdescribedherewasin operationat theMAX-lab from 1993until 1999.A differ-

ent taggerwasusedbefore1993anda new taggerwill be installedin 2001which hasdifferentcharacteristicsfrom theprevioustwo.


To ElectronBeam Dump

ExitFlange

γE = E − E’eeeE

eE’

γ eE = 0.1 E

γ eE = 0.8 E

Magnetic ElectronSpectrometer

Focal−planeDetectors

Moveable

Focal Plane

CollimatorPhoton Beam

Electron Paths

Target

EjectileRadiator

Electron Beam

Under Vacuum

Not To Scale

Detector

Figure 3.5: TheMAX-lab photontagger.

ring is approximately100nA. Thistranslatesinto acountratein eachfocalplane

detectorof about �� electronsper second(seeAppendixA). A complete

descriptionof thetaggerusedin theexperimentcanbefoundin Reference[60].

3.3 DetectingProtons

In order to measurethe reaction � Li �� He, it is necessaryto identify the

protonsamongsta rangeof particlesemitted from the � Li target. The pho-

tonuclearreactions� Li �� , � Li �� !� , � Li ��#"�� , � Li ��#$%� , � Li ��'& He� and� Li ��)( He� producecharged particlesthat are detectedtogetherwith protons

from the � Li �� He reaction. The detectorsystemthat was used,detected

chargedparticlesin sucha way that they canbesortedby typeusingcomputer

3.3. DetectingProtons 39

analysis.Thefollowing sectionsdescribetheprincipleof detectingprotonsand

thereactionchamberusedin this experiment.

3.3.1 The GLUE Chamber

In previous collaborationsbetweenGent University and Lund University [53,

61] theGentgroupconstructedtheGentLundUniversitiesExperiment(GLUE)

chamber. It consistsof ametalvacuumchamberwith targetholdersfor anarray

of *,+ - + detectortelescopes,shown schematicallyin Figure3.6.For thepresent

measurement,detectorswereplacedat anglesof 30- , 60- and90- .90

60

30

Photon Beam

Beam Exit PortBeam Entrance Port

Vacuum Chamber

Cold Metal Plates

Cold Fingersin Liquid NitrogenE

E∆

Target

Figure 3.6: Topview of thedetectorpositioningin theGLUE chamber.

Thephotonbeamentersandexits thechamberthroughthin mylar windows

attachedat eachend. In order to reduceany backgroundcausedby the beam

interactingwith the mylar, the entranceandexit pipesare madeas long as is

practicable.This configurationshieldsthe detectorsfrom a direct line-of-sight

view of charged particlesemittedfrom the exit and entrancewindows. Con-

nectedto theexit pipeis a turbopump,thatevacuatesthechamberto a pressure


of approximately��/. � torr.

A target holderthat canrotatethrough360 degreesandmove vertically, is

positionedin line with thebeam.Thespectrometersarearrangedaboutthecen-

tral axisof the targetholder, on a circle with a radiusof 100mm. Theproduct

particlesaredetectedin thetelescopearray.

In order to distinguishbetweenthe different type reactionproducts,each

spectrometerconsistsof a thin *+ detectoranda thick + detector. The *,+detectormeasuresthepartialenergy lossof aparticleasit passesthrough,while

the + detectoris thick enoughto stopall the chargedparticleof interest,and

measurestheremainingenergy. A comparisonof the *,+ -signalto the + -signal

in off-line analysisallowsthedifferenttypesof chargedparticlesto beidentified,

anddescribedin detail in thenext two sections.

3.3.2 Solid StateDetectorTelescopes

Design The detectortelescopesweredesignedto measurethe *,+ andthe +of a chargedparticlefor thepurposesof particleidentification.Theprincipleof

particleidentificationis describedin Section3.3.3.Figure3.7shows thedimen-

sionsof a telescopeandthematerialsusedfor construction.EachE detectorwas

mountedin a metalholderthatwasin thermalcontactwith a metalplate. The*,+ detectorsweremountedin aluminiumholdersandsuspendedfrom a rack

hangingfrom thetopof thevacuumchamber.

Thethin *,+ detectorwasmadefrom silicon 500 0 m thick, anddesignedto

allow particlesthroughinto the thicker germaniumdetector, while losing only

part of their kinetic energy. In turn, the + detectorwas 15 mm thick HPGe,

anddesignedto completelystopthe highestenergy chargedparticles,in order

to measuretheir total kinetic energy. In particular, the highestenergy protons

createdin the � Li ��1� Hereactionwith +32 = 50–70MeV havearound60MeV


85 mm

35 mm

Signal Lead Connectors

Brass Casing

Steel Holders

500 m Si

15 mm Ge

35 mmµ

Figure 3.7: Chargedparticledetectortelescopewith aSi-465 andaGe-5 .

of kineticenergy, anda rangeof 9.5mm in germanium.

Operation In orderto reducethe inherentrandomelectricalnoisethe HPGe

detectorsneedto be operatedat low temperatures,around-190 -%7 . This is

achievedby mountingthemon aplatethatis attachedto acold fingerimmersed

in liquid nitrogen(seeFigure3.8).

Thebiasvoltageson eachof thedetectorsweresetto maximisetheenergy

resolution.The full width half maximumof thepeaksproducedby 8 -particles

from 9�9�: Th wasusedasa measureof resolution.Thesepeakswerealsousedto

calibratethedetectors.


Dewars

−Sourceα

γ−Beam

Mylar Window

Pump

7Li

27Al

Mylar Window

Cold Fingers

Liquid

Nitrogen

Figure 3.8: Sideview of theGLUE chamber.

Calibration An energy calibrationof the *,+ and + detectorswasperformed

using 8 -particlefrom a 9�9�: Th source.The *,+ detectorsweremovedup from in

front of the + detectors,soeachdetectorwasirradiatedby thesource.A typical8 -particleenergy spectrumfrom the 9�9�: Th decay-chaincanbe seenin Figure

3.9. The energy of the 8 -particlesfrom this decaychainaretabulatedin Table

3.1. The *+ and + detectorswerecalibratedon a regularbasisto monitor the

stabilityof thegain.

PeakNumber ParentNucleus Energy (MeV)1 9�9�: Th 5.422 9�9 ( Ra 5.693 9<;�9 Bi 6.054 9<;�9 Bi 6.095 9�9�= Rn 6.296 9<; � Po 6.787 9<; � Po 8.78

Table3.1: A list of > -particleenergiesfrom a 9�9�: Th source.Thepeaknumbersarelabeledin Figure3.9.


Energy (MeV)?5

@6A

7B

8 9C

Cou

nts

(MeV

-1)

0D10

20

30

40E50@60A70B80

1

2F

3,4

5@ 6

A

7B

228Th α-Spectrum

Figure 3.9: The energy spectrumof > -particlesemittedfrom the calibrationsource9�9�: Th, energy valuesaregivenin Table3.1.


3.3.3 ChargedParticle Identification Method

The two-componenttelescopedetectorsare designedto provide datathat can

distinguishbetweendifferent typesof charged particles. This is achieved by

measuringthepartialenergy lossin thethin *+ Si detectorandthetotal energy

lossin thethick + HPGedetector, asshown in Figure3.10.

Charged Particle Path

µ500 m Si 15 mm Ge

t

EE+∆ E

E∆ E

Figure3.10: Schematicof the 465 - 5 telescopedetectorsystemusedfor parti-cle identification

Theenergy lossperunit pathlengthof a chargedparticlethroughmatter, is

accuratelydescribedusingtheempiricalBeta-Blochrelationship[62] givenby

G "H+"/IKJ L�MON (QP 9RTS#U 9%V�9 WYX[Z�\^]Y_a` RTS#U 9 V 9b c G \^] �<� G V 9 � G V 9ed � (3.2)

where RTS is the electronrest mass,the particle hasa rest mass f ghg RTS ,charge P , velocity V Jjilk U , energy loss "H+ alonga path "/I in a mediumwith

atomicnumberX

andW

atoms/cm& . The ionisingpotentialb

of theabsorbing

atomsis anexperimentallydeterminedparameterrelatedto theelectroncharge

distribution. For particleswith non-relativistic velocities,the energy loss in a

givenmediumcanbereducedto

"H+"/IKm f P 9+ n (3.3)


Sofor a given incidentenergy + andcharge P , for exampleprotons,deuterons

andtritons,particlescanbeseparatedoutaccordingto their mass.

Theenergy loss *+ in theSi detectorof thickness$ is givenby

*+ Jporq= "H+s��I��"/I "/I n (3.4)

UsingEquation3.3weget

*,+ mto q= R P 9+s��I�� "/I J R P 9+vu $w� (3.5)

where +s��$%�yxK+ u xz+s��H� . In mostcases,whereparticlesareproducedin pho-

tonuclearreactionswith +32 = 50–70MeV, *,+|{}+ andso + u�~ + . Thus,the

relationshipbetween*,+ and + in the detectortelescopecanbeapproximated

by *+ m f P 9 $+ n (3.6)

The f k + dependencecanclearly be seenin plots of *,+ against+ shown in

Figure3.11.Theability to measurethe *,+ and + of areactionproduct,provides

acleanmethodof particleidentification.

E (Channels)0�

200�

400�

600 800 1000

∆E (

Cha

nnel

s)

0�200

�400�600

800

1000

1200

electrons� protons�deuterons�tritons

�3He

4He�

Figure 3.11: A 465 - 5 from a particle spectrometer, showing the differentbandsof chargedparticlesthatareformed


3.3.4 � Li Target

Thelithium metaltargetwasa99%enriched� Li , measuring� �� L/� �� n�� mm,

andcoveredby8 0 m thick aluminiumfoil for protection.Lithium metalcorrodes

readily in air andhadto betransportedin anair-tight container, filled with inert

argongas.Thecontainerwasopenin theGLUE chamberwhich wasalsofilled

with argon gas. While the target wasbeingmounted,argon wascontinuously

flushedthroughtheGLUE chamberto prevent it comingcontactwith air. Once

the target wasmounted,the chamberwasevacuatedandcould not be brought

back up to atmosphericpressurewith air, until the experimentwas complete.

Thetaregt wasplacedat anangleof 60- to theincidentphotonbeam.

3.3.5 Nuclear Experimental Hall (Cave)

An overview of the nuclearexperimentalhall, or the cave, is shown in Figure

3.12. Thephotonbeamentersthe cave througha port in the leadandconcrete

shielding.A steelcollimatorwasplacedat theentranceport to definethebeam.

The GLUE chamberwas positionedas closeto the collimator as possibleto

minimisethebeamspotsizeat the target. Thebeamspotwasmeasuredat the

targetpositionusingPolaroidfilm, andhadadiameterof 20mm.

Part of theelectronicswasassembledin thecave to reducethenoisepickup

on thecables.Thenoisearosefrom strayfieldsassociatedwith theaccelerator

andotherelectricalequipment. The pre-amplifiersandthe amplifierswereas

closeto theexperimentalchamberaspossible,to ensurethata cleansignalwas

sentto the countingroom for further processing.The countingroom wasnear

thetagginghall, andcontainedthedataacquisitionsystem.


Collimator

Beam

Beam

� � ��

� � � ��

� � � � � ��

� ��

� � � � ��

Permanent Walls

Movable Pallets (Shielding)

Movable Detectors (Unused)

Entrance

GLUE

Electronics

Photon Beam

Tagger

Concrete Pylons

Dump

Dump

Figure 3.12: Schematicview of the layout of the experimentalhall showingthepositioningof theexperimentalchamberandthetaggingspectrometer.


3.4 Data Acquisition System

3.4.1 Overview

The dataacquisitionsystem(DAQ) processedthe signalsthat were generated

by charged particlesdepositingtheir energy in the detectors. To processthe

signals,an electroniccircuit wasassembledfrom NIM andCAMAC modular

electronics.If thesignalstriggeredthecorrectresponsein theDAQ, thedatafor

that event wasstoredby the computer. The minimum trigger conditionswere

a hit in both *,+ and + of any one of the detectortelescopesin the GLUE

chamber. The eventsstoredby the computercould alsobe viewed on-line, to

tunethecircuit andto monitor theprogressof theexperiment.Eachstepin the

acquisitionprocessis describein detail in thefollowing sections.

3.4.2 HardwareCir cuit

Thehardwareusedin theDAQ systemfor this experimentconsistedof modules

usingdifferentstandards;bothNIM andCAMAC.To optimisethesignalquality,

themodulesweresplit betweenthecaveandthecountingroom.

The pre-amplifierswere locatedin the cave andconnectedto the detectors

with veryshortcables( ~ 10cm). Keepingthemcloseto thedetectorsto reduce

their capacitive effect, andto minimisedany noisethey may addto the signal.

Eachpre-amphadtwo outputs;an + -outputandanintegrated� -output.The + -

outputsignalswereconnectedto spectroscopy amplifiersandsentto thecontrol

room. The � -outputsignalswereconnectedto a timing filter amplifier (TFA)

to remove high frequency noisefrom thesignal,andtherebyreducethe timing

jitter. Constantfractiondiscriminators(CFD) wereusedto determinethearrival

timeof the � -signals.Thedelaytimesandthresholdsof theCFDswerecarefully

optimisedfor eachdetector, to minimisethewalk-timeof thelogic output.

3.4. Data Acquisition System 49

The *,+ detectorsprovideda fasterandmorestabletiming signal,andwere

thereforeusedto establishthe coincidencebetweenthe *,+ and + detectors.

The requirementof a hardwarecoincidencebetweenthe *,+ and + detectors

eliminatedtheneedto processlow energy particlesthatarestoppedin the *+detectors.Figure3.13 shows how the narrow *+ signal is delayedso that it

falls within thewide outputfrom the + CFD andestablishesthecoincidencein

theAND gate.In thecountingroom,thesignalsfrom thecave wereattenuated

usingdecadeboxesto matchthedynamicrangeof theADCs andCFDs.

TFA CFD

E∆

E∆

CircuitTo X−Trigger

T

E

T

E

TFA

Amp

CFD

To ADC

To ADC

Pre−Amp

Pre−Amp

Charged Particle

More stable Ge detectordetermines the coin timing

E

E

Amp Delay

Delay

AND

Figure 3.13: 465 - 5 coincidencecircuit for for achargedparticletelescope

The timing betweenthe taggerandthe chargedparticletelescopes,i.e. the

photontaggingprocess,wasnot determinedin hardwareaswasthe *,+ - + tim-

ing,but ratherin softwareduringtheoff-line analysis.A timeto digital converter

(TDC) recordedthetime differencebetweenthetaggerandthetelescopes.The

presenceof thecoincidencepeakin theTDCs indicatesthatphotonsweresuc-

cessfullytagged(seeSection4.6.1).

Oncean event triggeredthe DAQ, an interruptsignalwassentto the VME

computerto readthe ADCs andTDCs that were in the CAMAC crate. After

theVME readtheevent,it senta donesignalto cleartheCAMAC modulesand

readythe DAQ for the next event. The VME operatedon a Linux kerneland


wasconnectedvia anEthernetnetwork to a Sunworkstation.Thedataratewas

low enoughfor the VME to readand temporarilystoreseveral events,before

transferringthemto theworkstation.Theworkstationsavedthedatato diskand

8 mm storagetape,aswell asdisplayingit on-screen.

TheDAQ circuit is shown in Figure3.14. For clarity thefigureshows only

schematicallyhow thecircuit wasconnected,omitting thedelaymodules,atten-

uatorsetc.

Delay

E∆

CFD

CFD

CAMAC

ADC

X−Trigger

MachineTrigger

Data S

tream

WorkstationData Tape

OR

Rea

d/C

lear

TDC

Inpu

t

Gat

eS

tart

Sto

p

o

o

90o60

30

Gate Generator

Inhi

bit

FIFO

Tagger

Ethernet

Bus

y

Interrupt

ComputerVMEI/O

NIME AND

� �� Figure 3.14: The Logic circuit diagramfor the dataacquisitionelectronics.Somemodulesexplainedin thetext wereleft out for clarity.

A list of themodulesandtheir functionin thecircuit follow:

3.4. Data Acquisition System 51

NIM Analog:

Ortec 140A Pre-amplifier

Ortec 590 Spectroscopy amplifier

Ortec 510 Timing filter amplifier(TFA)

Ortec 410 Constantfractiondiscriminator(CFD)NIM Logic:

LeCroy 222 Gateanddelaygenerator

LeCroy 622 Logic moduleCAMAC:

LeCroy 2259A Peak-sensinganalogue-to-digitalconverter(ADC)

LeCroy 2229 Taggertime-to-digitalconverter(TDC)

3.4.3 Event Trigger

Determiningif aneventwasof interestandshouldbekept,or bediscarded,was

theroleof theeventtrigger, or X-trigger. Theessentialcriterionfor acceptingan

eventwasthata chargedparticlewasobservedin boththe *+ and + detectors.

Signalsfrom the *,+ - + coincidencemodulewerefed into a gategeneratorto

producethe X-trigger. The gatecould be inhibited by the presencetwo other

signals:themicrotroninject signalandtheVME busysignal.

RF-noiseis producedduring the injection stagein the microtron, and is

picked up by the electronicsin the DAQ. In order to eliminatethis noise,an

inhibit signalis generatedfrom theinject signal.

Oncethe VME computerreceivesan interrupt,andwhile it is readingthe

CAMAC, it sendout a busysignal.To preventotherothereventsfrom trying to

triggertheDAQ, thebusysignalis usedto inhibit theX-trigger.

TheX-triggeralsoprovidedacommonstartsignalto the64 taggerTDCs. If

therewasahit in any of thetaggers,thatdetectorsignalwouldprovideastopfor

oneTDC. All 64 of the signalsfrom the taggerdetectorsaredelayedto arrive


after the X-trigger. Figure3.15 shows a single taggingevent and the relative

timing of thesignals.

X−trigger

Tagger Signal

Tagger Signal

Delayed

TDC CommonStart

TDC SingleStop

200 ns Delay

400 ns TDC Time−out

Figure 3.15: Therelative timing of theX-triggeranda singletaggersignal.

Thistypeof X-triggerresultedin essentially64separateexperiments,onefor

eachtagger. Eachdetectortaggeda narrow photonenergy range( ~�� keV).

In thedataanalysisprocess,all theexperimentsweresummedtogetherto form

the final result. This approachis valid provided the propercareis taken with

the analysisprocess.The detailsof the dataanalysisarepresentedin the next

chapter.

3.5 Summary of Experimental Parameters

Table3.2 lists someparametersof thebeamanddetectorsystemsasthey were

for thepresentexperiment.

53

Parameter Value+ S 92.45MeVTaggingMagnetField 0.31900T+ 2 50–70MeVRadiator 50 0 m Al foil*+32 310keVLeft taggerposition 391mmRight taggerposition 71 mmAnglesMeasured,¡ 30- , 60- , 90-AverageTaggingEfficiency, ¢ q 0.26DetectorSolidAngle, "H£ 54 msr� Li targetthickness 915 0 m� Li targetpurity 99.9%

Table3.2: List of experimentalparametersandtheir values.

Chapter 4

Data Analysis

Theaimof thedataanalysisprocedureis to extractthepopulationof statesin the

residualnucleus� He, following the reaction � Li ��!�� He. In order to achieve

this, it is necessaryto determinetheenergy of theemittedproton,andinitiating

photonin each �� reaction. A well establishedtechniquebasedon similar�� experimentspreviously performedat the Max-lab [54,63,64] is usedto

performthis analysis.

4.1 AnalysisOverview

All of theoff-line dataanalysiswasperformedon a Linux PCusingtheROOT

analysispackage.This systemwasfast,flexible, andprovided a dedicateden-

vironmentspecificallytasked with the complex datareductionprocedures.A

sequenceof constraintswasusedto reducethe raw data,andeachof theseis

furtherdiscussedin detail in thesubsequentsections.Thesestepsconsistedof:

1. Discriminatingtheprotonsfrom otheremittedchargedparticles.

2. Determiningtheenergy of thephotonthatinducedthereaction.

3. Determiningtheprotonenergy andconsequentlytheexcitationenergy in� He.

55

56 Chapter 4. Data Analysis

4. Removing any backgroundcontribution in theexcitationenergy spectrum.

An event-by-eventprocessingtechniquewasusedby theanalysissoftware,

allowing the experimentto be rerunon the computer, with stringenttriggering

requirements.As a resultof eachanalysisstepthedatawasreducedto smaller

subsets,therebyreducingthesubsequentanalysistime.

4.2 ROOT/CINT Software

The analysissoftwarewascompiledusingthe ROOT package,which wasde-

velopedat CERN for the NA49 experiment[65]. ROOT is essentiallya setof

C++classes, specificallydesignedto processdatageneratedin anuclear(or par-

ticle) physicsexperiment.Thedataacquisitionsoftware,written by staff at the

MAX-lab [66], wasalsocompiledusingROOT, andstoredthedatain a format

readableby ROOT. As a consequence,the analysiscould proceedwithout the

needto convert thedatainto anotherformat.

Integratedinto theROOT packageis a programcalledCINT (C interpreter),

thatcanexecutemacroswritten in theC/C++ language.CINT reducesthetime

associatedwith thedebugging,linking andcompilingof C-codeinto aprogram.

This is achieved by not requiring the full formalism of the C/C++ language

in the macros,andallowing real-timeinteractionwith the codeby meansof a

command-lineinterface.To make theC-coderun fasterandmoreefficiently, it

canlaterbecompiledinto aprogram.

The programsthat were usedto analysethe datafrom the presentexperi-

mentrequiredcodethatwasspecificto photonuclearreactions.This specialised

code,written by the author, wasfirst debuggedandtestedusingmacrosin the

ROOT/CINT package.Later, to speeduptheanalysis,themacroswerecompiled

into programsthatanalysedthedatato extractthepopulationof statesin � He.

4.2. ROOT/CINT Software 57

Othersoftwaredesignedto analysephysicsexperiments,suchasthepopular

packagePAW (PhysicsAnalysisWorkstation)[67], alsocreatedat CERN,often

userow-wise ntuples(RWN) format to soredata. By contrastthe dataformat

usedby ROOT is a more convenient tree structure,and the data is storedin

compressed-binaryfiles that canbe readby any operatingsystemwith ROOT

installed. Data storedin a tree structurecan be searchedand retrieved more

quickly andmoreefficiently thandatain a RWN structure.Eacheventrecorded

during the experimentwasstoredin a datatree. The ADC andTDC modules

werestoredin thetreeaslogical objectscalledbranches, while thevaluesread

from themoduleswerestoredasleaveson thebranches.

To extract the datafrom the treestructurestoredin the datafiles, a branch

addressis definedin memoryandlinkedto thefile containingthedatatree.In the

examplebelow, thetreeevent is linkedto datafile.root andahistogram

he60 is defined.Themacrothenloopsoverall theeventsin thetree,andif the

ADC channelis greaterthan163,the60¤ protondatais storedin thehistogram.

TFile *file = new TFile("datafile.root"); //open data fileEvent *event = new Event();file->SetBranchAddress("event", &event); //map eventTH1F *he60 = new TH1F("he60","E 60",256,0,1024);Int_t nentries = file->GetEntries();for(i=0; i<nentries;i++) { //start event loop

file->GetEvent(i);fe60 = event->GetADC1(e60); //E detector 60 degreesfde60 = event->GetADC1(de60); //dE detector 60 degreesif(fe60 > 163){

he60->Fill(e60);}event->Clear();} // end event loop

Choose detector angle

Determine Eγ

Calculate Emiss

Yes

No

Prompt/random?Timing

Add to prompt/randomspectrum

Correct for energy lossand determineT

Read event

Particle identificationProton?

p

Multiple tag?

Figure 4.1: Schematicoverview

of the event-by-event analysis

procedure.

Theeventloopin thecompleteanal-

ysiscode,containeda farmorecompli-

catedsetof trigger conditionsthanthe

precedingmacro. A flow diagramof


thetriggersandcalculationsrequiredto

generatethe missing-energy spectrum

of ¥ Li ¦�§�¨�©�ª , is shown in Figure 4.1.

Thestepsshownwerenotperformedby

a single program,but the processwas

broken up into smaller sectionsusing

dedicatedprograms.Eachprogramre-

ducedthe datato a smallersubset,so

that subsequentanalysiscould be per-

formed more rapidly. Derived values

that were calculatedfrom the exper-

imental data, such as missing-energy

( « ¬�¯®�® ), were addedas new variables

in theeventstructure,andsaved in the

datafile. Moreover, thesevaluescould

laterbeusedin triggerconditions,with-

outtheneedfor themto berecalculated.

4.3 Particle Identification

Protons were separatedfrom other

chargedparticlesthatweredetected,us-

ing a °,« - « particle identification(PI) method. The methodrelieson a varia-

tion in theenergy lossof particleswith differentcharge/massratios(seeSection

3.3.3).Plottingthetotal energy « , againstthepartialenergy loss °,« , separates

thesingly chargedparticlesinto four distinctbandsof differentmass:electrons,

protons,deuteronsandtritons. A polygoncut wasappliedto thePI plot to iso-

4.3. Particle Identification 59

late a small data-subsetthat containedonly protonevents. Figure4.2 shows a

2-D histogramof « plottedagainst°,« for ± = 30¤ , with thepolygoncut drawn

aroundtheprotonevents.Furtheranalysiswasperformedonly on theeventsin

theprotondata-subset.

E (Channels)²0

³200´

400µ

600¶

800 1000

∆E (

Cha

nnel

s)

0³

100

200

300

400µ500·600¶

electrons¸protons¹

deuteronsº

tritons»

Figure 4.2: A typical particleidentificationplot for the ¼ = 30¤ detector. Thepolygonrepresentsthecut usedto selecttheprotonevents.

The deuteronsand tritons seenin the PI plot wereproducedby ¦�§�¨%½¾ª and¦�§�¨#¿%ª reactionsin ¥ Li; however the numberof theseeventswastwo ordersof

magnitudesmallerthanthenumberof protonevents.Thereforelittle significant

informationcould be obtainedfrom thesereactionchannels.However, the su-

periorperformanceof the °,« - « detectionsystemis demonstratedby theclean

separationbetweenthechargedparticlegroupsin thePI spectrum.


4.4 PhotonEnergy Measurement

Thephotontaggerconsistedof two arraysof 32electrondetectors,locatedonthe

focalplaneof thespectrometermagnet(seeSection3.2.3).Themagneto-optical

propertiesof thespectrometermagnetdeterminestheenergy of theelectronthat

reachesa particularpositionon thefocal plane.Thustheresponseof a detector

on the focal planeidentifiesthis energy, and hencethe photonenergy that is

tagged.To determinethetaggingenergy of eachdetector, theprogramPOS[68]

wasused.This programcalculatedthephotonenergy asa functionof detector

positionusingtheknown propertiesof thespectrometermagnet.

Focal Plane Detector Position (mm)À-200 -100 0

Á100 200

�300

EγÂ (MeV)

50Ã55Ã60

65

70Ä

1

32

33

64

Figure 4.3: Thecalibrationplot of photonenergy correspondingto taggerde-tector

Figure4.3shows theresultsof thecalculationusedfor thepresentmeasure-

ment,with theincidentelectronbeamenergy setto « ÅaÆpÇÉÈHÊ�Ë/Ì MeV. Photonsin

theenergy rangeÍ 60–62MeV werenot tagged,dueto a gapbetweenthetwo

detectorarrays.Theelectrondetectorswereall ÍzÎ mm wide,andthecentreof

eachelectrondetectordefinedits positiononthefocalplane.Theprecisetagging

rangewasfrom 50.81MeV to 71.81MeV. Over this taggingrange,thephoton

energy resolutionvariedfrom 250keV at the lowest,to 270keV at thehighest

energy photons.

4.5. Proton Energy Measurement 61

4.5 Proton Energy Measurement

In orderto measurethe populationof statesin Ï He following the ¥ Li ¦�§�¨�©�ª1Ï He

reaction,theemittedprotonenergy mustbeknown. As astartingpoint, the °,« -« detectorsystemwascalibratedusingan Ð -particlesource(seeSection3.3.2),

so that the energy depositedin the « detectorby protonscould be measured.

However, theenergy depositedin the « detectoris not equalto theenergy with

which the protonswere emittedfrom the nucleus. Protonsemittedfrom ¥ Li

suffered energy lossesas they passedthroughpart of the target, and the °«detector, beforebeingstoppedin the « detector. So,an energy-losscorrection

wasmade,andappliedto thedetectedenergy, todeterminetheenergywith which

theprotonswereemitted.

4.5.1 Energy LossCorr ections

To calculatetheenergy lost by a protonpassingthroughthetargetandthe °« ,

thethicknessof eachmaterialmustbeknown. The °,« detectorwasmadefrom

siliconwith a thicknessof 500 Ñ m. However, thethicknessof thetargetthrough

which a protonpassesvariesfor eachevent, sincethe protoncanbe produced

anywherein the irradiatedregion of the target. To calculatethe energy lossin

thelithium, theapproximationwasmadethatprotonswereproducedatthecenter

of thetarget. Thethicknessof thetargetmaterialthroughwhich theprotonhad

to travel alsodependedon theemissionangle,andwasdeterminedby theangle

at which theprotonwasdetected.

Oncethethicknessesweredetermined,theenergy lost in eachmaterialwas

calculatedusinga tableof energy lossvalues[69]. First theprotonenergy loss

in the lithium target wascalculated,thenthis reducedkinetic energy wasused

to calculatetheenergy lossin thesilicon °,« . To determinetheoriginal proton


energy Ò�Ó1Ô1�Õ , the total calculatedenergy losswasaddedto the detectedproton

energy Ò�Ö<Å�× Ò�Ó1Ô1ØÕÙÆÚÒ�ÖÛÅ�×¾Ür°,« Li ÜÝ°« Si ¨ (4.1)

where °,« Li and °« Si are the calculatedenergy lossesof a proton in lithium

andsilicon respectively. At low protonenergiesthecorrectionswere Í 4 MeV,

whereasat thehighestprotonenergiesthey were Í 1 MeV.

Thevaluesof Ò�Ó1Ô1ØÕ wereplottedagainsta rangeof Ò�ÖÛÅ�× for eachdetectoran-

gle, an exampleof sucha plot is shown in Figure4.4. The curve shown is a

third-orderpolynomialfitted to thecalculatedpoints. This providesthecorrec-

tion Ò!Ó�Ô1ØÕ and Ò�ÖÛÅ�× andtheequationis shown in Figure4.4.

Detected Energy, TÞ

detß (MeV)

0Á

10 20 30 40 50Ã

60 70Ä

80 90à

Orig

inal

Ene

rgy,

T orig

(M

eV)

0Á10

20�30

40

50Ã60

70Ä80

90à

f lossá (x) = 3.979 + 0.8648 x + 0.001969 x2 - 9.817e-06 x3

Figure 4.4: A plot of the functionusedto convert thedetectedprotonenergyto theoriginal protonenergy for ¼ = 60¤ .

To checkthe consistency of the energy losscorrectionandthe protoncali-

bration,theexpectedvalueof theprotonenergy wascalculatedasdescribedin

thenext section,andcomparedwith Ò�Ó1Ô1�Õ .


4.5.2 ReactionKinematics

Thekinematicequationsof thereaction¥ Li ¦�§�¨�©�ª�Ï Hewereusedto determinethe

expectedprotonemissionenergy ( ÒHâ ), to checktheenergy losscalculationand

the detectorcalibration. A schematicdiagramof the ¥ Li ¦�§�¨�©!ª Ï He reactionis

shown in Figure4.5. Themassesusedin thecalculationweretakenfrom Audi

et al. [43].

Lim pθ

pm

pp

pγ

Hem

pHeEHe

THe

pE

Eγ

Tp

Figure 4.5: A schematicdiagramof the reactionkinematicsof photo-protonemissionfrom lithium.

To calculatethe proton kinetic energy ÒHâ , relativistic kinematicsand con-

servationof energy andmomentumwereapplied.Theequationsfor relativistic

energy andmomentumfor aparticleof massã aregivenby

«vä ÆÝå�äæÜÝãçä (4.2)«KÆÚÒèÜÝã (4.3)©TÆté Ò ä ÜrÈêÒëãì¨ (4.4)

where « is the total energy, Ò is the kinetic energy of the protonand å is its

momentum,and íîðïòñhï�ó. Theenergy andmomentumconservationrelations


aregivenby

« ôÆp« õ3ÜÝã Li Æp«�â3Ür« He (4.5)å õ ÆÝå â Üöå He (4.6)å�ä÷�ÆÝå�äâ Üöå�äõùø ÈQ©�â%©úõ�ûýü þ�±#â/¨ (4.7)

UsingEquations4.2 to 4.7 theprotonkineticenergy is givenby [70]

ÒlâÿÆ�� «ÙlÜÝ« õ�ûýü�þ!±#â � � ä ø Ë ã äâ ¦�« äyø « äõ ûýü þ ä ±#âÉªÈl¦�« ä ø « äõ û ü þ ä ±#â ª ø ã â/¨ (4.8)

where

� ï « ä Ü ã äâyø « äõyø ã äHe,«Ù is theinitial total energy,« õ , å õ arethetotal energy andmomentumof theincidentphoton,ã Li is themassof the ¥ Li targetnucleus,« â , å â , ã â , ±#â arethetotal energy, momentum,massandemissionangleof

theproton,« He, å He, ã He arethetotal energy, momentumandmassof theresidualÏ He

nucleus.

Theexpectedkinetic energiesof the ©�� protonswerecalculatedfrom Equa-

tion 4.8 above for eachvalueof « õ correspondingto the 64 tag channels(see

Section4.4 asto how «3õ wasdetermined).Thesevaluesof Òlâ werecompared

with the energy of the observed ©�� energies,asdeterminedusingthe Ð -source

calibrations,andtheagreementwithin � 300keV. Howeverthepoorstatisticsin

eachprotonspectrumlimited theaccuracy of this comparison.

In the experiment,64 proton-energy spectraareproducedby triggeringon

singletagchannels(i.e. oneprotonspectrumfor eachphotonenergy). Eachof


thesespectrawouldunderidealconditionsbeanalysedseparately. In thepresent

measurement,noneof the 64 protonspectracontainedmorethan10 countsin

the ©�� peak. This madeit very difficult to obtainmeaningfulresultsfrom the

individual spectra.To overcomethis difficulty, protonenergy spectrawerecon-

vertedinto missing-energyspectrasothey couldbesummedtogether. Sincethe

missing-energy is invariantwith respectto photonenergy, all the spectrawere

summedtogetherto producea missing-energy spectrumintegratedover « õ =

50–70MeV. Thestatisticsin thesemissing-energy spectraweresufficient to ac-

curatelycheckthecalibrationof the °,« - « detectors.Thenext sectiondescribes

how themissing-energy spectrawereobtained.

4.5.3 Missing-Energy

Referringto Figure4.5, themissing-energy, «Ù¬� ®�® , of the ¥ Li ¦�§�¨�©�ª1Ï He reaction

is definedas « ¬� ®�® Æ «3õ ø ÒHâ ø Ò He Ê (4.9)

Substitutingin Equations4.2 to 4.7andrearranginggives

« ¬� ®�® Æ��<¦�«3õÙÜ ã Li ø Òlâ ø ã â ª�ä ø « äõÿø Òëäâ ø ÈêÒHâ�ã âÜ�È�«3õ � Ò äâ Ü�ÈêÒHâ�ã â�ûýü þ ±#â�� ä Ü ã â ø ã Li (4.10)

The missing-energy is relatedto the excitation energy of the residualnucleusÏ Heby « ¬�¯®�® Æ « Å�� ø�� ¨ (4.11)

where� is thereactionthreshold,andfor ¥ Li ¦�§�¨�©!ª Ï He is givenby

� Æ ãT ø ã��yÆ ã ¦ ¥ Li ª ø ¦�ã ¦ Ï Heª�Ü ã ¦ ©�ªeª Æ ø ó� Ê � MeV ¨


where ãT is themassof the targetand ã�� is themassof thereactionproducts.

Thereforein amissing-energyspectrumof protonsfromthereaction¥ Li ¦�§�¨�©�ª Ï He,

thegroundstateprotonpeakshouldappearat « ¬� ®�® = 10 MeV.

In the initial « ¬�¯®�® spectrumproducedby summingtogetherthe datafrom

all the tagchannels,thegroundstatepeakappeared0.5 MeV above theknown

value. A discrepancy betweenthe measuredand known valuewas not unex-

pected,sincethecalibrationof the « detectorswasonly accurateto within afew

hundredkeV (seeSection4.5.2). In orderto align the ©�� peakin the summed

missing-energy spectrumwith «Ù¬� ®�® = 10MeV, thecalibrationof the « detector

wasmodifieddown by a few hundredkeV.

After aligning the ©�� peaks,missing-energy spectrawereproducedfor data

at 30¤ , 60¤ and90¤ . A typical missing-energy spectrumsummedoverall tagged

photonenergies «3õ = 50–70MeV is shown in Figure4.6.

Emiss� (MeV)0 10 20 30 40 50 60

Cou

nts

(MeV

-1)

0

50

100

150

200

250

300

350

400�

Figure 4.6: A missing-energy spectrumat ¼�� ¤ and � õ = 50– 70MeV.

The summedmissing-energy spectrumshows the ©�� peakcorrectlyaligned

at « ¬� ®�® = 10 MeV. Protonsemittedto thefirst excitedstatein Ï He, form the © �peakat «Ù¬� ®�®aÍ 12 MeV. Theenergy resolutionof thepresentmeasurementis

clearlysufficient to resolve thesetwo states.

4.6. Corr ection for Accidental Tagging 67

The fall off in the spectrumfrom 40 to 62 MeV is a resultof summingto-

gether64 spectrawith differentend-pointenergies.At « ¬� ®�®æÍ 50 MeV asmall

dip canbeobserved,thatis causedby thegapbetweenthetwo detectorarraysin

thetagger(seeSections4.4and3.2.3).Thespectrumhasbeenarbitrarilycut-off

at « ¬�¯®�® = 0 MeV.

The majority of eventsin the spectrumin Figure4.6 resultfrom accidental

protoncoincidences(accidentals). In order to correctfor this accidentalcom-

ponent,it wasnecessaryto examinetheTDC timing spectrathatestablishedthe

coincidences.The next sectionexplains the analysisof the TDC spectraand

how theaccidentaltaggingcomponentwassubtractedfrom themissing-energy

spectra.

4.6 Corr ection for Accidental Tagging

4.6.1 TDC Timing Spectra

TheTDCsmeasurethetime betweenthedetectionof a taggingelectronandthe

detectionof aproton.Accidentaltaggingeventsform anapproximatelyconstant

backgroundacrossthe whole spectrum.The exact shapeof the accidentaltag-

ging backgroundis discussedin moredetail in AppendixA. Correlatedtagged

eventslie in the range750 to 1000 leadingto the formationof a peakin this

range.A typical sumof 64 TDC timing spectrais shown in Figure4.7 (where

thefull rangeof theTDC was400ns).

To producethemissing-energy spectrumdescribedin Section4.5.3(seeFig-

ure4.6),acutwasmadeontheprompttiming regionshown by thedarkshading

in Figure4.7. However this region alsocontainsaccidentalevents,that could

not bedistinguishedfrom correlatedeventsin event-by-eventanalysis.In order

to remove this contribution, an “accidental”missing-energy spectrumwaspro-


Time (0.098 ns per Channel)�500

�1000 1500 2000

2500

3000!

3500!

Cou

nts

0"1000

2000 3000!4000

5000�6000#7000$8000

9000% Time (ns)

50�

100 150 200

250

300!

350!

Correlated&

Σ'

64#

4 ns FWHM

Uncorrelated(

500�

1000 1500 2000

2500

3000!

3500!

0"1000

2000 3000!4000

5000�6000#7000$8000

9000%

Figure 4.7: A TDC spectrumshowing theprompttiming region andtheacci-dentaltiming region.

ducedby cuttingon theaccidentaltaggingregion shown by thelight shadingin

Figure4.7.The“accidental”spectrumwasthennormalisedandsubtractedfrom

the“prompt” spectrumto produceacorrectedmissing-energy spectrum.

An overview of the correctionprocedureis shown in Figure 4.8, while a

detaileddescriptionof eachstepis presentedin thefollowing sections.


Time (Channels)500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500

Energy (MeV)0 10 20 30 40 50 60 70

Energy (MeV)0 10 20 30 40 50 60 70

Energy (MeV)0 10 20 30 40

)50 60 70

Calculate missing energyof protons

Calculate missing energyof accidentals and normalise

Subtract accidentalsand rebin

Figure 4.8: Overview of the techniqueusedto remove theaccidentaltaggingcontribution from theprotonmissing-energy spectra.


4.6.2 Prompt Missing-Energy Spectrum

Figure4.9shows thepromptmissing-energy spectrumfor ±sÆ 90¤ . The ©�� and

the © � peakscanbeseenat « ¬� ®�® = 10–12MeV. Thecountsbetween«Ù¬� ®�® = 0–

10MeV resultfromaccidentallytaggedevents,sincethey arebelow the ¥ Li ¦�§�¨�©�ªreactionthreshold. Indeedonly 22% of the countsin the protonspectrumare

from correlatedevents.

Missing Energy (MeV)*0

³5·

10 15 20 25 30 35 40

Cou

nts

(MeV

-1)

0³50·100

150

200

250

300

350

(γ+ ,p) Threshold

Figure4.9: Themissing-energy spectrumat ¼ = 90¤ showing the , � andthe , �peaks.

Oneway to remove thecontribution from accidentalsto themissing-energu

spectrumis to accuratelydeterminethe shapeof a “missing-energy” spectrum

constructedsoley fromaccidentals.Thesubtractionof thisspectrumafternormil-

isationshouldremoveall of thestrengthbelow thereactionthresholdat «Ù¬� ®�® =

10MeV, andrevealthetruemissing-energy spectrum.


4.6.3 Accidental Missing-Energy Spectrum

Theaccidentalmissing-energy spectrumshown in Figure4.10wasproducedby

cuttingon theaccidentaltiming region shown lightly shadedin Figure4.7,and

characterisedby a featurelessexponentialstructureup to «Ù¬� ®�® = 40MeV.

Missing Energy (MeV)*0

³5·

10 15 20 25 30 35 40

Cou

nts

(MeV

-1)

0³50·100

150

200´250

300

Figure 4.10: The characteristicshapeof the random coincidenceprotonmissing-energy spectrum,normalisedandfitted with apolynomial.

This spectrumwasnormalised,to ensurethat the total numberof countsin

thespectrumwasequalto thenumberof accidentalsin theprompttiming region.

The normalisationfactor, -/. , wascalculatedfrom the countsin two different

timing regionsof theTDC spectrum:accidentalin thecorrelatedregion 021 ; and

accidentalsin the uncorrelatedregion 043 . Theseregionsareshown in Figure

4.11. The functional form of the accidentalsin the TDC spectrumhasbeen

determinedby Owens[50] to be weakly exponential. However in the present

experiment,thereis an accelerator-relatedunderlyingsubstructurein the TDC

spectrumthat canbe approximatedby a sinusoidalfunction [52]. This feature


of the TDC spectrumis discussedin more detail in AppendixA. In order to

estimate021 , a functionof the form -æ¦�¿%ªëÆ6587:9O¦ ø<; ¿%ª�Ü>=�þ@?BA ¦ ×DCFEÖ ª wasfitted to

theTDC datain theregion 0vÔ .Thenormalisationfactoris givenby

-G.ÝÆ 021043 ¨ (4.12)

where 041 is determinedby theintegralof -�¦�¿%ª in theprompttiming region.

Time (Channels)H500

I1000 1500 2000

J2500J

3000K

3500K

Cou

nts

0L500

I1000

1500

2000

2500

3000K3500K4000

4500M

NN

a

f(t)O

NN

bP

Figure 4.11: TDC timing cutscontainingthe threedifferent regionsusedtocalculatethenormalisationfactorfor theaccidentalspectrum.

A third-orderpolynomialwasfitted to the normalisedaccidentalspectrum

spectrumbetween« ¬� ®�® 0–40MeV, asshown in Figure4.10. This fit wasthen

usedin the subtractionof the accidentaltaggingcomponentfrom the prompt

missing-energy spectrum.

Figure4.12shows the accidental-correctedmissing-energy spectrumat ± =

60¤ . Theerrorbarsshown arethestatisticalerrorsfrom theuncorrectedprompt

missing-energy spectrum(seeFigure4.9), andthedatahasbeenplottedin 400

4.7. ¦�§�¨�©�QOª Corr ection 73

keV energy bins.

EmissR (MeV)0³

5·

10 15 20 25 30 35 40

Cou

nts

(MeV

-1)

0³

100

200

300

400µ 7Li(

Sγ+ ,p)6He

Tθ = 60˚

Figure 4.12: Thebackgroundsubtractedprotonmissing-energy spectrumfor¼ = 60¤Below the ¥ Li ¦�§�¨�©�ª reactionthresholdat « ¬� ®�® = 10MeV, theaveragecounts

drop to zeroasexpected,providing justificationof the methodusedto remove

theaccidentaltaggingcontribution. Thesystematicerror in theaccidentalsub-

tractionprocessis estimatedto beabout2%.

4.7 UWVYX/Z\[^] Corr ection

Protonsproducedin multi-nucleonemissionreactions,suchas ¦�§�¨�©�Q�ª , ¦�§�¨�© ©�ª ,¦�§�¨�©�½úª and ¦�§�¨�©¾¿%ª , alsocontributeabackgroundin themissing-energyspectrum.

Protonsemittedby suchreactionsareindistinguishablefrom thoseemittedfrom

a ¥ Li ¦�§�¨�©�ª reaction,andconsequentlymustberemoved.

The ¦�§�¨�©�QOª channelis particularly important,sincethe ¥ Li ¦�§�¨�©�Q�ª reaction

thresholdis 11.91,MeV andfalls preciselyin themissing-energy region of the


low-lying excitedstatesin Ï He. Sincethecrosssectionsof the ¦�§�¨�© ©�ª reactionisÍ 100timesmallerthanthe ¦�§�¨�©�Q�ª reaction[71,72], andthe ¦�§�¨�©�½úª and ¦�§�¨�©ú¿%ªcrosssectionsareevensmaller, only the ¦�§�¨�©!ª channelwasconsidered.

An estimateof the ¦�§�¨�©�Q�ª contribution in themissing-energy spectrumwas

madeby MacGregor [73], usinga Monte Carlo programto calculatethe mo-

mentumof the emittedprotons. This calculationuseda quasi-deuteronmodel

of the nucleusin which photonswere absorbedon proton-neutronpairs. The

initial pairmomentumwasselectedfrom adistribution thatwasderivedfrom an

harmonicoscillatorwavefunction. On theassumptionthat the residualnucleus_He wasleft in its groundstate,andthat therewereno final stateinteractions,

conservation of energy andmomentumwereappliedto derive the momentum

with which protonswereemitted. The angulardistribution of the emittedpro-

tonsweredeterminedby theangulardistribution of the ä H ¦�§�¨�©�ª�Q reaction[74].

Thecalculationincludedall theexperimentalparametersof theGLUE chamber

detectionsystem,andcoveredthefull phasespaceof theexperiment.A detailed

descriptionof thecalculationappearsin Reference[75].

In orderto comparetheresultsof thecalculationwith theexperimentalmissing-

energy spectrum,themissing-energyof theprotonsfromthe ¦�§�¨�©�Q�ª reactionwas

calculatedassuminga recoil massof Ï Heandnot_He.

Figure4.13showsthe ¦�§�¨�©�Q�ª missing-energydistributionfor ± = 60¤ (shaded

area). The ¦�§�¨�©�Q ª contribution was normalisedsuchthat after subtractingit,

thenetmissing-energy spectrumwaspositiveat all energies.Thenormalisation

factorusedfor the 60¤ datawasalsousedfor the 30¤ and90¤ data,sincethe

calculationwasinternallyconsistentfor all angles.

Importantly, the ¦�§�¨�©�QOª contributionisessentiallystructureless,with itsbroad

resonancepeakingat approximately« ¬�¯®�® = 30–35MeV. This is well above the

region of interestwherenew statesarepredictedin Ï He, and leavesno doubt

4.7. ¦�§�¨�©�QOª Corr ection 75

E²

missR (MeV)0³

5·

10 15 20´

25´

30 35 40µ

Cou

nts

(MeV

-1)

0³

100

200´300

400

500·

7Li(S

γ+ ,pn)

Figure4.13: Thecalculatedprotonmissing-energy spectrumfrom thereaction¥ Li `badcD,:egf from aMonteCarlo2h photonabsorptionmodel.

that any structurebelow ikjmlon�n = 20 MeV is not dueto structurein the prqts�u�vtwbackground.The final missing-energy spectrumat x = 60y with the accidental

andthe pzqts�u�vtw contributionssubtractedis shown in Figure4.14.Thespectrafor

theotheranglesarepresentedin Chapter5. Fromthesemissing-energy spectra,

thepopulationof statesin { Hecanbedetermined.

76

E|

missR (MeV)0}

5~

10 15 20�

25�

30 35 40�

Cou

nts

(MeV

-1)

0}50~100

150

200�250

300

350

400�

Figure 4.14: The missing-energy spectrumof protons from the reaction�Li `bagcD��f { Heat � = 60y with theaccidentaland `bagcD�:egf contributionsremoved.

Chapter 5

Resultsand Discussion

5.1 Intr oduction

The goal of the presentexperimentwas to measurethe nuclearlevels of { He

in order to observe new statesthat have beenpredictedby theory. A tagged

photonexperimentwas conductedto measuredthe energy of protonsemitted

by thereaction�Li pzqts�udw�{ He. Thedatafrom this experimentwasanalysed,and

missing-energy spectrawere producedto determinethe relative populationof

statesin theresidualnucleus{ He.

0+

2+

HeJπ 6 MeV

13.6(1,2)−

0

15.5

23.2

1.8

Figure5.1: { Heen-

ergy levels[41].

Figure5.1 shows the known low-lying excited

statesof { Heupto anenergy of ik�� = 30MeV [41],

while Table 5.2 presentsa summaryof the most

recenttheoreticalpredictionsandexperimentalre-

sults.Thebasisof this chapteris to achievea recil-

iation betweenthe theoreticalpictureandthe real-

ity of theexperimentalresults.To achieve this, the

resultsfrom thepresentmeasurementwill becom-

paredandevaluatedagainsttheseotherexperimentsandpredictions.Through

thesecomparisons,a consistentunderstandingof the level structureof { He will

77

78 Chapter 5. Resultsand Discussion

bepresented.

Thelow-lying level structurein { He haslong beenconsideredcompleteand

consistent.It wasnotuntil theexperimentsby Tanihataet al. [2], andthesubse-

quentinterpretationsbyHansenandJonson[28], thatthepictureshown in Figure

5.1 requiredrevision. Fromthesestudiesit emergedthat thestructureof { He is

well describedasa � He corewith a two-neutronhalo. Using the halo model,

new stateswerepredictedin theregionbetweentheknown statesat1.8and13.6

MeV, including a new low-lying collective resonance,called the soft DR (see

Section2.1.4). However, experimentsdesignedto verify thesepredictionshave

so far failed to provide conclusive measurementsthat clearly identify the new

states.

As mentionedin Chapter2, theexperimentalstudiesof thestructureof { He

have primarily beenconductedusingbeamsof stableor radioactive ions. The

presentexperimentuseda tagged-photonbeamto provide a measurementof

thenuclearlevelsin { He that is independentof theotherexperimentalmethods.

Furthermore,theanalysistechniquesusedto extract thetagged-photondataare

morerigorousthanthoseusedin someof thepreviousexperiments.Therefore,

theresultsof measuringthe�Li pzqts�ugw { He reaction,provide a clearpictureof the

nuclearlevelsin { He,andany new statesthatexist shouldbeobserved.

Theinterpretationssectionof this chapterpresentadiscussionof thepresent

measurementin thecontext of halonucleiasdevelopedin Chapter2. Thediscus-

sion is separatedinto two sections:the low-lying statesin theregion ik��6�G�MeV, andthehigherstatesin theregion ik��4��G� MeV. Thisdistinctionis made

becausethe low region is formedby theexclusive prqms�ugw reactionleadingto the

populationof statesin { He;while thehighregionis formedby theinclusive pzqts�udwreactioninvolving morethantwo-particleemission.Thehigh region containsa

complicatedmix of contributionsfrom several reactionsthatdo not necessarily

5.2. Results 79

leadto statesin { He. The possiblenatureof both theseregionsis discussedin

Section5.3.

5.2 Results

5.2.1 Excitation Energy Spectra

This sectionwill presenttheexcitation-energy spectraof { He following the re-

action�Li prqts�ugw , measuredat 30y , 60y and90y . Prior to presetingtheseresults,

thevalidity of makingtheconversionfrom missing-energy to excitation-energy

will bediscussed.

Figure5.2showsthemissing-energyspectradescribedin Section4.7for each

angle.Therearethreesignificantfeaturesin eachof themissing-energy spectra:

1. Theclearandstrongpopulationof thegroundandfirst-excitedstate.

2. A dominantbroadstructureabove ikjmlon�n = 22 MeV.

3. Evidenceof strengthbetweenthesefeatures.

The thresholdsof eachof the inclusive prqms�ugw reactionsareindicatedon the

60y axis. Theregion from ikjmlon�n = 10–22MeV is exclusively populatedby pro-

tonsleadingto excited statesin { He, sincethe pzqts�u�vtw componenthasbeenre-

moved from the spectrum(seeSection4.7). Above ikjtl�n�n = 22 MeV several

otherthree-andfour-bodybreakupreactionsbecomepossible,andthestructure

in this region canno longerbe uniquely identifiedasstatesin { He. Therefore

convertingform missing-energy to excitation-energy is only valid from ikjmlon�n =

0–22MeV. Theregionabove i�jtl�n�n = 22MeV will bediscussedin Section5.3.3.


Cou

nts

(MeV

-1)

0�100

200�300�400

500�

θ = 30˚ 7Li(γ� ,p)6He

0�100

200�300�400�

θ = 60˚

5�

10 15 20 25 30�

35�

40

Emiss� (MeV)0�

5�

10 15 20�

25�

30�

35�

40�0

�50�100

150

200�250

5�

10 15 20 25 30�

35�

40

(�γ� ,p)6He

�(�γ� ,pn) (

�γ� ,pt)t (

�γ� ,pt)dn (

�γ� ,pd)4H

�(�γ� ,pp)5H

�

Figure 5.2: The missing-energy spectra of { He following the reaction�Li �b�g�D�� { He, integratedover � � = 50–70MeV at � = 30y , 60y and90y .

5.2. Results 81

Theexcitationenergy, ik�� , of theresidualnucleus{ Hefollowing thereaction�Li pzqts�udw { He, is relatedto themissingenergy, ikjmlon�n , by

ik��¢¡£ikjml�n�n¥¤§¦¨swhere ¦©¡«ª4�¬¯®°¬ MeV is the reactionthreshold.The missing-energy spectra

wereconvertedto excitation-energy, andintegratedoverall photonenergies( i �= 50–70MeV) andall angles(30y , 60y and90y ). Figure5.3shows theresultant

spectrum.

Cou

nts

(MeV

-1)

0}100

200

300

400

500~600±700²800

E|

ex³ (MeV)-10 -5 0

}5~

10 15

Figure 5.3: Theexcitation-energy spectrumintegratedoverall angles.

In orderto determinethe centroidenergy of the peaks,Gaussianfunctions

werefitted to thespectrum.Thesefits specificallyconsideredthelarge increase

in thecrosssectionat ik��4´ 12. Thevaluesobtainedfor thecentriodenergies

were0.0MeV for thegroundstate,2.0MeV for the �¶µ first excitedstate,anda

broadstateat 7.4MeV.

The excitation-energy spectraat x = 30y , 60y and90y werealsofitted with


Gaussianfunctions,asshown in Figure5.2. Theenergy andwidth of thepeaks

in thesefits werefixedto thevaluesobtainedfrom theangle-integratedspectrum,

andonly the heightof eachGaussianwasleft asa freeparameter. The quality

of thedatacanbeseenby theclearseparationof the ¬ µ groundstateandthe � µexcitedstate,at ik��¢´ 0 and2 MeV respectively. Theenergy resolutionat low

excitationenergy in eachspectrumis ·ïk��2´ 1.0MeV, which is mainly dueto

theuncertaintyin theenergy lossstragglingin thetargetandthe ·ï detectors.

The secondlargestcontribution to the resolutionis from the uncertaintyin the

photonenergy ( ·ï � ´ 0.3MeV). Theremainingwidth is dueto thekinematic

broadeningcausedby theangularacceptanceof thedetectorsandthestatistical

errorsin thedata.

Of the threeangles,the 60y datahasthe highestresolution. This is to be

expected,sincethetargetpresentsits thinestaspectto the60y detector, andasa

consequencethe energy stragglingis at a minimum in thatdirection. The high

excitation-energy region of eachspectrum,above i�� = 12 MeV, is formedby

low energy protons,for which thestragglingeffect is greaterthanfor thehigher

energy protons.Consequentlytheknow statesbetweenik�� = 13–24MeV (see

Figure 5.1) cannotbe resolved, but are part of a broadstructurein the high

excitation-energy regionof thespectrum.

Thefeaturesdescribedabove areall expectedfrom this typeof experiment,

andshow that theresultsareof a high quality. Significantly, evidenceof a new

broadstatecan be seenin eachspectrumin the region betweenik��´ 3–10

MeV. Thereareno well-definedstatesin this region, however thereis signifi-

cantstrengthabove backgroundsuggestingthepresenceoneor morebroadres-

onances.The structureat this excitation energy confirmssimilar observations

madein othermeasurements,which arediscussedin moredetail in Section5.3.

5.2. Results 83

Cou

nts

(MeV

-1)

0�50�100

150

200

250�300�350�400�

θ = 30˚ 7Li(¸

γ� ,p)6He�

0�50�100

150

200

250�300�350�

θ = 60˚

-5 0�

5�

10 15

-20

0�20

40�60¹80

100

120

θ = 90˚

Eexº (MeV)-10 -5 0

�5�

10 15

-5 0

�5�

10 15

Figure 5.4: The excitation-energy spectraof { He fitted with threeGaussianfunctions.


5.2.2 StatesIdentified

Theresultsof thefits to thedataarepresentedin Table5.1. Theenergy assign-

mentto thenew stateat 7 MeV wason theassumptionthat it is a singlebroad

resonance.Thequality of thefits canbeseenby how closelytheenergy of ¬ µandthe �»¤ statesweredeterminedcomparedwith theacceptedvalues.Theac-

curacy wasdeterminedquantitatively by calculatingthereducedchi-squaredof

thefits, which wasapproximately¼t½¾´ 1.5for eachangle.

¿dÀ ik�� [76] i�� (thismeasurement) Á¬ µ 0 0.0 Â 0.1 1.1 Â 0.1� µ 1.8 1.99 Â 0.3 1.79 Â 0.35.83 Â 0.5 7.88 Â 0.6¬ µ 0 0.0 Â 0.1 1.0 Â 0.1� µ 1.8 1.97 Â 0.3 1.76 Â 0.35.84 Â 0.4 7.88 Â 0.5¬ µ 0 0.0 Â 0.1 1.1 Â 0.1� µ 1.8 1.97 Â 0.3 1.76 Â 0.35.85 Â 1.0 7.84 Â 1.0

Table 5.1: A comparisonof { He energy levels from this measurementwithacceptedvalues[76] (in unitsof MeV).

It wasnot possibleto obtaina measurementof theenergy andwidth of the

known 13.6, 15.5 or 23.2 MeV states,becauseof the onsetof multi-particle

breakupreactionsabove i�� = 12 MeV (seeSection5.2.1). The ¬ µ and � µstatesarestronglypopulatedin mostreactionsleadingto { He; consequentlyit

is essentialfor thevalidity of thepresentmeasurementthat they areaccurately

identified. On the basisof the good agreementof theseknown states,within

experimentalerrors,anew broadstatewasfoundat i�� = 5.8 Â 0.5MeV with a

width on Á = 7.9 Â 0.7MeV.

5.2. Results 85

5.2.3 Angular Distrib ution

Theangulardistribution of theprotonsemittedfollowing thereaction�Li pzqts�ugw

to residualstatesin { Heis shown in Figure5.5.Eachdatapointwasobtainedby

integratingthecorrespondingGaussianfunction thatwasfitted to eachpeakin

theexcitation-energyspectrum.Thesefunctionsareindicatedby thedashedlines

in Figure5.4, andrepresentthe relative populationof statesin { He following�Li pzqts�udw .

Angle (θÃ

LABÄ )

0 20 40 60 80 100 120

Inte

grat

ed C

ount

s

102

103

0} +

2+

7Li(Å

γÆ ,p)6HeÇ

Figure 5.5: The angulardistribution of theground,first excitedstateandthenew resonancestructure(linesareaguideonly).

Thelinesaredraw in to guidetheeye,while theerrorson thepointsinclude

the statisticalerrorsin the integratednumberof counts,andan estimateof the

error in the fits. Very similar angulardistributionsareobserved for the ¬ µ and

the �Èµ states,while the7 MeV statedeviatemarkedly from this trend.An anal-

ysisof this distribution on thebasisof transitionsfrom continuumstatesin�Li

to statesof variousspin andparity in { He, might reveal the natureof this new


state.However, therearecurrentlyno calculationsavailablethatcanpredictthe

angulardistributionof protonsfrom the�Li prqts�ugw { Hereaction[77]. Calculations

of photonuclearreaction,suchasthoseby Ryckebusch[78], havebeensuccess-

ful atdeterminingmany aspectsof thereactionmechanism:for exampletherole

of mesonexchangecurrents,direct knockout, pairing forcesandfinal statein-

teractions.However, thesecalculationsarelimited to even-evennuclei,andthe

assumptionsthataremadeaboutthesymmetryin the nucleusarenot valid for

photonabsorptionon�Li [79]. Soat thisstage,noconclusioncanbedrawn from

theangulardistributionspresentedhere.

5.3 Inter pretations

5.3.1 Comparisonwith Previous Measurements

Despitethepresentinability to interprettheangulardistributionof thenew state

in { He, the energy levels that were measuredcan be comparedwith previous

measurements.Naturally a photonuclearreactionleadingto the populationof

statesin { He cannotbe directly comparedto the relative populationof states

following othertypesof nuclearreactions.However thepositionof thestatesin

theexcitationenergy spectrumof { He is independentof thereactionthatis used

to measureit. Thereforethe presentresultscanbe comparedwith thosefrom

the five key experimentsdescribedin Section2.2.3. Similarly, the calculation

discussedin Chapter2 canalsobe usedfor comparison.Table5.2 presentsa

survey of themeasuredandcalculatednuclearlevelsin { Heto which thecurrent

measurementwill becompared.

5.3. Inter pretations 87

TH

EO

RE

TIC

AL

CA

LC

UL

AT

ION

S

Suz

uki[1

]A

oyam

a[44

]D

anili

n[8

]E

rsho

v[9

]D

anili

n[3

8]

É ÊËÌËÌ

ËÌ

ËÌ

ËÌ

ÍÎÐÏ 00

00

0

ÑÎtÏ

1.81

0.26

1.75

0.04

1.72

0.04

1.78

0.1

ÑÎtÒ

3.43

4.75

4.3

1.2

4.0

1.2

3.7

1.2

ÓÎ

3.75

6.39

4.5

wid

e

Ô 24.

41.

84.

21.

8

ÍÎtÒ

4.69

9.45

5w

ide

Ô 46.

06.

06.

46.

0

Ó Õ 4–7

broa

dbr

oadn

onre

sona

ntbr

oadn

onre

sona

ntbr

oadn

onre

sona

ntbr

oadn

onre

sona

nt

EX

PE

RIM

EN

TA

LM

EA

SU

RE

ME

NT

S

Sak

uta[

15]

Jane

cke

[16]

Aum

ann[

17]

Nak

ayam

a[19

]N

akam

ura[

20]

Bol

and

[80]

É ÊËÌËÌËÌËÌ

ËÌÉ ÊËÌ

ÍÎtÏ

00

0

ÍÎ 0

ÑÎtÏ 1.80.

51.

920.

51.

80.

51.

80.

51.

80.

7

ÑÎ 1.99

1.04

ÑÎÐÒ

5.6

12.1

4.3

Ô 5(Ó Õ )

Ô 4?7.

411

.1

ÓÎ ÍÎÐÒ Ó Õ 67

14.6

7.4

44

Ô 15

Ô 6?

Ô 15bro

ad

Tab

le5.

2:A

sum

mar

yoft

heor

etic

ally

pred

icte

dand

expe

rimen

tally

mea

sure

dsta

tesin

Ö He

(all

valu

esin

MeV

).


Curr ently Known Energy Levelsin { He

Thecurrentlyknow structureof { Heis shown in Figure5.6next to theexcitation-

energy spectrumobtainedfrom thepresentmeasurement.Thegroundstateand

thefirst excitedstate,which have beenobservedin all theexperimentalstudies,

andarepredictedby mostcalculations,arealsoclearlyseenin the�Li pzqts�udw�{ He

measurement.Thegroundstatehasa half-life of 806.7msand¿gÀ ¡×¬ µ , while

thefirst excitedstateis at Øk�¨´Ù�»®ÛÚ MeV with¿ À ¡6� µ anda narrow width ofÁÜ¡£¬:®B� MeV. Thesetwo narrow states,alongwith aseriesof broadstatesin the

continuumabove Ø��\´�� MeV, dominatethecrosssectionin the�Li pzqts�udw�{ He

reaction.

Ee

x (M

eV

)0

51

01

52

02

53

0

0+

2+

HeJπ 6

(1,2)− 13.615.5

23.2

1.80

MeV

Figure5.6: An energy level diagramof Ý He[41] comparedwith theexcitation-energy spectrumfrom thepresentmeasurement,drawn with asmoothline.

Theexactcharacterof thebroadstatesabove 12 MeV have not beendeter-

mined,ascanbe seenby the ambiguousassignmentof the spin andparity of

the 13.6MeV state,andthe lack of any¿ À

for the 15.5and23.2 MeV states.

As previously mentioned,the region above Øk�� = 12 MeV cannotbe uniquely


identifiedasstatesin Ý He,but somecontributionto thecrosssectionis exspected

in this region (asindicatedby thearrows in Figure5.6).

Stateshavebeenmeasuredandpredictedin theregion Øk�� = 2–12MeV over

the past10 years,but dueto ambiguitiesin the resultsno definiteassingments

have beenmade. In particular, the predictionof the soft DR in Ý He dueto the

nuclearhalo[27,28] hasledto severalexperimentalattemptsto find statesin this

weaklypopulatedregion.

Thebroadnatureof theseresonancesandtherelatively low crosssectionof

the reactionsemployed,have madeit difficult for any definitive conclusionsto

bedrawn aboutthesoft DR [81]. However, the ion beamandradioactive beam

experimentswhich have thus far provided most of the data,have usedsome

ambiguousmethodsof backgroundsubtractionandmake controversialassump-

tionsin theiranalysis(seeSection2.2.3andReference[81]). In contrast,photon

taggingexperiments,suchas the presentmeasurement,usea well established

methodof backgroundremoval. Thefollowing sectionswill discussthepossible

natureof thenew structurein Ý He,by comparingthe�Li Þzßtà�ágâ Ý He datawith the

previoustheoreticalandexperimentalresults.

5.3.2 The Low-Lying Region, ãåäçæYè é�ê MeV

Evidencefor the Soft DR

Theearliestcalculationof the resonanceenergy of thesoft DR, on thebasisof

an energy weightedsumrule of electricdipole strengthin Ý He, wasmadeby

Suzuki[1] andfoundto be4.7 MeV. SubsequentlyZhukov et al. estimatedthe

resonanceenergy of thesoft DR, usinga clusterShellModel, to be ´ 7.3MeV.

Both thesevaluesagreedquitewell with thedatathatwasavailableat thetime.

Figure5.7showsacomparisonof a recentandmorecomplicatedcalculation

by Ershov et al. [9] andthreeexperiments.This calculationwasof thereaction


ë ë ëë ë ëë ë ëë ë ëë ë ëì ìì ìì ìì ìì ìí í í íí í í íí í í íî î î îî î î îî î î î

ï ï ï ï ïï ï ï ï ïð ð ð ð ðð ð ð ð ð ñ ñ ñ ñ ññ ñ ñ ñ ññ ñ ñ ñ ñò ò ò ò òò ò ò ò òò ò ò ò òó óó óó óô ôô ôô ô

õ õ õõ õ õö ö öö ö ö ÷ ÷ ÷ø ø øHe6He6

1−0+1+2+

6 t 3 6Li( , He) He

He6

1−

1−

Ershov et al. Nakamuraet al. Nakayamaet al.

Li( , ) Hen p 66 Li( , ) Heγ p 67

He60+0+ 0+ 0+

2+2+2+ 2+

0

5

14.6

MeV

4.3

0

4

Li( Li, Be) He76 67

Jπ

MeasurementPresent

0 0

1.81.8 1.8 2.0

5.8

Figure 5.7: A comparisonof the ùûú levelspredictedby Ershov et al. [9] withexperimentalresultsfrom Nakamuraet al. [20], Nakayamaet al. [19] andthepresentmeasurement,seetext for details. (The heightof the level diagramsrepresentsthe region of the excitation energy spectrumpresentedby eachofthereferences.)

üLi Þzýþà�ágâ Ý He,which waschosenbecauseit wasconsideredthemostappropriate

reactionto observe thesoft DR. Unlike previousresultsthatwereattemptingto

calculatea resonantstatein Ý He, Ershov predicteda broadstateresultingfrom

theoverlapof continuumstatesof variousspinandparity, including ÿ ú , �� , ÿ��and � � . Thestateshown at �� = 4.3MeV in Figure5.7 is predominantlyfrom

a ÿ ú component,indicatingthepresenceof asoftDR.

In thisdiscussion,only thepositionof thelevelsfoundin Ý Heareconsidered,

becausetherelativepopulationof statesdependson thetypeof reactionusedto

excite it. The 60 datafrom presentmeasurementis in good agreementwith

the resultsshown in Figure5.7, particularlythoseby Nakamuraet al. In both

experiments,aswell as the known � � 1.8 MeV state,a new stateis found at

� 5 MeV with a width of � 8 MeV. On the basisof a distortedwave Born

approximation(DWBA), Nakamuraet al. identifiedthestateaspredominantly

dipole in nature,with a strongnegative parity component.They alsoarguethat


the � Li �� He�� He reactionis a good spectroscopictool comparedwith other

chargeexchangereactions,becausetheangularmomentumtransferis limited to

the sametype of transitionsasthe �ý�� reactions,but the energy andangular

resolutionis better.

The stateat � 5 MeV in theüLi �� He reactionis also in closeagree-

mentwith that found by Nakayamaet al. usingthe � Li ü Li � ü Be� � He reaction.

Thisreactionis verycomplicated,with many possiblecombinationsof targetand

projectileangularmomentumtransfers.Howevertheanalysisproceduredemon-

stratedin Reference[49] wasusedto limit thedegreesof freedomin thereaction,

anda ÿ ú statewasidentifiedat �� = 4 MeV with � = 4 MeV. Thesamereaction

wasmeasuredby Sakutaet al. [15], who obtainedsimilar resultsandwerethe

first to claim to haveobservedthesoftDR.

As mentionedin Section5.2.3,the presentmeasurementis unableto make

a �! assignmentto the observed state. However it is consistentwith the other

measurementsin theenergy level andwidth of thenew statein � He.

MentiontheanalogybetweenthesoftDR in 6Heandthepygmyresonancein

13C[82]. Referto 5Heand12Cwhichhaveno low energy collectiveresonance.

The Casefor Other States

Despitethe evidencefor the soft DR discussedin the previous section,argu-

mentsaremountingagainstthe existenceof a ÿ ú resonantstate. The current

theoryfavoursa complicatedpictureinvolving many states,andthe simplein-

terpretationby Nakayamaetal. hascomeundersomecriticism(seefor example

Vaagenet al. [81]). However the experimentaldatato supportthe alternative

formulationis still quitepoor.

Resentcalculationsby Danilin et al. [38] suggestthatthelow-lying “states”

measuredin � Hearenot trueresonances,but theresultof theincreasein thetran-


sition strengthto ÿ � and � � continuumstatesthatcombineto form a “pseudo”

resonance.Thesecalculationsusethe methodof hypersphericalharmonicsto

accountfor the large spatialextent of the � He halo, andcontaina strongpres-

enceof admixturesin the groundstate. Figure5.8 show the resultsof Danilin

et al. comparedwith measurementsthatsupportthe �"� assignmentto thestate,

andtheresultsfrom thepresentmeasurement.

# # ## # #$ $ $$ $ $% % %% % %% % %% % %

& && && && &

' '' '' '' '' '' '

( (( (( (( (( (( (

) ) ) ) )* * * * *+ + + + +, , , , ,- - -. .

/ / // / // / // / /

0 00 00 00 0

1 1 1 1 11 1 1 1 12 2 2 2 22 2 2 2 2

He6He6 He60+

2+2+2+

0+ 0+

Li( Li, Be) He76 67

2+2+

1+2+

Danilin et al. et al.AumannJaneckeet al...

Li( , ) Heγ p 67

He60+

2+

0

14.6

1.8

MeV0

1.8

0

1.84

Jπ

He n+nHe+6 4

5.6

3

He( , ) He6 p’p 6

Measurement

0

Present

2.0

5.8

Figure 5.8: A comparisonof the 3 � levels predictedby Danilin et al. [38]with experimentalresultsfrom Janecke et al. [16], Aumannet al. [17] andthepresentmeasurement(at 4 = 60 , seetext for details.

Analysisof thedataby Janecke et al., on thebasisof a DWBA calculation,

agreewith Danlini [38] (andothers,for exampleMyo et al. [83]) that the low-

lying statebetween�� = 3–5 MeV is a � � resonance.However it hasbeen

suggestedby Timufeyuk [18] that the threeresonancesidentified by Janecke

arepositionedat thethresholdenergiesandmight bemistakenfor non-resonant

backgroundfeatures.Despitenot taking this non-resonantbackgroundinto ac-

count,theresultsby Janeckearemostoftencitedastheexperimentalbenchmark

for chargeexchangereactions.

Thelargestinconsistency in theexperimentalresultshascomefromthebreakup


reactionof � Heon PbandC, measuredby Aumannet al. [17]. Thehigherexci-

tationenergy regionin this ��57698;: He < ý=< ý reactionappearssmoothandfea-

tureless,whichseemsincongruouswith theüLi �� Heandthe � Li ü Li � ü Be� � He

results.Aumannetal. is theonly measurementthathasseenanarrow low-lying

resonance,but somecalculationshave predictedsuchstates[13,83], andarein

reasonableagreementconsideringpoorstatisticsof thedata.

Theprobability of populatingcertainstatesin the residualnucleusdepends

onhow stronglyits wavefunctionoverlapswith thatof thetargetnucleus.Timo-

feyuk [18] suggeststhatfor boththe �� andthesinglechargeexchangereac-

tionsleadingto � He,theoverlapintegralsareverysmallandthatnostatesshould

bepopulatedbetween�� 2–13MeV. Indeedit is possiblethatthebroadstates

shown in Figures5.7and5.8area combinationof very weaklypopulatedstates

predictedby Aoyamet al. [7] andothers.

If thelatesttheoreticalinterpretationsareto befollowed,thestructurein � He

followingüLi ��>�� He is morelikely to be the � � statepredictedby Danilin et

al. [38], with smallcontributionsfrom �� , ÿ�� and ÿ@? unboundcontinuumstates.

5.3.3 The High Region, ACBEDGF HJI MeV

largebumpabove12MeV madeupof:

��J�K� reaction

14,16,23MeV continuumstates

GDRcomponent

With theimprovementof theexperimentaldataa moreconsistentpictureof

thehalonucleus� He is emerging. Thepresentmeasurementhasprovidedclear

dataon thenuclearlevelsin � He. Futuremeasurementsshouldincludea higher

resolutionmeasurementof theangulardistribution to provide a betterpictureof


Figure 5.9: A missing-energy spectrumof protons following the reaction� Li LNM�OQPSR�T He. (Source:J.F. Diasetal., NuclearPhysicsA 587,434(1995).)

the �! assignmentto thenew state.

The validity of the conversionfrom missing-energy to excitation-energy is

basedon theassumptionthatthedetectedprotonscomefrom decaysto � Hefol-

lowing exclusiveüLi �� reactions:i.e. thattheonly missingenergy is theexci-

tationin theresidualnucleus.Thisconversionis notvalid if protonsaredetected

from reactionsthatinvolvemultipleparticleemission.Thecontaminationscould

comefromüLi ��ýU� T He,

üLi �� T H,

üLi ��WVJ� : H and

üLi ��J�K� : H. In Sec-

tion 4.7 the ��ýU� contribution wasconsidered,anda correctionof � 20%was

madeto themissing-energy spectrum.

TheüLi ��X� totalphotoabsorptioncrosssectionwasmeasuredby Nefkens

etal. [72] to be100timessmallerthantheüLi ��ýY� crosssectionmeasuredby

Steinet al. [71].

mentiontherelativecrosssectionsfor the(g,t)3Hand(g,t)dnetc.

Chapter 6

Conclusion

A measurementof thereactionüLi �� He hasrevealeda new statein theex-

citationenergy spectrumof � He. By carefulhandlingof thedata,thecharacter-

isticsof thenew statewasidentifiedasfollows:

Z Excitationenergy, ��\[^]�_£ÿ MeV;

Z Energy width, �7[a`�_ ÿ MeV.

The significanceof this measurement,over the previous measurementsof

� He, is the unambiguousbackgroundremoval process.Unlike the radioactive

beamand the ion beammeasurementtechniques,taggedphotonexperiments

measuretherandombackgroundcontribution. This enablestheexclusive ��componentof the datato be extractedvery cleanly. Consequently, convincing

evidencehasbeenfoundfor a new state,predictedby thetheoryof neutron-rich

nuclei.

Clearly, radioactive beamexperimentsare the only methodsuitablefor a

systematicandcompletestudyof thepropertiesof unstableneutron-richmatter.

It is serendipitousthatphotontaggingcanbeusedto study � He: very few halo

nuclei can be formed by impinging a photonbeamon a stableand naturally

abundanttarget. Nevertheless,it is importantwherepossible,to confirm the

95

96 Chapter 6. Conclusion

exciting new resultsfrom studiesat thelimits of stability.

UnfortunatelytheüLi �� He resultsare limited in what they can reveal

aboutthenatureof thenew statein � He. Althoughandistributionwasmeasured,

the lack of a theoreticalcalculationmeasthespinandparity of thestatecannot

bedetermined.Currentlynocalculationexistsfor theüLi �� Hereactionwith

correctquantum-mechanicaltreatmentof themany-bodyproblem[77].

Nonethelessthe presentexperimentconfirmsthe existanceof a new low-

lying statein the nulearenergy levels of � He. For the first time photonuclear

techniqueshavebeenusedto supportthefindingsmadeby ion- andradioactive-

beamexperiments. This thesispresentsconvincing evidenceof the new state

usingwell known andunambiguousanalysistechniques.

Appendix A

Analysis of TDC Spectra

A.1 Structur eof UncorrelatedContrib ution

In orderto determinetheuncorrelatedcontribution to theTDC timing spectra,it

is necessaryto accuratelydeterminethe structureit produces.The structureis

determinedby thecountratein thetaggerandthemicrostructureof theelectron

beam.

FigureA.1 shows threetypical TDC spectra,eachtakenwith differentbeam

currents.Theuncorrelatedbackgroundhasanexponentialstructurethatdepends

on thecountratein thetagger[50]. At highercountratestheexponentialdecay

is morepronouncedthan for the lower rates. Furthermorethe signal to noise

ratio is worseat high countrates,wherethecorrelatedeventsat channel800 is

hardto distinguishabove background.So for thepresentexperimentthecount

ratein thetaggerwassetto �cb�dfeYÿ�� s?cg , asshown in FigureA.1(c), in orderto

optimisethesignalto noiseratio.

Superimposedon the exponentialshapeof the TDC spectrais a sinusoidal

like variationof theuncorrelatedbackground.This variationhasbeenobserved

in eachdetectorandeachtagchannel,andin previousexperimentsat theMAX-

lab,andis dueto microstructurein theelectronbeam.

97

98 Appendix A. Analysisof TDC Spectra

(a)

(b)

(c)

Figure A.1: Typical taggingspectraof 64 TDC channelssummedtogetherforcountratesof (a) hjik3mlnhpo � s?cg , (b) o�ikqrlChpo � s?cg and(c) o�ikstlChpo � s?cg .

A.2. Timing Resolution 99

The time scaleon which the electronbeamvariesis approximately50 ns,

half of thetime it takesfor thebeamto make onefull revolution in thestretcher

ring. An analysisof the microstructurein the beamby [52] revealedthat this

translatedinto aperiodicvariationin theTDC spectraof � 100ns.Thevariation

canbeinterpretedasaprobabilitydistributionof thetimedifferencebetweenthe

protonsandelectrons,andthepromptpeakwill alwaysappearon a crestof the

uncorrelatedbackground.FigureA.1 alsoshows a sinusoidalvariationwith a

periodof � 100ns,andwasmodeledasanexponentialplusasinefunction.This

modelwassuccessfulin estimatingthe uncorrelatedcontribution in the TDCs

(seefit in Figure4.11), andconsequentlythe correctionfactorwasaccurately

determinedfor theuncorrelatedprotonspectrum(seeSection4.6.3).

A.2 Timing Resolution

Thetiming resolutionwasdeterminedfrom thewidth of thepeakformedby cor-

relatedeventsin theTDC,calledthepromptpeak(seeFigure4.7). In thepresent

measurementa timing resolutionof 4 nsfull width half maximumwasachieved.

Part of thewidth of thepromptpeak,wasdueto a 1 nstime differencebetween

thetime-of-flightof thehighestandlowestenergy protons.Theremainingwidth

wascausedby a smallwalk-time in thepick-off time of thedetectorsignalsby

theCFDs.

Thefocal planeelectrondetectorsweremadeof NE102scintillationplastic.

Thepulsesproducedby electronsinteractingwith NE102have a very fastchar-

acteristicrise time of u 2 ns. In comparison,the rise time of pulsesproduced

in the Si andGe detectorsis typically �wv �"� ns, thereforeit moredifficult to

getaccuratetiming from thesedetectors.As a consequence,theoverall timing

resolutionis determinedpredominantlyby the timing signal from the charged

100 Appendix A. Analysisof TDC Spectra

particledetectors.

To optimisethe timing signal from the xy� - � detectors,the integrated z -

outputfrom thepre-amplifierswasprocessedby aTFA. TheTFA removedsome

of thenoise-jitterin thepulses.Thewalk-timewasminimisedby accuratelyset-

ting the delayandthresholdlevel of the CFDs. Previous experimentswith the

GLUE chamberachievedaresolutionof 6–9ns[54]. Thereforethepresentmea-

surement,with a resolutionof 4 nsFWHM, achievedsignificantimprovements

in thetiming resolution.

Appendix B

ExperimentsConductedat the

MAX-lab

B.1 ÿ�{ O |�}G~��f}�� ÿ�] NDecember1996 This experimentwas a full-scale implementationof a pilot

studyperformedby Kuzin et al. [63]. A novel techniquewasusedto detectthe

de-excitation � -raysfollowing g � O �� to measurethe populationof statesin

g T N. Sincetheresolutionwasdeterminedby theNaI � -ray detector, theproton

energy resolutionwassacrificedby usinga thick target to maximisethe count

rate.

Theaim of thestudywasto determinetheimportanceof sort rangecorrela-

tions in thenucleus,suchasthemesonexchangecurrents(MEC) andnucleon-

nucleoninteractionsin the photonabsorptionmechanism.Modelssuchasthe

directknock-outmodel(DKM) andthequasi-deuteronmodel(QDM) areinad-

equateat describingthephotonuclearcrosssection.If thecorrectadmixturefor

thenuclearwavefunctionsis used,andthepopultationof positive andnegative

parity statesis measured,it is possibleto determinethe relative importanceof

101

102 Appendix B. ExperimentsConductedat the MAX-lab

theshortrangecorrelations.

B.2 ÿj{ O |p}�~c��} � � ÿ�] OJune 1997 The samede-excitation techniquewasemployed on g � O, but this

time the � -raysweredetectedin coincidencewith the emittedneutrons.Once

againthe resolutionwasdeterminedby the NaI � -raydetector, so the neutron

detectorswereplacedacloseto thetargetaspossibleto maximisethecountrate.

Like the �� reaction,the relative populationof statesin the residualnu-

cleuscanhelpdeterminetherole of theshortrangecorrelations.Theresultscan

alsohelpto find themostappropriateadmixtureof statesin thewavefunctionfor

g � O, basedon acalculationof thereactioncrosssection.

B.3 ÿj{ O |p}�~c�� ÿ�] NDecember1997 In orderto measurethephotoneutroncrosssection,thesame

experimentalconfigurationwasusedasin June1997. However, this time only

theneutronsweredetectedin acontinuationof thepilot studydoneby Sims[84].

The photonuclearcrosssectionwasmeasuredat a rangeof forward andback-

ward angles,so as to measurethe angularasymmetryof the reaction. From

the asymmetryand the crosssection, it is possibleto measurethe isovector

quadrupoleresonance(IVQR), oneof anumberof collectivenuclearresonances

thatcanbeobservedusingphotons.Theaim of theexperimentwasto confirm

the predictionsof the continuingdownward trend of the backward-to-forward

angularasymmetry, with decreasingphotonenergy.

During this run a wedge-shapedelectrondetector, desingedfor the focal

planetagger, wasalsotested. It wasmadeto trigger undertestconditions,al-

thoughtheresolutionachieveddid notcomparefavourablewith theconventional

B.4. g � C ��!� g� B 103

electrondetectors.This testwasa continuationof thework donefor anhonours

project[85] in 1996at the AustralianRadiationProtectionandNuclearSafety

Agency (ARPANSA), Yallambie,Victoria.

B.4 ÿ�d C |p}G~�� ÿ�� BJune 1998 The motivation for this experimentstemmedfrom the success-

full resultsof Kuzin et al. that measuredthe residualstatesin g�g B following

g� C ��J�S��g�g B. Sincethe populationof statesin g�g B wereso clearly resolved,

theaim of this measurementwasto seeif the g� B structureresembledthestates

in g�g B coupledto a valenceneutron. The experimentwas conducted“down-

stream”of themainexperimenton g : N [64], which meantthatthebeamquality

waspoorerthanusual.Consequently, thesignal-to-noiseratio in thetiming spec-

trawasverypoorandthetaggingpeakwasdifficult to define.Thefinal analysis

did not resultin anenergy spectrumof theresidualstatesin g� B asplanned,be-

causethestatisticsweretoo poor. However, anomouslylow proton-to-deuteron

andproton-to-tritonratioswereobserved in the particle identificationplots. It

wassuggestedthatthis couldbecausedby thepresenceof thevalenceneutron,

breaking-upthe otherwisestrongly clusteredg� C core. Another possibility is

thattheneutroncausedaninterferencewith anoutgoingreactionparticle,caus-

ing unusualfinal stateinteractions.

B.5 � Li |p}G~�� { He

June 1999 This run wasusedto collect thedatapresentedin this thesis.Un-

fortunately, therun wasendedprematurelydueto technicaldifficultieswith the

electronaccelerator. So, only four daysofüLi datawere taken insteadof the

scheduledtwo weeks.Nevertheless,enoughdatawastakento analysethereac-

104 Appendix B. ExperimentsConductedat the MAX-lab

tion successfullyandobtaingoodresults.

The experimentwas motivatedby one of the first experimentswhich was

performedatMAX-lab ona � Li target.A subsequentmeasurementsofüLi using

theGLUE chambershowedaninterestingasymmetryin thefirst excitedstatein

� He. Thisstructurewasalsobeinginvestigatedin radioactivebeamexperiments

at thetime, while theoreticalcalculationswerepredictinga new haloexcitation

in the sameregion of the � He excitation spectrum.Given the ability to easily

separateproton eventsfrom the randombackgroundusing the taggedphoton

technique,it wasdecidedto carefullymeasuretheexcitedstatesin � Hefollowing

theüLi �� reaction.

Appendix C

Papers

C.1 ConferencePapers

Theauthorpresentedpapersat thefollowing conferences.An abstractof thetalkis givenin eachcase.

4th Workshop on EM Induced Two-Hadron Emission

Granada, Spain,May 29,1999.

Protons,deuteronsand tritons fr om g� C and g � C: What do they tell us?M. J.Boland,R. P. Rassool,M. N. Thompson,P. D. Harty, M. A. Garbutt

Schoolof Physics,TheUniversityof Melbourne, Melbourne, AustraliaJ.Jury

TrentUniversity, Ontario,CanadaJ-O.Adler, K. Hanson,B. Schroder, M. Lundin,M. Karlsson,D. Nilsson

Departmentof NuclearPhysics,LundUniversity, LundSwedenT. Davison,S.A. Morrow, K. Foehl

Departmentof Physics,Universityof Edinburgh,ScotlandJ.R. M. Annand,J.C. McGeorge

Departmentof PhysicsandAstronomy, Universityof Glasgow, ScotlandAbstract:

A recentintermediate-energy photonuclearexperimenton g � C at �=��[ 50–70MeV indicatessignificantly more deuteronsand tritons are emittedthan fromg� C. The reasonfor this is not clear, but maywell be relatedto thedifferencesinducedin the g� C ground-statewavefunctionwith theadditionof theextraneu-tron. An understandingof the experimentalobservationsmay be relevant inunderstandingthephotonuclearreactionmechanismin the intermediate-energy

105

106 Appendix C. Papers

region. Thedatapresentedhereresultsfrom a measurementmadeat theMAX-Labat LundUniversitylastyear. It wasmadein collaborationwith groupsfromLundUniversity, Universityof Glasgow, Universityof EdinburghandTrentUni-versity.

American Physical Society, Annual Meeting

Long Beach,USA, April 28,2000.

Searching for Statesin the Halo Nucleus � He Using Intermediate EnergyTaggedPhotons

M.J.Boland,M.A. Garbutt, R.P. Rassool,M.N. Thompson,A.J. BennettTheUniversityof Melbourne

J.W. JuryTrentUniversity

J.O.Adler, B. Schoder, D. Nilsson,K. Hansen,M. Lundin,M. KarlssonLundUniversity

Abstract:

A recentphotonuclearexperimentwe conductedat the MAX-Lab in Swedenappearsto supportcalculationsthatpredictnew statesin � Hebetweentheknownfirst andsecondexcited states.The reaction

üLi �� He wasmeasuredusing

taggedphotonsin theenergy range�� = 50– 70MeV andhighresolutionprotontelescopesat angles��[�d��"��p{��p��ûÿ��"�� and ÿ�]"�� . Preliminaryresultsshowsomeevidenceexiststo supportthepresenceof previously unseenstatesin � Hethat arepredictedby Ershov et. al. on the basisof a distortedwave impulseapproximation(DWIA) reactiontheorycalculation.S.N.Ershov etal., Phys.Rev. C 56, 1483(1997).

C.2 Journal Papers

Thefollowingpaperwaspublishedby theAmericanPhysicalSocietyin PhysicalReview C, Vol. 64,031601(R),2001. It is in theRapidCommunicationsectionof the journal, andcontainsa brief summaryof the experimentalmethod,theanalysistechniquesandthenew stateobservedin � He.

C.2. Journal Papers 107

Excitations in the halo nucleus 6�He following the 7Li � � ,p� � 6

�He reaction

M.�

J. Boland,M. A. Garbutt,R. P. Rassool,M. N. Thompson,andA. J. BennettSchool�

of Physics,TheUniversityof Melbourne,Victoria 3010,Australia

J.�

W. JuryTrent University, Peterborough,Ontario, CanadaK9J 7B8

J.-O.�

Adler, B. Schroder�

, D. Nilsson,K. Hansen,M. Karlsson,andM. LundinDepartment

of Physics,Universityof Lund,P.O. Box 118, S-22100 Lund,Sweden

I. J. D. MacGregorDepartmentof Physicsand Astronomy, Universityof Glasgow, GlasgowG12 8QQ, Scotland¡

Received¢

22 April 2001;published26 July 2001£A broadexcitedstatewasobservedin 6He with energy Ex¤ ¥ 5

¦ §1 MeV andwidth ¨ © 3

ª «1 MeV, following

the¬

reaction 7Li( ,® p¯ )° 6He. The state is consistentwith a numberof broad resonancespredictedby recent

cluster± modelcalculations.The well-establishedreactionmechanism,combinedwith a simpleandtransparentanalysis² procedureconfersconsiderablevalidity to this observation.

DOI:³

10.1103/PhysRevC.64.031601 PACS number´ sµ ¶ :· 25.20.Lj, 24.30.Cz,27.20. n¹Thephysicsof nucleiapproachingtheneutrondrip line is

ofº interestasameansof furtherrefiningourunderstandingofthe»

nucleon-nucleonpotential. Amongst these so-called‘‘halo’’ nuclei, 6He hasreceivedconsiderableattention.Theestablished¼ level structureof 6He

½ ¾1¿ hasÀ

beenquestionedforsomeÁ years in a numberof theoreticalcalculations.TheseconsideredÂ extendedneutrondistributionsby modeling 6He

½asÃ a 4He

½ ÄnÅ Æ nÅ three-body

»cluster. A commonfeatureof

these»

calculations is low-lying structure, above the wellknownÇ

2 È firstÉ

excitedstate.Thenatureof this structurewasinitially thoughtto bea soft dipoleresonanceÊ 2,3Ë ,Ì with twohaloÀ

neutronsoscillating againstthe core. However, morerecentÍ calculationsrefute this andpostulatethat it is causedbyÎ

three-bodydynamicsÏ 4–6Ð .ÑExperimentalÒ

measurementson the 6He½

systemhavesofar beenconcentratedon charge exchangereactionsof thetype» 6Li( 7Li, 7Be)6He Ó 7–1

Ô0Õ andÃ 6Li( tÖ ,Ì 3He)6He × 11Ø .Ñ All

these»

resultshavereportedlow-lying strengthin the reactioncrossÂ sectionat roughly the energies predictedby calcula-tions,»

but noneare able to determinethe natureof the ob-servedÁ structure.

InÙ

each casethe analysisof theseexperimentshas in-volvedÚ severalcontroversialassumptionsin the backgroundremovalprocess.In particular, the nonresonantbackgroundinÛ

the (7Li,Ü 7Be)Ý

reactionwas calculatedbut not measured.This processmust include degreesof freedomdue to theexcited¼ statesof both the projectile and the ejectile. In onecaseÂ Þ 9ß à ,Ì nonresonantbackgroundcontributionsto the crosssectionÁ werenot includedat all.

BackgroundÝ

subtractionis only oneof the complicationsinvolved with heavy-ionreactions.Anotherdifficulty is thatmanyá possiblecombinationsof angular-momentumtransferexist¼ betweenprojectile and target. One of the simplestcharÂ geexchangereactions,namely(nÅ ,Ì pâ )

ã, doesnot suffer the

sameÁ problem.However, the poor resolutionof these(nÅ ,Ì pâ )ã

experiments¼ makesit difficult to see even the commonlyresolved2 ä state.Á Reactionsof the type (tÖ ,Ì 3He) alsosuffer

from poor resolution,andusethe samebackgroundremovalprocesså as the (7Li, 7Be) reactionsæ 11ç .Ñ In contrast,taggedphotonå measurementshave a relatively simple and unam-biguousÎ

backgroundremoval procedurethat is proven andwellè establishedé 12–15ê ë andÃ referencesthereinì .Ñ

This paperreportsthepresenceof a broadresonanceat anexcitation¼ energy of 5 MeV in 6He that hasbeenobservedfollowingí

the 7Li(Ü î

,Ì pâ )ã 6He½

photonuclearreaction.The mea-surementÁ wasmadein theenergy rangeof E ï ð 50

ñ–70 MeV,

usingò theMAX-lab taggedphotonfacility ó 16ô atÃ Lund Uni-versityÚ . The protons and other charged particles were de-tected»

with solid-statespectrometers,each consistingof athick»

HP-Ge Eõ

detector�

and a thin Si ö Eõ

detector�

. These

FIG.÷

1. The time correlation spectrumbetweenprotons andtagged¬

photonsfor ø ù 60°ú

. The6 ns wide promptpeakû shadedµ ü isclearly± visible on top of a randombackgroundý labeled

þ ÿ.�

RAPID COMMUNICA TIONS

PHYSICAL�

REVIEW C, VOLUME 64, 031601� R¢ �

0556-2813/2001/64� �

3ª �

/031601� �

3ª

/$20.00�

©2001TheAmericanPhysicalSociety64

031601-1�

108 Appendix C. Papers

wereè placedat anglesof � � 30°

,60°,90°,120°, and150° tothe»

photon beam,similar to the configurationdescribedin�17� .Ñ A 1 mm thick target of 99.9%pure 7Li

Üwasplacedat

60°�

to the photonbeam.Protons

�wereselectedfrom otherchargedparticleevents

byÎ

useof a particle-identificationplot of the energy lost inthe»

full-energy detector, versusthat lost in the � E detector�

.Protons

�correlatedwith taggedphotonswere located in a

narrowpr� ompt timing»

peak,shownshadedin Fig. 1, sittingonº a timing spectrumof random events. Missing-energyspectraÁ wereproducedfrom a cut on thepromptpeakat eachangleÃ � filled dotsin Fig. 2� .Ñ Themissingenergy is definedasEõ

miss� Eõ � �

T�

p� � T�

R ,Ì whereT�

R isÛ

the kinetic energy of the6He nucleus,and Tp� is the kinetic energy of the emittedproton.å The excitationenergy, shownin Fig. 3, is relatedtoEõ

miss byÎ

Eõ

x� � Eõ

miss� Q�

,Ì where Q�

isÛ

the proton separationener¼ gy, and for the reaction 7Li( ,Ì p� )

ã 6He, Q� !

10.0 MeV.The

"contributionof randomprotoneventsin the prompt re-

gion,# was measuredby making a cut on the randomback-ground# region $ labeledin Fig. 1% .Ñ The resulting featurelessbackgroundÎ

spectrum& openº circlesin Fig. 2' wasè normalizedandÃ fitted, beforebeingsubtractedfrom the spectrumof thepromptå region.

The contribution due to the ( ( ,Ì pn� )ã

reaction ) threshold»

Emiss* 11.9 MeV+ alsoÃ neededto be considered.The mo-mentumá distribution of this backgroundchannelwas calcu-latedusinga MonteCarlomodelof directtwo-nucleonemis-sionÁ , 18- ,Ì which included all the experimentalparameters,andÃ coveredthefull phasespaceof theexperiment.Thepeak

ofº the ( . ,Ì pn� )ã

missing-energy distribution is located atE

/miss0 1 29

2MeV 3 seeÁ Fig. 24 andÃ assuchcannotaccountfor

allÃ the strengthobservedbetweenE/

miss5 13–20 MeV. Thepn� backgroundÎ

wasnormalizedin a consistentmannerfor allangles,Ã then subtractedsuch that the net missing-energyspectrumÁ waspositiveat all energies.The resultingmissing-ener¼ gy spectrumof protonsemittedat 6 7 60°

�is shown in

Fig.8

3.Protonsleading to the groundstateand the first excited

stateÁ at E/

x� 9 1.8 MeV canbe clearly seen.Evidencefor theknownÇ

secondexcitedstatenearE/

x� : 14 MeV canbedistin-guished# at theonsetof thehigh missing-energy regionof thespectrum.Á Significantly, theevidencefor a broadstatecanbeseenÁ in the region betweenEx� ; 3

–10 MeV. A fit of three

Gaussians<

to the data in Fig. 3 gives a width of = > 3 ?

1MeV�

and a centroidenergy of E/

x� @ 5A B

1 MeV to the newstructure,Á on the assumptionthat it is a singleresonance.

The"

presentexperiment,like thoseusingchargeexchangereactions,is unableto definetheexactnatureof theobservedresonance.The strongestcandidatesseemto be a 1 C softÁdipole�

modeanda second2 D state,Á predictedby Suzuki E 3 F

andÃ othersG 19–22H .Ñ A calculationof the E1 breakupof 6HeI6

� JshowsÁ anenhancementto the1 K continuumÂ at anenergy

consistentÂ with the measurementpresentedhere. It is pos-sibleÁ that the strengthwe observein the 7Li( L ,Ì p� )

ã 6He crosssectionÁ at 5 MeV is evidenceof the 1 M dipole

�andthe posi-

tive»

parity states,both of which were predictedby DanilinetN al. O 5

A P.Ñ A completeanalysisof our data,including the an-

gular# distribution,mayclarify thenatureof thestructureandthereby»

validatesomeof the modelassumptions.

FIG.÷

2. Protonmissing-energy spectrumat Q R 60°ú

showing S iT U

the¬

randombackgroundV openW dotsX withY a polynomial fit Z dotted[

lineþ \

,® ] iiT ^

the¬

calculated( _ ,® pn¯ )°

backgroundsolidµ linea ,® andb iiiT c

the¬

promptd protonse filledf

dotsg .�

FIG. 3. Protonmissing-energy spectrumat h i 60°ú

following thereactionj 7Li(

k l,® p¯ )° 6He

mwith the background contributions sub-

tracted.¬

The 6He excitationenergy scaleis drawnfor reference.


M.n

J. BOLAND eto al. PHYSICAL�

REVIEW C 64p

031601� q

R¢ r

031601-2�

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B. V. Danilin, I. J.Thompson,J.S.Vaagen,andM. V. Zhukov,Nucl.

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6ú �

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J. Thompson,B. V. Danilin, V. D. Efros,J. S. Vaagen,J. M.Bang,andM. V. Zhukov, Phys.Rev. C 61

p,® 024318� 2000� .��

7� �

J.�

Janecke¹ eto al.,® Phys.Rev. C 54�

,® 1070 � 1996� .��8

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