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Vector and Tensor Analyzing Powers of the 1H(~d,γ)3He–capture reaction T. Klechneva,1,2 C. Carasco,1 I. Goussev,2 M. Hauger,1 J. Jourdan,1,∗ B. Krusche,1 H. Mu¨hry,1 Ch. Normand,1 D. Rohe,1 D. Seliverstov,2 I. Sick,1 G. Testa,1 G. Warren,1 H. Wöhrle,1 and M. Zeier1 1Dept. fu¨r Physik und Astronomie, Universität Basel, Switzerland 2St.Petersburg Nuclear Physics Institute, Gatchina, Russia (Dated: February 8, 2008) PrecisemeasurementsofthedeuteronvectoranalyzingpowerAd andthetensoranalyzingpower y Ayy of the 1H(~d,γ)3He–capture reaction havebeen performed at deuteron energies of 29 MeV and 45MeV.Thedatahavebeencompared totheoretical state–of–the–art calculations available today. Dueto the large sensitivity of polarization observables and theprecision of the data light could be shed on small effects present in thedynamicsof thereaction. 6 0 PACSnumbers: 21.45.+v,24.70.+s,25.20.Lj,25.40.Lw,25.45.-z 0 2 I. INTRODUCTION lows for a study of the small amplitudes. Based on the n following arguments one can expect that measurements a of polarization observables in capture reactions provide J Experimental studies of the three–body system are insight into the different roles played by nucleonic and 6 particularlyinterestingasithasbecomepossibletosolve mesonic degrees of freedom. the Schrödinger equation of the three–body system for 2 boththeground–andthecontinuumstates. Suchthree– In the energy range of 10-50 MeV the 1H(~d,γ)3He– v body calculations, based on different techniques, are capture process is dominated by the electric dipole tran- 8 available from several groups [1, 2, 3, 4, 5, 6]. Data for sition(E1). AlthoughMEC’scangivelargecontributions 0 d–p elastic scattering, two–, and three–body breakup, to the E1-transition,they can be taken into account im- 0 9 and radiative capture reactions (or its inverse reaction, plicitly when performing calculations with operators de- 0 photo-disintegration)nowallowforaprecisequantitative rived using Siegert’s theorem. Thus, due to the angular 5 comparison with theory. dependence of the E1-E1 contribution (sin2(θc.m.)), po- 0 larization observables at medium range reaction angles Combinedwiththesecalculationstheradiativecapture / (θ ) are little affected by the explicit contribution of x reaction provides an especially attractive framework as c.m. e the electromagneticinteractionis a wellunderstoodpro- MEC’s. On the other hand MEC’shave to be calculated - explicitly in the magnetic transitions,particularlyM1 in cess. Capture reactions in few–body systems have been l c studied for quite some time and provided, even at very which they may give contributions up to 50% [12]. Con- u tributionsofM1andthusMEC’sareparticularlylargeat low energy [7], valuable information on the dynamics in n small and large reaction angles. At these angles the E1- these systems. In the two–body system the cross section : v data at low energy indicated the importance of mesonic M1interferenceterm,inwhichthesmallM1amplitudeis i enhanced via E1 becomes dominant. Thus, angular dis- X degrees of freedom [8] and the forward angle cross sec- tributions of polarization observables with sensitivities tion of the two–body photodisintegration could only be r a understood when accounting for relativistic effects [9]. toboththeelectric–andthemagnetictransitionscanbe expectedtoofferexcellentwindowsonsmallcomponents The important role of of meson exchange currents oftheinteractionandprovideauniqueexperimentaltest (MEC)canbeobservedinmanyelectromagneticobserv- of MEC’s. ables. The electromagnetic form factors of the A=3 sys- Measurements of polarization observables for the tem as measuredin elastic electronscattering[10] or the 1H(~d,γ)3He–capture reaction with adequate precision electrodisintegrationcrosssectionofthetwobodysystem are rather scarce. Difficulties associated with polarized [11] can only be understood when MEC’s are taken into beam and/or target production, and with the measure- account. In these observables MEC’s are intimately re- mentofspinobservablesoftenledtoexperimentaluncer- latedtothenucleonicS–Dtransitionsastheygiveeffects tainties which do not permit a significant check of the- of similar size, but opposite sign. Thus, the quantitative oretical predictions. Although the techniques are well studyofMEC–effectsrequiresapreciseknowledgeofthe under control today, one can not expect a significant in- nucleonic S–D transition. The effect of such transitions crease of the data base as the required experimental fa- canbeenhancedinmeasurementsofpolarizationobserv- cilities are no longer at hand [13]. A rather complete ablesasthe S–Samplitude, whichusuallydominatesun- account of the existing data is given in the publication polarized cross sections, is strongly suppressed and al- by Anklin et al. [14] which also discusses the results of our previous work in this area. Here we report on new measurements of vector– and ∗Electronicaddress: [email protected] tensor analyzingpowers of the d~−p capture reactionin- 2 ducedwithapolarizeddeuteronbeam. Inthepresentex- to minimize systematic errors. perimentwe haveextended the measurementsby Anklin et al. in three ways. One extension concerns more ex- Pol. state SF2 SF1 WF pî pî treme anglesat adeuteronbeam energyof45MeV for a z zz a off off off 0 0 larger sensitivity to the magnetic transitions. A second b on off off +1/3 +1 extensionconcernsthemeasurementofacompleteangu- c off on off +1/3 −1 lardistributionofthepolarizationobservablesatabeam d on off on −1/3 −1 energy of 29 MeV. This is particularlyimportant for the e off on on −1/3 +1 tensoranalyzingpowerA atintermediateanglesasthe yy beam energy dependence shows a maximum at 29 MeV while at 45 MeV it is close to zero (see figure 1). As TABLEI: Polarized beam source modesand nominal polar- will be discussed in the last section the tensor analyzing ization values. power at these two energies has rather different sensitivities to the underlying physics. As a third extension we Following the source, the beam was deflected into the also measured the data of the deuteron vector analyzing injectorcyclotron,acceleratedtoenergiesof29MeVand power Ad at the same kinematical points. 45 MeV, respectively, and guided to the experimental y area. A schematic view of the experimental setup in the area is shown in Figure 2. The beam passed first a scattering chamber, where deuterons scattered elastically from a thin carbon foil. The distribution of their time of flight relative to the radio-frequency(RF)signalfromthecyclotronwasmea- sured using a fast plastic scintillation detector placed at 30o below the beam axis. The cyclotron was tuned for a minimal beam burst width of typically 1.5 ns FWHM. d Z d Q He−pol Q TC D d FC C(d,d) D FIG. 2: Schematic overview of the beam line in the experimental hall NE-C. Here C(d,d) - carbon scattering chamber, Q-quadrupoledoublet,He-pol-4He-polarimeter,TC-target FIG. 1: Beam energy dependence of Ayy at θc.m. = 90deg. chamber,D-dipolemagnettoseparate3Heandunscattered Thedatapointsarefrom [12,14,15,16,17,18]. Thedashed deuterons, FC - Faraday cup. line represents theFaddeev calculation by Golak et al. [2] In a second target chamber (He-pol), a polarimeter was employed for measurements of the polarization of the beamatregularintervals. Detailsofthe polarization II. EXPERIMENT determination will be explained in section IIA. Finally the beam was refocused onto a liquid hydrogen target The experiment was performed at the Philips injector mounted in the third scattering chamber (TC) for the cyclotronof the PaulScherrerInstitute (PSI)in Villigen measurement of the capture reaction. Downstream of (Switzerland). It used a polarized deuteron beam which the main target station a C–shaped dipole magnet (D) was prepared in the PSI atomic beam ion source [19]. separated the beam from recoil particles of the capture The source was equipped with a 30K cold atomic beam reaction. A Faraday cup (FC) stopped the beam and dissociator, two sextupole fields to focus (defocus) the measured the current. atomic electrons from 2H with spin up (down), a set of twostrong(SF1,SF2)andoneweakfieldradiofrequency (RF)–transitionunitstoinducethenuclearpolarization, A. Polarimetry andanelectron–cyclotronresonance(ECR)ionizer. The RF–unitsselectedtransitionsbetweendifferentZeemann levels of the 2H-atom hyperfine structure in an external Elastic 4He(d~,α)-scattering was used to measure the magnetic field. Depending on the combination of active absolutedeuteronbeampolarization. Intheenergyrange RF–units the nominal nuclear vector and tensor polar- ofthisexperimentatacenterofmassangle(ϑ )of150 c.m. ization as listed in table I could be prepared. In the deg the analyzing powers are high and precisely known present experiment all five modes have been used, the [20]. In table II the specific values used here for the source being cycled through them with a rate of 0.3 Hz polarization determination of the beam are listed. 3 FIG. 3: Energy spectra at ϑ = 15o, E =29 MeV (left) and E =45 MeV (right). The integration limits are shown as αlab d d vertical lines. Beam Energy Ay Ayy section. Coordinate system and symbol definitions fol- 29 MeV 0.846±0.020 0.910±0.016 low the Madison convention [21]. Based on the general 45 MeV 0.497±0.011 0.921±0.013 expression the following equations can then be written for each polarization state i: TfoArBelLaEstiIcI:d~V−ecαtosrca(tAteyr)inagndatteanscoernt(eAryoyf)manasaslyazningglepoofw1e5r0s pîzz =(K+iNN+i 0−N+0 + K−i NN−i 0−N−0)A1 deg. + − yy pî =(K+i N+i −N+0 − K−i N−i −N−0) 1 (2) z N0 N0 3A A 4He gas cell with 5 µm thin Havar windows, oper- + − y ating at a pressure of 50 kPa,served as the target of the polarimeter. At laboratory angles of ±15o correspond- with N+i (N−i) the number of events detected by the left ing to ϑc.m. = ±150deg recoil α–particles were detected (right) detector and K+i (K−i ) correction factors which account for dead time (DT) and Faraday cup (FC) dif- with two symmetrically arranged “passivated implanted ferences for the different states i. Cross sections can be planar silicon” (PIPS) detectors. A double slit system replacedbyaccumulatedcountsbecausesolidanglesand withTa-collimatorsatdistancesof12cmand45cmfrom efficiencies cancel. thecenterofthescatteringchambershieldedbackground The polarization of the deuteron beam was measured particles from beam–target window reactions. The colli- matorslimitedtheangularacceptanceto±0.5deg. PIPS every 8 hours. As already observed in the previous experiment by Anklin et al. [14] the polarizations of the detectors with thicknesses of 700 µm (500 µm) at beam source have been very constant over a run period of 14 energiesof45MeV(29MeV) allowedforthe discrimina- days. Typical mean polarization values were pî = 0.25 tion between the stopped recoilα–particles andthe high z forthe vectorandpî =0.65forthe tensorpolarizations energy elastically scattered deuterons which deposited zz for states i=b−d with accuracies of 2–3%. lessenergyas comparedto the stoppedα–particles. Fig- ure3displaystwosampleenergyspectrameasuredatthe two deuteron energies. B. Setup for the 1H(~d,γ)3He analyzing power Thepolarizationhasbeendeterminedwiththeexpres- measurements sion for the cross section of a reaction with a mixed– polarization deuteron beam: Figure4givesadetailedviewofthesetupforthemea- dσ i dσ 3 3 surements of the 1H(~d,γ)3He–capture reaction. The po- = 1+ pîA + pî A (1) (cid:18)dΩ(cid:19) (cid:18)dΩ(cid:19) (cid:18) 2 z y 2 zz yy(cid:19) larizeddeuteronbeamwasincidentonaliquid hydrogen a target (LH-T) with a thickness of 14 mg/cm2 enclosed with i = b,c,d,e. Vector (tensor) polarizations of the by 2.5 µm Havar windows. The target cell was cooled beam for source state i = b,c,d,e are denoted with pî to about 16 K with a closed–cycle helium–refrigerator z (pî ) (see table I) and (dσ/dΩ) is the unpolarized cross and operated at a pressure of 0.25 bar. It was mounted zz a 4 in a specially designed scattering chamber with 3 mm Bayer Silicons GmbH). A light emitting diode, operated Al–walls and a conical entrance beam tube to allow for at a frequency of 10 Hz, allowed to monitor the gain measurements at very large scattering angles. during the experiment. At forward angles the standard The capture photons were detected by four large µ-metal shielding of the photomultiplier tubes has been BaF –counters in coincidence with the recoil 3He parti- complementedwithtwoclosedµ-metalboxeswithawall- 2 clesdetectedinthinplasticscintillators(R).Toseparate thickness of 1.5 mm, shielding the whole detectors from the beam from the recoil particles a C–shaped dipole– the magnetic field of the C–magnet of about 50 G. magnet (D) with a vertical pole-tip distance of 90 mm was used downstream of the interaction point. 2. Recoil-detectors BaF To detect the deflected recoil particles with energies 2 BaF 2 of 17–21 (26–31) MeV at the beam energy of 29 MeV BaF2 BaF2 (45 MeV) plates of plastic scintillator Pilot U with a thickness of 1.2 mm were used. The 3He recoiled in a BaF2 BaF2 conebetween0.4o and2.6o atbothdeuteronenergiesde- pending on the photon angle. The strength of the mag- X BaF 2 neticfieldwaschosentodeflecttheinitialdeuteronbeam d Z by ∼ 8o such as to separate the 3He and deuterons by LH−T Y more than 10o. d TC 3He R The position and size of the recoil detectors were de- FC fined by numerical simulations of deuteron and 3He tra- D jectories in a magnetic field based on measurements of the magnetic field map determined at PSI. Angular and FIG.4: (Coloronline)Schematicoverviewofthesetup: LH- T-liquidhydrogentarget,D-dipolemagnettoseparate3He spatialdeviationsduetobeamdivergence,beamsizeand andunscattereddeuterons,R-recoil-detectors,FC-Faraday multiple scattering in the target was taken into account. cup. The detectors were designed to accept 99% of the recoil particles. The size of the individual Pilot U-pieces was chosentoyieldnearlyequal3Hefluxesinalldetectorsto protect the electronics from signal over-load. The thick- 1. γ-detectors nesswaschosenbytherequirementtostoptherecoil3He but not the Rutherfordscattereddeuterons andthe pro- tonsfrombreak–upreactions. Thephotomultiplierswere The photons from the capture reaction with energies mounted vertically at a distance of about 50 cm where from 13 MeV to 16 MeV for E =29 MeV and from d the magnetic field from the deflection magnet could be 17 MeV to 24 MeV for E =45 MeV were detected with d sufficiently shielded. four BaF –scintillators. The detectors were placed at a 2 distanceof80cmfromthetargetatvariousanglesinthe range from 27o to 169o. Each detector consists of four large cubic crystals 8×8×25cm3 placed in aluminium 3. Electronics containers with a wall-thickness of 5 mm. The boxes were shielded with 5 cm of lead on the sides and 5 cm All the detector signals were multiplexed to form a borated plastic in front. trigger signal and to process the signal for time and am- The scintillator material was chosen because of its ex- plitude measurements. The trigger signals were clipped cellenttimingcharacteristics. ThelightresponseofBaF to correct for base line shifts at high rates and fed to 2 is characterized by two decay times of 0.7 ns (short) constant fraction discriminators to minimize the signal and 620 ns (long) and a light emission spectrum with amplitude dependence. A coincidence was requested be- maxima at 220 nm and 310 nm, respectively [22]. The tween each recoil and BaF detector within a time win- 2 BaF fast component allows for an excellent discrimina- dow of 25 ns. The sum of all coincident signals was used 2 tion between the capture photons and the copious neu- for a further coincidence with the RF–signal of the cy- trons from break–up reactions and beam–target window clotron. To form these coincidences first is important to interactions. This is particularly important for the mea- minimize electronic dead time effects at the high rates. surementsatextremeangleswherethecapturecrosssec- The final trigger signal with the RF time provided the tion is very small. Due to its high density of 4.89 g/cm3 start of the TDC and triggered the read–out of the CA- BaF has a very good efficiency and an acceptable en- MAC system. For each detector the retimed coincidence 2 ergyresolutionofabout16%(shortcomponent)forE ≈ signal was used for the gate of the charge integrating γ 20MeV.Eachcrystalisconnectedtofastphotomultiplier ADC.Forredundancycoincidencesbetweentherecoilde- tubes Philips XP4318B with special optical gel trans- tectors and the BaF detector were also formed. For the 2 parent for UV–radiation(Baysilone O¨l M 600000by GE BaF detectors two amplitudes were recorded. One with 2 5 ashort25ns gateforthe fastcomponentandone witha software time cuts on the prompt γ events. In order to 700 ns gate for the long one. For a time of flight (TOF) achieve this result software cuts have been applied on measurement,theTDC’swerestartedwiththebeamRF the BaF –recoil–TOF, the BaF –RF–TOF, and on the 2 2 signal and stopped with the individual fast component energy information of the recoil–detectors. In addition, detector signal. The same was done for the recoil de- dueto the kinematicalangularcorrelationthe properre- tector signals. A signal from the digitized beam current coil detector is selected for a given BaF . This selection 2 of the Faraday cup, a real-time clock and pulser signals provides for a significant reduction of background. as well as the current polarization state signal were fed Figure 5 shows an example of a two-dimensional his- into scalers. These signals were relevant to correct false togram with a BaF detector lightoutput versus its 2 asymmetriesfromdeadtimeandbeamcurrentvariations BaF –recoil–TOF of the corresponding recoil detector. 2 correlated with the polarization state. All the informa- The cuts on the BaF –RF–TOF and recoil lightoutput 2 tion was written on an event–by–event basis on disc for are applied. The two-dimensional histogram shows a on–line analysis and also written to tape for backup and clearseparationbetweentheγ−3Hecoincidencesandthe replay. unstructuredaccidentalones. With anadditionalcut on the coincidence time BaF –energy spectra like the one 2 shown in figure 6 have been achieved. III. ANALYSIS AND RESULTS FIG.6: (Coloronline) Exampleofaγ–energyspectrumwith all cuts applied and the integration limits for the capture events. For studies of the background analyzing power as discussed in the text, a third integration line including the background is also shown FIG. 5: Example of a spectrum of the short component am- In figure 6 a γ–energy spectrum (BaF2 short compo- plitude of the BaF response versus the TOF between the nent) with allmentioned cuts applied(except the cut on 2 γ-raysandtherecoilparticles. Cutsareappliedontherecoil BaF -lightoutput) is shown. The spectrum also shows 2 energy and on theBaF2–RF–TOF. the integration limits applied to determine the capture events. The left part of the spectrum is due to the re- The main challenge of the data analysis is to single maininglowenergyγ backgroundwhichalsocontributes out the few capture events from a huge background due to the region of the γ-peak within the integration lim- to hadronic reactions. Particularly for data taken at the its. Todeterminetheeffectofthisremainingbackground very large and very small scattering angles the applied contribution the response function of the BaF2–detector hardware coincidence is indispensable. The coincidence to monoenergetic photons must be known. requirement results in a signal to noise ratio of the or- For this determination an additional experiment with der of 1 for these data. The remaining background is monoenergeticγ-rayswasperformedatthePhysicsInsti- mostly due to accidentalcoincidences and n−p breakup tute of the University of Basel. Monoenergetic 20 MeV reactions of deuterons on hydrogen and the target win- γ-rays were produced in a 3H(p,γ)4He reaction with a dows. Depending on the kinematics the signal to noise 1 MeV proton beam provided by a Cockroft-Walton ac- ratiocouldbeenhancedtoatleast25duetotheexcellent celerator. The detector was placed at 110 deg close to timing resolution of the BaF detectors and the efficient the maximumofthe angulardistributionofthe photons. 2 6 FIG. 7: (Color onlie) On the left the short component of the BaF response function for 20 MeV γ–rays. On the right 2 experimentalγ-spectrumincomparison with thefit-function. Theintegration limitsarerepresentedbytwoverticallines. The contribution of theexponential function and thefolded peak function are also shown separately The distance between the tritium target and the BaF - its can be interpreted as a dilution factor Ntot/(Ntot− 2 detector was 80 cm in order to reproduce the geome- Nbackgr). To accountfor this dilution the correctedana- try of the d~−p-capture experiment. The target was a lyzing powers are then given as 0.45 mg/cm2 Ti layer on a Cu–plate with 2 Ci absorbed Ntot tritium. The electronics was a simplified version of the Acapture =Aextracted· (3) d~−p-captureexperimentusingthe sameelectronicmod- y, yy y, yy Ntot−Nbackgr ules and gate widths. The measuredshort componentof Here Ntot is the total number of events within the inte- the BaF2 response function for the monoenergetic pho- gration limits and Nbackgr is the total number of counts tons from this study is shown on the left in figure 7. of the fitted exponential function within the integration The sum of the experimentally determined response limits. Aextracted are the vector–,tensor–analyzingpow- y, yy functionandanexponentialfunctionfoldedwithaGaus- ers determined from the total number of counts in the sian is used in the analysis to fit the spectra of the short different polarization states, respectively. componentoftheBaF detectors. Thepeakposition,the 2 In order to verify the assumption of an unpolarized amplitude,thewidthoftheGaussianandtheslopeofthe background the following tests have been performed. exponential function are used as parameters. An exam- First, the corrected analyzing powers at a given kine- ple of such an analysis is shown on the right in figure 7. matic point must be independent of the dilution factor. The reduced χ2 of the fits varies from 0.8 to 2.2. The Different sets of runs with different background condi- upper end of the peak is distorted due to pile–up during tionsduetodifferentbeamcurrentshavebeencompared. thed~−p–captureexperimentandthusisexcludedinthe Within the statistical errors no systematic deviations fit. have been found. Second, if the analyzing powers of the As the energy of the photons in the d~−p-capture ex- backgroundwould not be zero,they would contribute to perimentvariedbetween13MeVand24MeVtheenergy the extracted analyzing power values as: dependence of the response function was studied with a GEANT-Monte-Carlosimulation. Photonswithenergies Ntot Acapture = Aextracted· of 13 MeV or with 24 MeV incident on a BaF2 crystal y, yy y, yy Ntot−Nbackgr foldedwithaGaussiantofittheexperimentalpeakwidth Nback have been compared to a simulation at 20 MeV, the en- −Abya,cyky· Ntot−Nbackgr (4) ergy of the model peak. Scaling the response functions to the model peak energy resulted in an energy depen- Large background contributions with finite analyzing dence of the response of less than 5% for the integration powers would significantly distort the corrected capture limits applied in the analysis. This results in a negligi- values. This can be checked by artificially increasing in- ble relative error contribution of 0.2% for a background tegration limits in order to include a large background contribution of 4.6%. fractioninthelow-energypartofthespectrum(seefigure Withtheassumptionofanunpolarizedbackgroundthe 6). The corrected analyzing powers from these integra- contributionfrom0%to4.6%withintheintegrationlim- tion limits can be compared to analyzing powers within 7 integration limits with essentially no background contri- IV. COMPARISON TO THEORY bution. It is found that the analyzing powers calculated with the larger integration limits are completely consis- Thepresentdatatogetherwithpreviousdatatakenat tentwiththeanalyzingpowerscalculatedforthecapture the same deuteron energies are compared to three dif- peak. This confirmsthat within the statisticallimits the ferent recent calculations [23, 24, 25]. The calculations background contribution is unpolarized, hereby justify- are all exact in the sense that they provide a full solu- ing the correction described with equation 3. tionoftheSchrödingerequationfromarealisticnucleon– The resulting deuteron vector (Ady) and tensor (Ayy) nucleoninteractionfor both the ground–and continuum analyzing powers from the capture reaction are given in states. An exact treatment using the same Hamiltonian tableIIIandIV. Thestatisticalandthesystematicerrors for initial and final state is known to be essential for a arelistedseparately. Ascanbeseenthestatisticalerrors successful description of polarization observables of the dominate the total error for all data points measured. d~−pcapturereaction. Whereasforthedescriptionofthe differential cross section the use of the Born approximation leads to an underestimate of order 15%, the tensor θc.m.(dd−eγg) Ay±δAsytat±δ×A1sy0y0s Ayy±δAsytyat±δ×A1syty0a0t analyzing power Ayy is underpredicted by more than a factorof2. The importanceofinitialstate interactionin 33.52 −3.821±0.335±0.084 3.010±0.383±0.090 these observables has been observed already in the cal- 55.32 −1.808±0.252±0.061 2.197±0.288±0.070 76.41 −0.443±0.262±0.050 2.236±0.300±0.053 culation by J. Torre [12]. More recently a calculation 116.16 0.465±0.253±0.051 2.452±0.289±0.054 by A.C. Fonseca and D.R. Lehman [26] confirmed that 134.94 1.030±0.285±0.052 2.182±0.326±0.055 re-scattering effects in the initial state are crucial for a 153.19 0.325±0.470±0.044 0.438±0.538±0.045 determination of polarization observables. 170.21 1.097±0.412±0.060 −2.934±0.520±0.067 Thetechniquesappliedinthecalculationsbythethree groups are very different. The Bochum–Cracow group [23] obtains the wave functions by solving the Faddeev TABLE III: Vector (Ady) and tensor (Ayy) analyzing powers equations in a non–relativistic framework. In the cal- for the d~−p radiative capture reaction at a deuteron energy culation of the PISA group [24] the wave functions are of 29 MeV. calculated using the pair–correlated hyperspherical har- monics method [4]. Both groups use the Argonne v18 two–body potential [27] as underlying nucleon–nucleon θc.m.(dd−eγg) Ay±δAsytat±δ×A1sy0y0s Ayy±δAsytyat±δ×A1syty0a0t ptioatle[n2t8i]ails. aInlsoadindcitluiodne,dthbeyUborbthangaroIuXptsh.rIene–tbheodayppprootaecnh- by the Hannover group[25] the three–particle scattering 31.04 −5.134±0.186±0.095 4.610±0.228±0.113 equationsarecalculatedexactlywithaChebyshevexpan- 51.20 −1.955±0.160±0.042 1.199±0.197±0.048 112.88 1.837±0.190±0.042 1.891±0.236±0.049 sionofthe two–baryontransitionmatrix. This approach 137.89 2.986±0.139±0.057 2.014±0.171±0.068 employs the CD–Bonn potential [29] as the underlying 170.48 4.507±0.328±0.081 1.334±0.407±0.095 two–body–potential. The three–nucleon–force (3BF) is generated here via a coupled channel extension of CD– Bonn which allows for a single nucleon transition to a TABLE IV: Vector (Ady) and tensor (Ayy) analyzing powers static ∆ isobar. The CD–Bonn + ∆ extension is as ex- for the d~−p radiative capture reaction at a deuteron energy act as CD–Bonn as it is also fitted to the experimental of 45 MeV. two–nucleon data up to 350 MeV [30]. In figure 8 the results of the three calculations for Varioussystematicerrorsareaccountedfor. Arelative the analyzing powers at the energies of the experimental 10% error is estimated for the background contribution. data are compared. In this comparison only one–body– Inaddition, correlationsbetweenluminosities andpolar- currentsareincludedinthecalculations. Inaddition,the ization states could lead to false asymmetries. To deter- results of one calculation by Skibinsky et al. (dash) is mine a systematicerrorthe asymmetriesoftwounpolar- shown which neglects the 3BF. The figures confirm that ized runs with different current have been used to deter- when accounting for one–body–currentsonly, the results mine a false asymmetry due to different dead times and are essentially the same. Small deviations can be ob- luminosities. The determined effect can be scaled to the served for the calculation which does not include a 3BF differencesincurrentsanddeadtimesfordifferentpolar- (dash)andforthe calculationwhichincludes the 3BFas ization states present during normal running conditions. astatic∆isobar(solid). Thus,theeffectsofthe3BFare A resulting systematic uncertainty of 0.00043 (0.00024) small but notable in Ad when a different 3BF–model is y resultsduetocurrentdifferencesof0.005(0.003)nAdur- employed. ing the data taking at E =29(45) MeV. Including the Figure 8 also shows the experimental results of the d uncertainty of the polarization determination the total present work together with the results of [14] and [12]. systematicerrorsvarybetween0.00044and0.00113com- Whereasthe resultsofthe threeexperimentsareingood pared to the statistical errors from 0.00187 to 0.00470. agreement the comparison to the calculations shows a 8 FIG. 8: Ady (top) and Ayy (bottom) for 29 MeV (left) and 45 MeV (right) incident deuteron energy as a function of the center–of–mass angle between deuteron and outgoing γ. Data of the present experiment (•) together with thedata by Anklin et al [14] (◦) and Jourdan et al. [12] ((cid:3)) are compared to the one–body–calculations by Deltuvaet al. (solid), Skibinskiet al. with/without 3BF (dotdash/dash), and Viviani et al. (dot). largediscrepancy. As will be shown,the dominantcause in which the π– and ρ–exchange currents are taken into ofthese deviationsarethe missingtwo–body–currentsin account explicitly using the Riska prescription [32]. the calculations. One should note that all the theoreti- The effect of the two–body–currents is shown in fig- cal results have been folded with the acceptances of the experimental data of ±5.7 deg. ure 9. The description of the data has largely improved which confirms the presence of large two–body–current Incalculationsofcapture–andphotodisintegrationob- effects. The solid lines give the results including the π– servables the dominant part of many–body–currents is and ρ–exchange currents explicitly whereas dashed lines usually included using the Siegert theorem [31]. The show the results from the Siegert approach. In general, standardSiegerttheoremisformulatedinamultipoleex- the description of the data is much better with the ex- pansioninwhichpartofthetransitioncurrentscanbere- plicit treatment of the exchange currents. This suggests placed by the charge operator. Alternatively is has been that magnetic transitions, for which MEC’s are not ac- shownbyGolaketal. [2]thatinmomentumspaceamul- counted for in the Siegert approach, are a relevant part tipoleexpansionofthecurrentoperatorisnotnecessary; of the transition. As expected, this holds particularly this approach is applied in the calculations by Skibinski for the wings of the A data. In the intermediate an- yy et al. Whereastwobody currentsareimplicitly included gular range, which is dominated by the E1–transition, in the dominant part of the electric transitions, they are one would expect the Siegert calculation, which implic- notaccountedforinthemagnetictransitionsandasmall itly accounts for MEC’s, to be the more successful ap- part of the electric ones. In the calculation by Skibinski proach. However, only the A data at the 45 MeV are yy et al. only the one–body–current is used in these latter described well. This is surprising as these data are par- parts of the transition. An alternative approach is used ticularlysensitivetosmallingredientsofthecalculations. 9 FIG. 9: Same as figure8. Herethedata are compared to thecalculations by Skibinskiet al. with an explicit treatment of the exchange currents(solid) and within the Siegert approach (dash). Thus,oneshouldconcludethatonlyamorecompleteex- the two protons is straightforward in these calculations plicit accountof the two–body–currentscanimprovethe as they are performed in configuration space. The ef- description of the data. fectissmallforthe analyzingpowersofthepresentwork but, as will be discussed below it improves the compar- Such a more complete approach for many body cur- ison between data and calculation. Figure 10 shows the rentshasbeenemployedbythe PISAgroup. Thiscalcu- comparison of the data with these theoretical results. lationincludes π–, ρ–,ω–,andσ–exchangecurrentscon- sistentwiththeNN–potentialaswellasthecurrentsasso- In particular the description of the Ad data for both y ciatedwith the ρπγ andωπγ transitionmechanisms and energies improved with this approach in most of the an- with the excitation of intermediate ∆–resonances. One gular region. If three–body–current effects are included shouldnotethattheρπγ andωπγ termsarenotfittedto the description alsoagrees with the A data at 30 MeV yy data but used with the standard coupling constants[33]. but still shows deviations at 45 MeV. In particular, the Inaddition,thesetermsgiveveryminoreffects. Analter- fall–offofthecalculationsinA at45MeVatbackward yy native approach to the one by Skibinski et al. to derive angles cannot be removedby many–body–currents. De- the exchangecurrentsisemployed[24]. The currentsare viationsfromthe data are alsopresentatverybackward strictly consistent with the interaction potential. Thus, angles for the Ad data. This suggests that additional ef- y three–body–currents are included for calculations with fects are relevant for a complete description of the data. the Urbana IX three–body potential. An essential as- pect of the calculation is that the current conservation Asimilardiscrepancywasalongstandingpuzzleinthe relation is satisfied in all calculations. 0 deg cross section of the two–body photodisintegration AnadditionalimprovementofthecalculationsbyMar- becauserelativisticeffectshadbeenconsideredunimpor- cucci et al is the inclusion of the point Coulomb inter- tantattheselowenergies. Cambi,Mosconi,andRicci[9] action. To account for the Coulomb interaction between solved this puzzle demonstrating the importance of the 10 FIG.10: Sameasfigure8. HerethedataarecomparedtothecalculationsbyMarcucciet al. with2–bodycurrents(dash)and with 2– and 3–body currents(solid). Thecalculations by Skibinskiet al. with theexplicit treatment of theexchangecurrents are also shown (dot–dash). relativisticspin–orbitcontributiontoexplainthediscrep- this calculation the data can be reproduced over most ancies between data and calculations. of the angular range. The dotted line represents the Ina(k/m )–expansionofthe currentoperatorwith k results without relativistic– and Coulomb effects. The N andm thenucleonmomentumandmass,relativisticef- dashedlineshowstheresultswithrelativisticcorrections N fectsoforder(k/m )2 areincludedinthe calculationby includedandtheresultsshownwiththesolidlineinclude N Deltuva et al. [25]. The two–body currents are included alsotheCoulombinteraction. Inparticularthebackward inthiscalculationusingtheSiegertapproachwithoutthe angle fall–offof A can be removedwith the relativistic yy long–wavelength approximation often applied. In con- spin–orbit effect. In addition, also the backward angle trast to the calculation by Skibinski, explicit one– and deviations of the non–relativistic calculations in Ad are y two–body currents in the non–Siegert parts are also ac- improved. counted for. In addition to relativistic effects, also this calculation includes the Coulomb interaction between the two pro- V. CONCLUSIONS tons[34]. Forcalculationsperformedinmomentumspace the Coulomb potential is usually omitted due to con- vergence difficulties. To include it a screened Coulomb Precisedeuteronvectoranalyzingpowers,Ady,andten- potential is used, corrected for the unscreened limit us- sor analyzing powers, Ayy, have been measured for the ing a renormalization procedure. A recent compari- 1H(~d,γ)3He–capture reaction at two incident deuteron son with the calculations of the PISA–group discussed energies. The energies have been chosen in order to em- above demonstrates the reliability of the momentum phazise different dynamical effects. A for intermediate yy space calculation[35]. Figure 11 shows the data in com- angles shows a maximum at 29 MeV, whereas it crosses parison with the calculations by Deltuva et al. With zero around 45 MeV.