Table Of ContentMeasurements of scattering observables for the pd break-up reaction
M.Eslami-Kalantari1,2,a,H.R.Amir-Ahmadi1,A.Biegun1,I.Gasˇparic3,L.Joulaeizadeh1,N.Kalantar-Nayestanaki1,
St.Kistryn4,A.Kozela5,H.Mardanpour1,J.G.Messchendorp1,H.Moeini1,A.Ramazani-Moghaddam-Arani1,6,S.V.
Shende1,E.Stephan7,andR.Sworst4
1 KVI,UniversityofGroningen,Groningen,TheNetherlands
2 FacultyofPhysics,YazdUniversity,Yazd,Iran
0 3 RudjerBosˇkovic´Institute,Zagreb,Coratia
1 4 InstituteofPhysics,JagiellonianUniversity,Kracow,Poland
0 5 HenrykNiewodniczan´ski,InstituteofNuclearPhysics,Kracow,Poland
2 6 DepartmentofPhysics,FacultyofScience,UniversityofKashan,Kashan,Iran
n 7 InstituteofPhysics,UniversityofSilesia,Katowice,Poland
a
J
0 Abstract. High-precision measurements of the scattering observables such as cross sections and analyzing
1
powersfortheproton-deuteronelasticandbreak-upreactionshavebeenperformedatKVIinthelasttwodecades
andelsewheretoinvestigatevariousaspectsofthethree-nucleonforce(3NF)effectssimultaneously.In2006an
]
x experimentwasperformedtostudytheseeffectsinp+dbreak-upreactionat135MeVwiththedetectionsystem,
e BigInstrumentforNuclearpolarizationAnalysis,BINA.BINAcoversalmosttheentirekinematicalphasespace
- ofthebreak-upreaction.Theresultsareinterpretedwiththehelpofstate-of-the-artFaddeevcalculationsandare
l
c partlypresentedinthiscontribution.
u
n
[
Inthelastfewdecades,severalnucleon-nucleonpoten- gions,theeffectcanbesmall,whichmakethem,therefore,
1 tials(NNPs)havebeenstudiedextensivelytodescribethe suitableforbenchmarkstudies.Inelasticandbreak-upre-
v properties of bound nuclear systems by comparing high- actions, precision data for a large energy interval for the
2 precisiontwo-nucleonscatteringdatawithmodernpoten- differentialcross section and analyzingpower have come
1 tialsbasedontheexchangeofbosons[1,2,3,4].Themod- fromrecentexperimentalstudiesatKVI[6,7,8,10,9,12,13].
5 ernNNPsreproducetheworlddatabasewithareducedχ2 Break-upcrosssectionsandanalyzingpowersforabeam
1
close to one and have, therefore, been accepted as high- energyofEd =130MeVhavebeenpublishedinRefs.[17,18,19,20,
. lab
1 quality potentials. Deficiencies of theoretical predictions For a furtherstudyof 3NFeffects, we have measuredthe
0 based on pair-wise nucleon-nucleonpotentials have been break-upcrosssectionsandvectoranalyzingpowersfora
0 observed in three-nucleonscattering observables. For ex- protonbeamenergyofEp =135MeV.Inthisexperiment,
1 lab
ample, exact solutionsof the Lippmann-Schwingerequa- cross sections and vector analyzing powers in p + d →
:
v tions (Faddeev calculations) [5] solely based on modern p+ p+nreactionweremeasuredusingapolarizedbeam
i NNinteractionsfailtodescribehigh-precisiondifferential onaliquid-deuteriumtarget[22].Theresultsarecompared
X
cross sections of proton-deuteronelastic scattering at in- withpredictionsderivedfromstate-of-the-artFaddeevcal-
r
termediateenergiesobtainedat manylaboratoriesinclud- culationsandarepartlyreportedhere.
a
ing KVI [6,7,8,9], Research Center for Nuclear Physics
Theproton-deuteronbreak-upexperimentdescribedin
(RIKEN) [14,15] and RCNP [16]. Calculations based on
thispaperwasperformedusingtherecently-developedde-
NNPsincluding2π-exchangetypethree-nucleonforces(3NFs)
tectionsystem,BINA.Theenergycorrelationbetweenthe
removethisdiscrepancyforalargepartandleadtoagood
two outgoingprotons, E vs. E , as shown in Fig. 1, was
descriptionofthemeasuredcrosssectionsforenergiesbe- 1 2
studiedforalargenumberofkinematicconfigurations.To
low 100 MeV/nucleon. However, the description of spin
obtain the cross section and the analyzing power, several
observablessuchasvectorandinparticularthetensoran-
slices along the S-curve were made. The angular ranges
alyzingpowersisnotsatisfactoryandaninclusionof3NFs
fortheintegrationofeventswaschosentobe∆θ =∆θ =4◦
isnotsufficienttoremedytheobserveddiscrepancies[11,6,7,8]. 1 2
and∆φ =10◦,whichwerewideenoughtohavesufficient
12
Thebreak-upreactionhasarichphasespacewhichal-
statistics,whilevariationsofthecrosssectionwithinthese
lowsasystematicstudyofthe3NF.Predictionsshowthat
rangesare small. In this way, the experimentalcross sec-
large 3NF effects can be expected at specific kinematical
tionscanbedirectlycomparedwiththetheoreticalpredic-
regionsinthebreak-upreaction.Forotherphasespacere-
tionscalculatedforthecentralvaluesofaspecificconfig-
uration.TheprojectionoftheindicatedregioninFig.1on
a e-mail:[email protected] the line perpendicular to the S-curve is shown in Fig. 2.
EPJWebofConferences
θ=25° θ =25° φ =180° tribution is fitted using a third-order polynomial together
140 1 2 12 with the main peak represented by a Gaussian function.
The number of eventsunderneaththe Gaussian peak will
120 be referred to as the number of break-up events and will
100 D−axis be used to obtain the cross section and analyzing power
after making efficiency corrections such as the one from
V] 80 hadronicinteraction.
e
M Figure3showsthecrosssection, d5σ [µb/(sr2MeV)],
[E160 asa functionofS [MeV]forthesdyΩm1dmΩ2edtSricandcoplanar
configuration with (θ ,θ ,φ ) = (25◦,25◦,180◦). In this
40 1 2 12
20
00 20 40 60 80 100 120 140
E [MeV]
2
Fig. 1: The coincidence spectrum between the ener-
o o o
gies E versus E of the two protons registered at =25 =25 =180
1 2 1 2 12
(θ ,θ ,φ )=(25◦±2◦,25◦±2◦,180◦±5◦). The solid line shows 4
1 2 12
the kinematical curve, the so-called S-curve calculated for the )]
V
centralvaluesoftheexperimentalangularranges.
e
M 3
2
r
s
(
b/
Thisspectrumcontainsbreak-upeventsaroundchannel0
[
S
and backgroundfrom accidental eventsand contributions d 2
2
resulting from the hadronic interaction of particles in the
1
scintillatormaterialofthedetector.Thisprojectionaxisis
d
denotedtheD-axis.ThecrossingpointoftheS-curvewith /
theD-axisdefinesthezeropoint. 5d NN
NN+TM’
CDB+
ThisExp.
4400 6600 8800 110000 112200 114400
S[MeV]
400
350
300
Fig. 3: The cross section is plotted as a function of S [MeV]
s 250 forthekinematicalconfiguration,(θ ,θ ,φ )=(25◦,25◦,180◦).
nt 1 2 12
u LinesrepresentFaddeevcalculationsfromtheHannover-Lisbon,
o 200
C andBochum-Krakowgroups.Thedottedlinerepresentsthecross
150 sectionusingtheCD-Bonntwo-nucleonpotential,thesolidline
shows the CD-Bonn+TM’ calculation. The dashed line repre-
100
sentstheresultsofacalculationbytheHannover-Lisbongroup,
50 whichisbasedontheextendedCD-Bonnpotential,includinga
0-30 -20 -10 0 10 20 30 virtual∆excitationinacoupled-channelapproach.
D [MeV]
Fig. 2: The projection of the slice chosen in Fig. 1 along the
figure,thelinesrepresentthepredictionsbytheBochum-
D-axis. The solid line is the sum of a third-order polynomial
KrakowandHannover-Lisbontheorygroups[23,24,25,26,27].
backgroundfunctionandaGaussiandistributionrepresentingthe
ThedottedlineistheresultofcalculationsusingtheCD-
peak.
Bonntwo-nucleonpotentialandthesolidlinepresentsthe
calculation including the three-body force, TM’, as well.
Thedashedlinerepresentstheresultofacalculationbythe
Theaccidentalbackgroundislocatedatchannelshigher Hannover-Lisbon group, which is based on the extended
thanthemainpeakinFig.2andisalreadysubtractedex- CD-Bonn potential including a virtual ∆ excitation in a
ploitingtherelativetime-of-flightinformationbetweenthe coupled-channelapproach.
two protons. The contributions from hadronic interaction Inthefollowing,wedescribethedeterminationofthe
are located at lower channels on the D-axis which corre- vector analyzing power, A , by using a polarized proton
y
spondtoeventsbelowtheS-curveinFig.1.Theseevents beamandbymeasuringtheinducedasymmetryinthecross
aremostly“true”break-upevents.Atthisstage,thiscon- section. The relation between dσs= dσ↑,↓ and the unpo-
19thInternationalIUPAPConferenceonFew-BodyProblemsinPhysics
larziedcrosssection,dσ0,is
dσ↑,↓ =dσ0(1+p↑,↓·A ·cosφ), (1)
y
foranincomingprotonbeamwithspinup(↑)orspindown =25o =25o =180o
(↓) and a vectoranalyzingpower, A . Hereφ is the angle 0.3 1 2 12
y
between quantization axis for the beam polarization and
the normalto the scatteringplanein the laboratoryframe 0.2
of reference. From the two cross sections, dσ↑ and dσ↓,
withpolarizations, p↑ and p↓,theanalyzingpowercanbe 0.1
obtainedfromtheasymmetry,
Ay 0.0
dσ↑−dσ↓
Aycosφ= dσ↓p↑−dσ↑p↓. (2) -0.1
Thereactionasymmetrycanbemeasuredbyexploiting -0.2
thedistributionofeventsobtainedwithbeampolarizations NN
up and down together with the values of the beam polar- -0.3 NN+TM’
CDB+
izationinthesetwomodes.Thisgivesaperiodicfunction
ThisExp.
in φ with an amplitude that corresponds to A . Figure 4
y 4400 6600 8800 110000 112200 114400
showstheasymmetryasafunctionofφforaparticularbin S[MeV]
in S. By exploiting the asymmetry distribution for each
Fig.5:Analyzingpowersofthebreakupreactionforthecoplanar
0.6 kinematics,(θ1,θ2,φ12)=(25◦,25◦,180◦),asafunctionofS.For
theexplanationofthecurves,seeFig.3.
0.4
↓)
p
↑
σ
↑- 0.2 (3.85±0.2mm→∼5%),thecorrectionforthehadronicre-
p
↓σ actionefficiencyforbothprotonsobtainedviaaGEANT-3
↓)/( 0 simulation (92±3%→ ∼6% for two protons), the correc-
σ
↑- tionfortheefficiencyoftheMWPC(92±1%→2%fortwo
σ(-0.2 protons),andthecorrectionforthegeometricalinefficien-
cies obtained via GEANT-3 simulations which is at most
-0.4 12% for small azimuthal opening angles, φ = 20◦, and
12
0 50 100 150 200 250 300 350 atmost2%forthelargerazimuthalopeningangles.Alto-
φ [deg] gether, by adding the systematic uncertainties in quadra-
ture, the maximum systematic uncertainty for cross sec-
Fig. 4: The asymmetry, A cosφ, in the break-up reaction as a
y tions at small azimuthal opening angles is less than 14%
functionoftheazimuthalscatteringangleofoneoftheprotons,
and atlargerazimuthalopeninganglesless than9%. The
φ.
systematic error for the analyzing power stems primarily
fromtheuncertaintyinthemeasurementofthebeampolar-
S-bin,thevector-analyzingpower, A , isobtainedforev- izationviatheproton-deuteronelastic-scatteringreaction.
y
erykinematicalconfiguration,(θ ,θ ,φ ).Figure5repre- Forinstance,thebeampolarizationforthedown-modehas
1 2 12
sentstheanalyzing-powerfortheconfiguration(θ ,θ ,φ ) beenmeasuredatavalueof∼0.70±0.04,whichgivesrise
1 2 12
=(25◦,25◦,180◦).Thevariouslinesrepresentcalculations toa6%systematicuncertaintyintheanalyzingpower.
fromtheHannover-LisbonandBochum-Krakowtheorygr- ThepredictionsoftheFaddeevcalculationsusingdif-
oupsasexplainedbefore. ferentNNand3NFmodelsareaddedtoeverypanelwith
We determinedthe crosssectionsand analyzingpow- differentlinecolorsandstyles.Theblue(long-dashed),red
ersfor configurationsin which 14◦ < θ < 30◦, andthe (dash-dotted),green(dashed),andblack(solid)linescor-
1,2
azimuthalopening angle, φ , varied from 20◦ to 180◦ in respond to calculations based on CDB (NN), CDB+TM’
12
stepsof20◦.Fig.6showstheresultsofthefixedcombina- (3NF)fromtheBochum-Krakowgroup[23,24,25],CDB+∆
tion (θ ,θ ) = (25◦,25◦) with differentazimuthalopening (3NF),andCDB+∆+CoulombcalculationsfromtheHann-
1 2
angles, φ , as a functionof S. The top panels depict the over-Lisbon group [26,27], respectively. Here, all theory
12
cross sections and the bottom panels show the analyzing curveshavebeencalculatedinafullynon-relativisticframe-
powers. work with non-relativistic observablesand, therefore, the
Thepresentederrorbarsinallthefiguresarestatistical. length of S for these calculations is slightly shorter than
Themainsourceofsystematicuncertaintiesforthebreak- that in the data. The typical difference in length of S for
upcrosssectionsare:theuncertaintyinthetargetthickness the relativistic and non-relativistickinematicsis less than
EPJWebofConferences
=20 =40 =60
12 12 12
5
2
]
)
V =80 =100 =120
12 12 12
e
M
10
2
r
s
(
/
b
[
S
d
2
5
1
=140 =160 =180
12 12 12
d
/
2
5
d
10
5
30 60 90 120 150 60 90 120 150 60 90 120 150
00..44
00..22
00..00
--00..22
=20 =40 =60
12 12 12
00..44
00..22
y
A 00..00
--00..22
=80 =100 =120
12 12 12
--00..44
00..44
00..22
00..00
--00..22
--00..44 =140 =160 =180
12 12 12
3300 6600 9900 112200 115500 60 90 120 150 60 90 120 150
S[MeV]
Fig.6:Thecrosssectionsandtheanalyzingpowersat(θ ,θ )=(25◦,25◦)asafunctionofS fordifferentazimuthalopeningangles.The
1 2
errorbarsreflectonlystatisticaluncertainties.Theblue(long-dashed), red(dash-dotted),green(dashed),andblack(solid)linesshow
predictionsofFaddeevcalculationsusingCDB(NN),CDB+TM’(3NF),fromtheBochum-Krakow group[23,24,25],CDB+∆(3NF)
andCDB+∆+CoulombcalculationsfromtheHannover-Lisbongroup[26,27],respectively.
19thInternationalIUPAPConferenceonFew-BodyProblemsinPhysics
1-2MeV,dependingontheazimuthalopeningangle,φ . 7. K.Ermischetal.,Phys.Rev.C68051001(R)(2003).
12
Thisdifferenceisless than the experimentalresolutionin 8. K.Ermischetal.,Phys.Rev.C71064004(2005).
S of4MeV(FWHM),andwe,therefore,didnottransform 9. H. Amir-Ahmadi et al., Phys. Rev. C 75 041001(R)
thenon-relativisticS-curvestotherelativisticones. (2007).
For the configurationsat large azimuthal opening an- 10. H. Mardanpour, Ph.D. thesis, KVI, University of
gle,φ ≥40◦,andtakingthesystematicuncertaintiesinto Groningen,2008.
12
account, a reasonable agreementis observed between the 11. R.Bieberetal.,Phys.Rev.Lett.84606(2000).
cross-section data and the corresponding theoretical pre- 12. A. Ramazani-Moghaddam-Araniet al., Phys. Rev. C
dictions. For the configuration with a small relative az- 78014006(2008).
imuthalangle,thepicturechanges.Here,themeasuredcro- 13. M.Eslami-Kalantari,Ph.D.thesis,KVI,Universityof
ss sections show a large discrepancy with a calculation Groningen,2009.
whichincludestheTM’3NP.Inthisregion,theCDB+∆+C- 14. H.Sakaietal.,Phys.Rev.Lett.845288(2000).
oulomb calculation has a smaller deficiency when com- 15. K.Sekigushietal.,Phys.Rev.C65034003(2002).
paredwiththeexperimentaldata,butthedeficiencyisstill 16. K.Sekigushietal.,Phys.Rev.Lett.95162301(2005).
largefor smallvalueof polarangle, φ = 20◦, as shown 17. A.Biegunetal.,Acta.Phys.Pol.B37213(2003).
12
inFig.6. 18. St.Kistrynetal.,Phys.Rev.C68054004(2003).
Fortheanalyzingpowers,themajordiscrepanciesbe- 19. St.Kistrynetal.,Phys.Rev.C72044006(2005).
tweenthedataandthetheoreticalcalculationsariseatsmall 20. St.Kistrynetal.,Phys.Lett.B23641(2006).
azimuthal opening angles. In this range, the predictions 21. E.Stephanetal.,Phys.Rev.C76057001(2005).
basedsolely ona NN potentialare closestto the data,al- 22. N.Kalantar-Nayestanakietal.,Nucl.Instr.andMeth.
though,thedisagreementisstillsignificant.Theinclusion inPhys.Res.A417215(1998).
of3NPsincreasesthegapbetweendataandpredictionsas 23. H.Witałaetal.,Few-BodySystems1567(1993).
can be seen from bottom panels of Fig. 6. The contribu- 24. H.Witałaetal.,Phys.Rev.Lett.811183(1998).
tionoftheTM’3NPappearstobelargerthantheimplicit 25. H.Witałaetal.,Phys.Rev.C63024007(2001).
inclusionofthe∆resonancebytheHannover-Lisbonthe- 26. A.Deltuvaetal.,Phys.Rev.C71054005(2005).
orygroup.Itis interestingto note thata similar,buteven 27. A.Deltuvaetal.,Phys.Rev.C72054004(2005).
larger,discrepancyhasbeenobservedinabreak-upstudy
atanincidentbeamenergyof190MeV[10].
This paper discusses some of the preliminary results
ofaproton-deuteronbreak-upexperimentcarriedoutwith
anincidentprotonbeamof135MeV.Thedataweretaken
usinganearly4πdetectionsystem,BINA,andexploiting
a polarized beam of protons. With this, precision differ-
entialcrosssectionsandanalyzingpowersweremeasured
and compared to Faddeev calculations based on modern
two- and three-nucleon potentials. The large coverage of
the detection system provides an ideal tool to systemati-
callyexploretherichphasespaceofthebreak-upreaction.
Wehaveidentifiedvariousconfigurationsatwhichsignifi-
cantdiscrepanciesareobservedbetweenourdataandpre-
dictionsbyFaddeevcalculationsbased uponstate-of-the-
art potentials.Intriguingdeficienciesare observedfor the
analyzing power for configurations at which the relative
energybetweenthetwooutgoingprotonsbecomessmall.
ThediscrepanciescannotbeexplainedbytheCoulombin-
teractionandhigher-orderrelativity,sincetheseeffectsare
accounted for in the present state-of-the-art calculations.
Therefore,thedataprovideanidealbasistodevelopabet-
ter understanding of three-nucleon force effects in few-
nucleoninteractions.
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