ASTROPHYSICAL S FACTOR FOR PROTON CAPTURE ON Sm-147 AND Sm-149
Dorel Bucurescuvisibility
…
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The cross sections of the 147 Sm(p,γ) 148 Eu and 149 Sm(p,γ) 150 Eu reactions have been measured with the activation method, in the Gamow window for the astrophysical p process. The experiments were carried out at the IFIN-HH Tandem accelerator. The cross sections have been derived by measuring the decay γ radiations of the reaction products. The results are compared with the predictions of the Hauser -Feshbach statistical model calculations performed with the code NON-SMOKER.
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Dedicated to Professor Oliviu Gherman’s 80th Anniversaryă
ASTROPHYSICALăSăFACTORăFORăPROTONăCAPTUREăă
ONă147SmăANDă149Smă
M.ăIVAŞCU1,ăI.ăC TA-DANIL1,ăD.ăFILIPESCU1,ăL.ăSTROE1,2,ăT.ăGLODARIU1,ăă
D.ăBUCURESCU1,ăG.ăC TA-DANIL1,2,ăD.ăDELEANU1,2,ăD.G.ăGHI 1,ăN.ăM RGINEAN1,ăă
R.ăM RGINEAN1,ăC.ăMIHAI1,ăS.ăPASCU1,2,ăT.ăSAVA1,ăG.ăSULIMAN1,ăN.V.ăZAMFIR1ă
1
ăNationalăInstituteăforăNuclearăPhysicsăandăEngineering,ăP.O.BoxăMG-6,ăRO-077125ăBucharestMagurele,ăRomania,ăE-mail:ă[email protected];ăE-mail:ă[email protected]ăă
2
ăUniversityă“Politehnica”ăofăBucharest,ăPhysicsăDepartment,ăBucharest,ăRomaniaă
Received August 24, 2010
Theă crossă sectionsă ofă theă 147Sm(p,γ)148Euă andă 149Sm(p,γ)150Euă reactionsă haveă
beenămeasuredăwithătheăactivationămethod,ăinătheăGamowăwindowăforătheăastrophysicală
păprocess.ăTheăexperimentsăwereăcarriedăoutăatătheăIFIN-HHăTandemăaccelerator.ăTheă
crossă sectionsă haveă beenă derivedă byă measuringă theă decayă γă radiationsă ofă theă reactionă
products.ă Theă resultsă areă comparedă withă theă predictionsă ofă theă Hauseră –ă Feshbachă
statisticalămodelăcalculationsăperformedăwithătheăcodeăNON-SMOKER.ă
Key words:ăactivationămethod,ăfusionăreactions,ăcross-section,ăSăfactor.ă
1. INTRODUCTION
TheăstudyăofăEuănucleiăisăveryăimportantăinăorderătoăobtainănewăinformationă
concerningătheăsynthesisăofăpătypeănuclei.ăTheănuclearăsynthesisăofăpătypeănucleiăisă
definedă ină nucleară astrophysicsă asă aă “pă process”ă [1,2].ă Thisă processă consistsă ofă
differentănuclearăsynthesisăscenarios,ăinăwhichăeachăpătypeănucleusăisăprecededăbyăaă
(γ,ăn),ă(γ,ăp)ăoră(γ,ăα)ăreactions.ăInăsomeăofătheseăscenariosă(p,ăγ),ă(α,γ),ă(p,ănγ)ăandă
(α,ă nγ)ă reactionsă mayă beă present.ă Thereă areă 32ă stableă pă typeă nucleiă heavieră thană
iron,ălocatedăbetweenă 74Seăandă 136Hg.ăTheă 148Euăandă 150Euăbelongătoăthisăfamilyăofă
nuclei.ăOneăofătheămajorăenigmasăofăallătheănuclearăsynthesisă păprocessămodelsăisă
theăpredictionăofătheăpătypeănucleiăabundances.ăAtătheăpresentătime,ăităisăwellăknownă
thatătheănuclearăsynthesisămodelsăareăcapableătoăreproduceătheăpănucleiăabundancesă
withinăaăfactorăofăthreeă[3,4].ăTheseădiscrepanciesăoccurădueătoăuncertaintiesăinătheă
astrophysicalăsideăofămodelingătheă păprocessesăorăcanăresultăfromăuncertaintiesăofă
theăinputăsideăofănucleară physicsăusedăinăabundanceăcalculations.ăWeăhaveătoăsayă
thată captureă crossă sectionă measurementsă areă stillă rareă dueă toă theă measurementă
difficulties.ăIfăweăreferătoă(p,γ)ămeasurementsăforănucleiăhavingăAă>ă140,ăweăhaveă
toăunderlineăthatătheyăhaveătoăbeădoneăusingăenergiesăsmallerăthată3ăMeVăforăprotonă
Rom.ăJourn.ăPhys.,ăVol.ă55,ăNos.ă9–10,ăP.ă1006–1012,ăBucharest,ă2010ă
2ă
AstrophysicalăSăfactorăforăprotonăcaptureăonă147Smăandă149Smă
1007ă
andă 12ă MeVă foră alphaă particles,ă thată is,ă ină theă regionă ină whichă theă reactionă crossă
sectionsăareăveryăsmall.ăInăthisăcase,ătheăbeamăintensityămustăbeăinătheăinătheărangeă
ofămicroamperes,ăandătheăirradiationătimeăhasătoăbeăinătheătenthsăofăhoursărange.ăInă
conceivingăandăbuildingăanăexperimentalăsetupăforămeasuringătheătotalăcrossăsectionă
forăprotons,ăwhichămayătakeăintoăaccountătheăpreviouslyămentionedădifficulties,ăoneă
hasă toă respectă threeă importantă aspects:ă a)ă studyă suchă experimentală setupsă usedă ină
thisămomentăinăotherălaboratories,ăb)ăselectăandătestătheăequipmentăhavingăoptimumă
parameters,ăandăc)ăfinishăbuildingătheăexperimentalăsetupăwhichămayăbeătestedăandă
usedăinăourăgroup’săprojectsăregardingănuclearăastrophysics.ă
Ităisătheăgoalăofătheăpresentăworkătoăpresentătheămeasuredăcrossăsectionsăofătheă
147
Sm(p,γ)148Euăandă 149Sm(p,γ)150Euăreactionsăinătheăenergyărangeărelevantăforătheă
astrophysicalăpăprocess,ăandătoăcompareăthemăwithătheăpredictionsăofătheăHauseră–ă
Feshbachăstatisticalămodelăcalculations.ă
2. EXPERIMENTAL SETUP AND PROCEDURES
Theăexperimentalăsetupăandătheăentireăexperimentalăprocessăareă presentedăină
ourăpreviousăarticleă[5].ăTheăcharacteristicăactivitiesăofă 148Euă(5–ăgroundăstate)ăandă
150
Euă(0–ăisomericăstate)ăwereămeasuredăwithăaăpairăofălargeăvolumeăGeădetectorsăină
closeăgeometryătoămaximizeătheădetectorăefficiency.ăDuringăirradiationătime,ă 148Euă
nucleiăareăobtainedăinăgroundăstateă(5–,ă54.5ăd)ăwhileă 150Euănucleiăareăobtainedăină
isomerică stateă (0–,ă 12.8ă h).ă Theă totală numberă ofă nucleiă populatedă onă groundă oră
isomericăstateăatătheăendăofătheăirradiationătimeă ta ăcanăbeăobtainedăas:ă
ă
N M (ta ) = σM ρh
a
NA
I (t )
p e−λM ta ∫ eλM t
dt ă
AT
Z pe
0
t
(1)ă
whereă σM ăisătheăpartialăcaptureăcrossăsectionătoăgroundăorăisomericăstate,ă λM ăisătheă
correspondingă decayă constantă pă isă theă isotopică enrichmentă ofă theă target,ă ρ hă –ă
target’săspecificăthickness,ă N A –ăAvogadroănumber,ă Z P –ăprojectileăatomicănumber,ă
AT ă –ă targetă meană massă number,ă eă –ă electronă charge,ă andă I (t ) ă –ă electricală beamă
intensity.ă
Ifătheătargetăisămeasuredăafterăaăwaitingătimeă t w ,ăoverătheămeasuringătimeă tm ,ă
theăfollowingănumberăofăactivatedănucleiăwillăbeădisintegrated:ă
ă
NMdez (tw , tm ) = NMi e−λM tw (1 − e−λM tm ) ă
(2)ă
withă N Mi ăobtainedăfromăEq.ă(1).ă
Thisănumberăcanăbeăconnectedădirectlyăwithătheăpeakăsurfaceă Ai ăofăaăcertaină
gammaăradiationăγi,ăwhichăhaveătoăbeăemittedăonlyăinătheădecayăofăpopulatedăstateă
ă
Ai = I γi εi N Mdez,G (tw , tm ) ă
(3)ă
M.ăIvaşcuăet al.
ă
1008ă
3ă
whereă εi ă representsă absoluteă peakă efficiencyă foră γiă radiationă ină theă specifiedă
detectionăgeometry,ăandă I γi ăisătheăabsoluteăgammaărayăintensityăofăγiăradiation.ă
Besidesă 148Euăandă 150Eu,ăgroundăstatesăofă147Euă(5/2+,ă24.1ăd)ăandă149Euă(5/2+ă
93.1ăd)ăareăalsoăpopulatedăthroughă(p,n)ăreactionsăthusămakingăpossibleătoămeasureă
theăcorrespondingăcrossăsectionăusingătheăsameătechnique.ă
Basedă onă theă totală experimentală cross-sectionă valuesă oneă cană calculateă theă
astrophysicalăfactorsăS,ăusingătheăfollowingăequation:ă
S ( E ) = σT ( E ) ⋅ E ⋅ e2 πη ă
ă
(4)ă
whereă ηă isă theă Somerfeldă parameter,ă σTă isă theă totală reactionă cross-sectionă ină theă
centerăofămass.ă
Enrichedă 147Smă andă 149Smă targetsă havingă moreă thană 95%ă isotopică
abundances,ăinătheăformăofăselfăsupportingăfoilsăofă~ă1.8ămg/cm2ăwereăusedăinăthisă
experiment.ăTheăsamariumăfoilsăwereămountedăonăcircularăAlăholdersăwithătheăholeă
diameterăofă12ămm.ăAăstackăwasăpreparedăhavingătwoăsamariumătargetsăinterspacedă
byăaluminumăfoilsăofăthicknessă~ă80µm.ăTheăaluminumăfoilsăservedăasăincidentăαbeamăenergyădegradersăandăalsoăasăcatchersăforărecoilănucleiăfromătheăSmăfoilsăusedă
forăestimatingătheărecoilăfraction.ă
TheăstackăwasămountedăinăaăFaradayăcup,ăisolatedăfromătheărestăofătheăbeamă
line,ă andă bombardedă withă aă protonă beamă deliveredă byă IFIN-HHă Tandemă
Accelerator.ăToăgetăanăaccurateămeasurement,ăaăringăwasăplacedăatătheăFaradayăcupă
entranceăhavingăaă–300ăVăbiasăvoltageădesignatedătoăsuppressăsecondaryăelectrons.ă
Ană importantă parameteră neededă toă performă theă calculationsă isă theă beamă
intensityăandăitsătimeădependence.ăTheăbeamăcurrentăwasăacquiredăinărealătime,ăină
stepsăofăoneăsecond,ăsmallăenoughătoăperformătheăintegration,ăusingăanăORTECă439ă
digitalăcurrentăintegrator.ăTheătypicalăcurrentăwasăbetweenă100ăandă500ănAăasăcană
beăseenăinăFigureă1.ă
700
p+
Beam current (nA)
600
149
Sm
500
400
300
200
100
0
0
3
6
8
11
14
17
Irradiation time (hours)
Fig.ă1ă–ăTimeădependenceăofăbeamăintensity.ă
19
ă
AstrophysicalăSăfactorăforăprotonăcaptureăonă147Smăandă149Smă
4ă
1009ă
Absolute efficiency (%)
Allă measurementsă haveă beenă performedă withă aă speciallyă designedă lowbackgroundăsetupă–ăbothădetectorsăwereăsurroundedăwithăPbăwallsăclothedăwithăCuă
andăAlăplatesăonătheăinside.ăForătheădead-timeăcorrection,ăweăusedăaăpulseăgeneratoră
withăaăfixedăfrequencyăofătheăoutputăsignală(20ăHz).ăEfficiencyăcalibrationăofăGeHPă
detectorsăwasădoneăusingăcalibratedăpointăsourcesăofă 152Eu,ă 133Ba,ă 241Am,ă 60Coăandă
137
Cs,ă placedă ină theă sameă geometryă asă theă targets.ă Theă calibrationă curveă foră oneă
HPGeădetectorăusedăinătheăexperimentăisăpresentedăinăFigureă2.ă
ă
1
10
Calibration sources:
152
Eu
133
Ba
60
Co
137
Cs
241
Am
0
10
2
3
10
10
Eγ (keV)
ă
Fig.ă2ă–ăAbsoluteăpeakăefficiencyăforăoneăHPGeădetectorăusedăinăourăexperiment.ă
3. THEORETICAL CALCULATIONS
Theăpredictionăofătheătotalăreactionăcrossăsectionsăandătheă Săfactorsăfromătheă
NONSMOKERă code,ă asă weă previouslyă stated,ă encouragedă usă byă itsă promisingă
resultsă ină usingă theă (p,γ)ă reactionă foră obtainingă astrophysicală informationă
concerningă148Euăandă150Eu.ăInăFigureă3ăweăshowătheă(p,γ)ăcross-sectionăvariationăasă
aăfunctionăofăECM(MeV)ăforătheăenergyărangeăfromă1ătoă15ăMeV.ăOneăcanăfindăoută
thatăforăthisăenergyăintervalătheăσTăvariesăfromă10-12ătoă10-1ămillibarns.ăThisăbringsă
oută theă difficultyă ină doingă suchă sortă ofă experiments,ă interestingă fromă theă
astrophysicalăpointăofăview.ăThisădifficultyăisăevenămoreăobviousăfromătheăfactăthată
foră onlyă 1ă MeVă variationă ofă ECMă (fromă 2ă toă 1ă MeV),ă aă 5ă ordersă ofă magnitudeă
changeăofătheătotalăcrossăsectionăisăregisteredă(fromă10-7ătoă10-12ămillibarn).ăFromă
theseă difficultiesă ită resultsă oură bigă effortă toă obtaină higheră intensityă (tenthsă ofă µA)ă
M.ăIvaşcuăet al.
ă
1010ă
5ă
protonă andă alphaă particleă beamsă ină orderă toă maintaină theă irradiationă withină
reasonableălimitsă(tenthsăofăhoursăofătargetăirradiation).ă
10
1
1
0.1
0.1
0.01
0.01
1E-3
1E-3
Cross section (mb)
Cross section (mb)
10
414 keV
550 keV
571 keV
629 keV
1E-4
1E-5
1E-6
1E-7
1E-8
1E-9
1E-4
1E-5
1E-7
1E-8
1E-9
Sm(p,γ) Eu (54.5(5) d)
147
1E-10
1E-11
333 keV
406 keV
831 keV
1165 keV
1E-6
148
1E-10
Sm(p,γ) Eu (12.8(1) h)
149
1E-11
150
1E-12
5
10
5
15
ăăă
Ep (MeV)
Fig.ă3ă–ăExperimentală(p,γ)ăcrossăsectionsăonă
10
15
ă
Ep (MeV)
147,149
SmăcomparedăwithăNONSMOKERăresults.ă
Additională pointsă foră (p,n)ă crossă sectionsă areă representedă ină Figureă 4,ă ină
comparisonăwithăNONSMOKERăcalculations.ă
InăFigureă5ăweăpresentătheăvariationăofătheăastrophysicalăfactorăS.ăAsăităcanăbeă
seen,ă thisă variationă isă smallă ină comparisonă withă thată ofă theă 147Sm(p,γ)148Euă andă
149
Sm(p,γ)150Euăcrossăsectionsăforăaăsimilarăenergyăinterval.ăOtherwise,ăweăhaveătoă
emphasizeă thată discrepanciesă ofă theă theoreticală valuesă ină comparisonă withă theă
experimentală onesă areă muchă biggeră ină thisă massă region.ă Therefore,ă moreă preciseă
andădetailedămeasurementsăareărequiredăinătheăfutureăforătheseătwoăSamariumăisotopes.ă
Theseăfirstăresultsăpresentedăinăpresentăwork,ăencouragedăusătoăprepareăfutureă
experimentsă concerningă theă sameă targets,ă whichă willă beă performedă ată loweră
incidentăenergiesăthatăareămoreăinterestingăfromătheăastrophysicalăpointăofăview.ă
10
1
-1
10
Cross Section (b)
0.1
Cross section (b)
0
0.01
197 keV
601 keV
798 keV
856 keV
933 keV
1E-3
1E-4
178 keV
277 keV
327 keV
535 keV
558 keV
-2
10
-3
10
-4
10
-5
10
1E-5
147
1E-6
0
149
5
10
Eα (MeV)
149
Sm(p,n) Eu (93.1(4) d)
148
Sm(p,n) Eu (24.1(2) d)
-6
10
15
ăă
0
5
10
Ep (MeV)
15
ă
Fig.ă4ă–ăExperimentală(p,n)ăcrossăsectionsăonă147,149SmăcomparedăwithăNONSMOKERăresults.ă
AstrophysicalăSăfactorăforăprotonăcaptureăonă147Smăandă149Smă
10
14
10
13
10
12
10
11
10
10
10
9
10
8
10
7
414 keV
550 keV
571 keV
629 keV
S factor (keV * barn)
S factor (keV * barn)
6ă
Sm(p,γ) Eu (54.5(5) d)
147
0
148
5
10
Ep (MeV)
15
10
14
10
13
10
12
10
11
10
10
10
9
10
8
10
7
10
6
1011ă
333 keV
406 keV
831 keV
1165 keV
Sm(p,γ) Eu (12.8(1) h)
149
150
0
ăă
5
10
Ep (MeV)
Fig.ă5ă–ăExperimentalăastrophysicalăSăfactorsăforăstudiedăreactionsăcomparedăă
withăNONSMOKERăevaluations.ă
15
ă
4. DISCUSSION AND CONCLUSIONS
Ină theseă measurementsă theă activationă techniqueă wasă shownă toă representă ană
efficientătoolăforătheădeterminationăofătheă(p,γ)ăcrossăsectionsăforă p-processăstudies.ă
Thoughă restrictedă toă measurementsă onăstableă targetă nuclei,ă thisămethodă offersă theă
possibilityă toă establishă ană extendedă setă ofă dataă foră testingă andă normalizingă theă
parameteră systematică foră Hauser-Feshbachă interpolationă toă theă actuală networkă ofă
theă p-process.ăDespiteătheirăsimplicity,ămeasurementsăwithătheăactivationătechniqueă
requireăgreatăcareăinătechnicalădetailsăifăthisăfullăpotentială isătoăbeăexploited.ăMostă
importantăinăthisărespectăareătheăpreparationăandăcharacterizationăofătheătargetsăandă
alsoătheă monitoringăofătheăprotonăbeamăandăofătheătargetăperformanceăthroughoută
theă irradiationă period.ă Theă subsequentă γă countingă requiresă carefullyă calibratedă
detectors,ă includingă countingă rateă correctionsă dueă toă cascadeă effectă and/oră
coincidentă observationsă ofă theă relatedă γ-rays.ă Theă crossă sectionsă areă determinedă
withăuncertaintiesăofăfewăpercentăifătheseăprecautionsăareăconsidered.ă
ă
Acknowledgements. Theă resultsă reportedă ină thisă paperă wereă obtainedă ină theă
frameăofătheăPNII-IDEIăProgram,ăthroughătheăexploratoryăresearchăprojectăID-362,ă
theă contractă 48/28.09.2007,ă financedă byă theă Executiveă Unită foră Financingă theă
HigherăEducationăandăUniversityăScientificăResearch.ă
REFERENCESă
1.ăG.ă Wallerstein,ă I.ă Iben,ă P.ă Parker,ă A.M.ă Boesgaard,ă G.M.ă Hale,ă A.E.ă Champagne,ă C.A.ă Barnes,ăă
F.ă Käppeler,ă V.V.ă Smith,ă R.Dă Hoffman,ă F.X.ă Timmes,ă C.ă Sneden,ă R.N.ă Boyd,ă B.S.ă Meyer,ă
D.L.ăLambert,ăG.ăMünzenberg,ăRev.ăMod.ăPhys.ă69,ă995–1084ă(1997).ă
2.ăM.ăArnould,ăS.ăGoriely,ăPhys.ăRep.ă384,ă1–84ă(2003)ă
ă
1012ă
M.ăIvaşcuăet al.
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3.ăM.ăRayet,ăM.ăArnould,ăN.ăPrantzos,ăinăOrigin and Distribution of the Elements,ăed.ăG.J.ăMathewsă
(WorldăScientific,ăSingapore),ăp.ă625,ă1988.ă
4.ăT.ăRauscher,ăA.ăHeger,ăR.D.ăHoffman,ăS.E.ăWoosley,ăAstrophys.ăJ.ă576,ă323ă(2002).ă
5.ăI.ăC ta-Danil,ăN.V.ăZamfir,ăD.ăBucurescu,ăG.ăC ta-Danil,ăD.ăGhi ,ăT.ăGlodariu,ăM.ăIvaşcu,ăC.ăMihai,ă
T.ăSava,ăL.ăStroe,ăG.ăSuliman,ăRom.ăRep.ăPhys.ă58,ă397–408ă(2006).ă
6.ăT.ăRauscher,ăF-KăThielemann,ăAt.ăDataăNucl.ăDataăTables,ă75,ă1–351ă(2000);ăAt.ăDataăNucl.ăDataă
Tables,ă79,ă47–64ă(2001).ă
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