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
x
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
xiv
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
xvi
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.
4
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
8 Chapter 2. Moti vation
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
10 Chapter 2. Moti vation
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
12 Chapter 2. Moti vation
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
14 Chapter 2. Moti vation
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.
16 Chapter 2. Moti vation
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].
18 Chapter 2. Moti vation
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@�� ,
2.2. The Halo Nucleus � He 19
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.
20 Chapter 2. Moti vation
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������: 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
2.2. The Halo Nucleus � He 21
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-
22 Chapter 2. Moti vation
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
2.2. The Halo Nucleus � He 23
� 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
24 Chapter 2. Moti vation
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.
2.2. The Halo Nucleus � He 25
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 � He T��T� 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
26 Chapter 2. Moti vation
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( 7Ûà A � ) excitationsby
measuringde-excitation � -raysin coincidencewith � Be ejectiles[49]. It was
2.2. The Halo Nucleus � He 27
thenassumedthatthe 7ÛÃÝA � spectrumcontainedexclusively GDRexcitations,
andthe 7ÛëA½� 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�ãA � 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 �������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.
28 Chapter 2. Moti vation
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-
30 Chapter 2. Moti vation
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.
34 Chapter 3. Experimental Method
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.
36 Chapter 3. Experimental Method
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.
38 Chapter 3. Experimental Method
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
40 Chapter 3. Experimental Method
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
3.3. DetectingProtons 41
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.
42 Chapter 3. Experimental Method
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.
3.3. DetectingProtons 43
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.
44 Chapter 3. Experimental Method
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)
3.3. DetectingProtons 45
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
46 Chapter 3. Experimental Method
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.
3.3. DetectingProtons 47
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.
48 Chapter 3. Experimental Method
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
50 Chapter 3. Experimental Method
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
52 Chapter 3. Experimental Method
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.
54
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
58 Chapter 4. Data Analysis
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.
60 Chapter 4. Data Analysis
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
Eγ (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
62 Chapter 4. Data Analysis
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. Proton Energy Measurement 63
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
64 Chapter 4. Data Analysis
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 ±#âɪÈl¦�« 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
4.5. Proton Energy Measurement 65
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 ¨
66 Chapter 4. Data Analysis
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-
68 Chapter 4. Data Analysis
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.
4.6. Corr ection for Accidental Tagging 69
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.
70 Chapter 4. Data Analysis
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. Corr ection for Accidental Tagging 71
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
72 Chapter 4. Data Analysis
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
74 Chapter 4. Data Analysis
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.
80 Chapter 5. Resultsand Discussion
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
82 Chapter 5. Resultsand Discussion
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 ·¨ik���2´ 1.0MeV, which is mainly dueto
theuncertaintyin theenergy lossstragglingin thetargetandthe ·¨i detectors.
The secondlargestcontribution to the resolutionis from the uncertaintyin the
photonenergy ( ·¨i � ´ 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.
84 Chapter 5. Resultsand Discussion
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  0.1 1.1  0.1� µ 1.8 1.99  0.3 1.79  0.35.83  0.5 7.88  0.6¬ µ 0 0.0  0.1 1.0  0.1� µ 1.8 1.97  0.3 1.76  0.35.84  0.4 7.88  0.5¬ µ 0 0.0  0.1 1.1  0.1� µ 1.8 1.97  0.3 1.76  0.35.85  1.0 7.84  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  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 �ȵ 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
86 Chapter 5. Resultsand Discussion
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
).
88 Chapter 5. Resultsand Discussion
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
5.3. Inter pretations 89
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
90 Chapter 5. Resultsand Discussion
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
5.3. Inter pretations 91
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-
92 Chapter 5. Resultsand Discussion
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
5.3. Inter pretations 93
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
94 Chapter 5. Resultsand Discussion
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.Theseconsidered extendedneutrondistributionsby modeling 6He
½asà 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 andà 6Li( tÖ ,Ì 3He)6He × 11Ø .Ñ All
these»
resultshavereportedlow-lying strengthin the reactioncross 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 simplestchar 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 andà 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 atà 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 eachangleà � 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 normalizedandà fitted, beforebeingsubtractedfrom the spectrumof thepromptå region.
The contribution due to the ( ( ,Ì pn� )ã
reaction ) threshold»
Emiss* 11.9 MeV+ alsoà neededto be considered.The mo-mentumá distribution of this backgroundchannelwas calcu-latedusinga MonteCarlomodelof directtwo-nucleonemis-sionÁ , 18- ,Ì which included all the experimentalparameters,andà coveredthefull phasespaceof theexperiment.Thepeak
ofº the ( . ,Ì pn� )ã
missing-energy distribution is located atE
/miss0 1 29
2MeV 3 seeÁ Fig. 24 andà assuchcannotaccountfor
allà 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
andà othersG 19–22H .Ñ A calculationof the E1 breakupof 6HeI6
� JshowsÁ anenhancementto the1 K continuum at anenergy
consistent 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.
RAPID COMMUNICA TIONS
M.n
J. BOLAND eto al. PHYSICAL�
REVIEW C 64p
031601� q
R¢ r
031601-2�
C.2. Journal Papers 109
s1t F. Ajzenberg-Selove,Nucl. Phys.A490, 1® u 1988v .�w2
x yP
�. G. HansenandB. Jonson,Europhys.Lett. 4
z,® 409 { 1987| .�}
3ª ~
Y. Suzuki,Nucl. Phys.A528,® 395 � 1991� .��4
� �A.
�Csoto¬ ´,® Phys.Rev. C 49
z,® 2244 � 1994� .��
5¦ �
B. V. Danilin, I. J.Thompson,J.S.Vaagen,andM. V. Zhukov,Nucl.
�Phys.A632,® 383 � 1998� .��
6ú �
I.�
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
� �T. Annakkageeto al.,® Nucl. Phys.A648, 3® � 1999� .��
9� �
S.
Nakayamaeto al.,® Phys.Rev. Lett. 85¡
,® 262 ¢ 2000x £
.�¤10¥ S.
B. Sakuta,A. A. Ogloblin, O. Y. Osadchy, Y. A. Gluukhov,
S.
N. Ershov, F. A. Gareev, andJ. S. Vaagen,Europhys.Lett.22
¦, 5® 11 § 1993 .�©
11ª T. Nakamuraeto al.,® Phys.Lett. B 493,® 209 « 2000¬ .�12® R.¢
O. Owens,Nucl. Instrum.MethodsPhys.Res.A 288¦
,® 574¯1990° .�±
13² I. J. D. MacGregoreto al.,® Nucl. Phys.A533,® 269 ³ 1991 .�µ14¶ L.
kV. Hoorebeke,Nucl. Instrum. MethodsPhys.Res.A 321
·,®
230 ¸ 1992¹ .�
º15» A. Kuzin eto al.,® Phys.Rev. C 58
�,® 2167 ¼ 1998½ .�¾
16¿ J.-O.�
Adler, B.-E. Andersson,K. I. Blomqvist, K. G. Fissum,K.
ÀHansen,L. Isaksson,B. Nilsson,D. Nilsson,H. Ruijter, A.
Sandell,
B. Schroder[
, andD. A. Sims,Nucl. Instrum.MethodsPhys.Res.A 388
·, 1® 7 Á 1997 .�Ã
17Ä J.�
F. Dias,D. Ryckbosch,R. V. deVyver, C. V. denAbeele,G.D. Meyer, L. V. Hoorebeke,J.-O.Adler, K. I. Blomqvist, D.Nilsson,
ÅH. Ruijter, and B. Schroder
[, Nucl. Phys.A587
Æ,® 434Ç
1995È .�É18Ê J.
�C. McGeorge eto al.,® Phys.Rev. C 51
�,® 1967 Ë 1995Ì .�Í
19Î B. V. Danilin, T. Rogde,S.N. Ershov, H. Heiberg-Andersen,J.S.
Vaagen,I. J.Thompson,andM. V. Zhukov, Phys.Rev. C 55
�,®
R577 Ï 1997Ð .�Ñ20
x ÒS.
N. Ershov, T. Rogde,B. V. Danilin, J. S. Vaagen,I. J. Th-
ompson,W andF. A. Gareev, Phys.Rev. C 56�
,® 1483 Ó 1997Ô .�Õ21
x ÖM.
nV. Zhukov, D. V. Fedorov, andB. V. Danilin, Nucl. Phys.
A539,® 177 × 1992Ø .�Ù22Ú S.
N. Ershov, B. V. Danilin, andJ.S.Vaagen,Phys.Rev. C 62
Û,®
041001� Ü
R¢ Ý Þ
2000x ß
.�
RAPID COMMUNICA TIONS
EXCITATIONS IN THE HALO NUCLEUS 6He . . . PHYSICAL REVIEW C 64Û
031601� à
Rá
031601-3�
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