Measurements 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. References 1. V.G.J.Stoks etal.,Phys.Rev.C48792(1993). 2. V.G.J.Stoks etal.,Phys.Rev.C492950(1994). 3. R.B.Wiringa etal.,Phys.Rev.C5138(1995). 4. R.Machleidt,Phys.Rev.C63024001(2001). 5. W.Glo¨ckleetal.,Phys.Rep.274107(1996). 6. K.Ermischetal.,Phys.Rev.Lett.865862(2001).