A measurement of the analyzing powers for the 1H(~d, pp)n breakup reaction at 130MeV polarized deuteron beam energy was carried out at KVI Groningen. The experimental setup covered a large fraction of the
phase space. Obtained tensor analyzing powers T22 for selected kinematical configurations have been compared to theoretical predictions based on various approaches: the rigorous Faddeev calculations using the realistic nucleon–nucleon potentials with and without three nucleon force (3NF) models, predictions of the chiral perturbation theory, and coupled channel calculations with the explicit   degrees of freedom. In the presented
configurations the results of all predictions are very close to one another and there are no significant 3NF influences. Not all of the data can be satisfactory reproduced by the theoretical calculations

Biegun, A.

Bodek, K.

Ciepał, I.

Deltuva, A.

Epelbaum, E.

Glockle, W.

Golak, J.

Kalantar-Nayestanaki, N.

Kamad, H.

Kis, M.

Kistryn, S. T.

Kozela, A.

Kuroś-Żołnierczuk, J.

Kłos, Barbara

Mahjour-Shafiei, M.

Meissner, U. G.

Micherdzińska, A.

Nogga, A.

Sauer, P. U.

Skibiński, R.

Stephan, Elżbieta

Sworst, R.

Witała, H.

Zejma, J.

Zipper, Wiktor

Acta Physica Polonica B

English

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Three-nucleon force effects in the analyzing powers of the dp breakup at 130 MeV  Author: A. Biegun, Elżbieta Stephan, S.T. Kistryn, K. Bodek, I. Ciepał, A. Deltuva, Barbara Kłos, Wiktor Zipper  Citation style: Biegun A., Stephan Elżbieta, Kistryn S.T., Bodek K., Ciepał I., Deltuva A., Kłos Barbara, Zipper Wiktor. (2006). Three-nucleon force effects in the analyzing powers of the dp breakup at 130 MeV. "Acta Physica Polonica B" (Vol. 37, no. 1 (2006), s. 213-218).   Vol. 37 (2006) ACTA PHYSICA POLONICA B No 1THREE-NUCLEON FORCE EFFECTSIN THE ANALYZING POWERS OF THE ~dp BREAKUPAT 130 MeV∗ ∗∗A. Bieguna, E. Stephana, St. Kistrynb, K. Bodekb, I. CiepałbA. Deltuvac, E. Epelbaumd, W. Glöcklee, J. GolakbN. Kalantar-Nayestanakif , H. Kamadag, M. Kišf , B. KłosaA. Kozelah, J. Kuroś-Żołnierczukb, M. Mahjour-ShafieifU.-G. Meissneri,j, A. Micherdzińskaa, A. Noggai, P.U. SauerkR. Skibińskib, R. Sworstb, H. Witałab J. Zejmab, W. ZipperaaInstitute of Physics, University of Silesia, 40-007 Katowice, PolandbInstitute of Physics, Jagellonian University, 30-059 Cracow, PolandcUniversidade de Lisboa, CFN, 1649-003 Lisboa, PortugaldJefferson Laboratory, Theory Division, Newport News, VA 23606 USAeRuhr Universität Bochum, ITP II, 44780 Bochum, GermanyfKernfysisch Versneller Instituut, 9747 AA Groningen, The NetherlandsgDepartment of Physics, KIT, 804-8550 Kitakyushu, JapanhInstitute of Nuclear Physics PAN, 31-342 Cracow, PolandiUniversität Bonn, ISKP (Theorie), 53115 Bonn, GermanyjForschungszentrum Jülich, IKP (Theorie), 52425 Jülich, GermanykUniversität Hannover, ITP, 30167 Hannover, Germany(Received November 15, 2005)A measurement of the analyzing powers for the 1H(~d, pp)n breakupreaction at 130MeV polarized deuteron beam energy was carried out atKVI Groningen. The experimental setup covered a large fraction of thephase space. Obtained tensor analyzing powers T22 for selected kinemati-cal configurations have been compared to theoretical predictions based onvarious approaches: the rigorous Faddeev calculations using the realisticnucleon–nucleon potentials with and without three nucleon force (3NF)models, predictions of the chiral perturbation theory, and coupled chan-nel calculations with the explicit ∆ degrees of freedom. In the presentedconfigurations the results of all predictions are very close to one anotherand there are no significant 3NF influences. Not all of the data can besatisfactory reproduced by the theoretical calculations.PACS numbers: 21.31.–x, 21.45.+v, 25.10.+s∗ Presented at the XXIX Mazurian Lakes Conference on PhysicsAugust 30–September 6, 2005, Piaski, Poland.∗∗ Supported by the Polish State Committee for Scientific Research (KBN), grantNo. 1P03B02627.(213)214 A. Biegun et al.1. IntroductionDevelopments within the meson exchange theory resulted in constructingof modern nucleon–nucleon (NN) potential models, like Argonne AV18 [1],CD-Bonn [2] and Nijmegen I and II [3]. Calculations with the use of thesepotentials, when applied to the three-nucleon (3N) system, are also supple-mented with three-nucleon force (3NF) models. At present, the most com-monly used models of such additional dynamics are the upgraded Tucson-Melbourne (TM99) [4] and the Urbana IX [5] forces. It is worth mentioningthat there exist different methods of including non-nucleonic degrees of free-dom in describing the 3N system. An example is the explicit ∆-isobartreatment in the coupled-channel formalism as the method of generating aneffective 3NF [6], also quite successful in reproducing the data.In parallel to the meson exchange theory of semi-phenomenological NNand 3N potentials an alternative way of constructing the interaction modelsfor the few nucleon system is being pursued within the effective field theoryapproach. Developed and applied to describe interactions between pions andmatter fields (nucleons, ∆’s, heavy mesons) as well as of pions themselvesin a systematic and, to a large extent, model-independent manner, this ap-proach is called chiral perturbation theory (ChPT). Recent developments inChPT lead to NN potentials where the multi-pion exchanges are treatedunambiguously according to chiral symmetry. In this way the inconsisten-cies in constructing the NN and 3N potential of the meson exchange basedmodels have been mostly removed and the theory of nuclear forces is setup on a more solid and formal basis. First calculations within the ChPTframework at the NNLO order are quite successful in describing the data forthe 3N system [7].The 1H(~d, pp)n breakup process, with its three particles in the final state,is an extremely reach field to study non-trivial aspects of the interaction dy-namics in the simplest many-nucleon system. Especially, the polarizationobservables are expected to provide many hints on the details of the struc-ture of the 3NF models. The paper presents the first results of the tensoranalyzing powers of the deuteron breakup reaction, which signal a forthcom-ing large data set of polarization observables, covering a large fraction of thephase space.2. Measurement and detection systemThe experiment was performed at KVI Groningen, with the use of vectorand tensor polarized deuteron beam of 130MeV. The beam was extractedfrom the ion source, accelerated in the superconducting cyclotron AGORand guided to the experimental setup, where it was focused to a spot ofone millimeter diameter on a liquid hydrogen (LH2) target. The target waslocated approximately in the center of the vacuum scattering chamber whileThree-Nucleon Force Effects in the Analyzing Powers of the . . . 215the whole detection system was mounted outside the chamber, in the air.The experimental setup, so-called SALAD (Small Angle Large AcceptanceDetector), was designed for registering and identifying charged particles —protons and deuterons. It consisted of two layers of a scintillator hodoscope,transmission ∆E detectors of 2mm thickness and stopping E detectors,11.2 cm thick, accompanied by a three-plane Multiwire Proportional Cham-ber (MWPC), allowing to reconstruct polar and azimuthal angles of thecharged reaction products. The detection system covered laboratory polarangles θ between 10◦ and 35◦ and the full range of the azimuthal angle φ,from 0◦ to 360◦ [8].3. Determination of the beam polarizationThe main goal of the reported here work was to obtain the experimentalvalues of the tensor analyzing powers T22 for the breakup reaction.First, the values of the vector and tensor polarizations of the deuteronbeam were determined with the help of the elastic scattering events. Thesedata were collected for two polarization states with pure tensor beam polar-izations (Pz=0, nominal values of Pzz equal to −2 and +1, respectively) andfor an unpolarized beam (Pz = Pzz = 0). The actual values of Pzz for thetwo polarized beam states have been found for a few selected kinematicalconditions (several angles θp). For each θp events were sorted with respectto the proton azimuthal angle φ with the binning of 10◦, and the ratiosfθpP (φ) =NθpP (φ)−Nθp0 (φ)Nθp0 (φ), (1)were constructed. NθpP (φ) and Nθp0 (φ) denote the numbers of the elasticevents registered with the polarized and unpolarized beam, respectively, con-nected by the relation:NθpP (φ) = Nθp0 (φ)[1 + g(φ) + h(φ)] , (2)with g(φ) = +PziT11(θp)√3 cosφ ,h(φ) = Pzz(−T22(θp)√32cos 2φ− T20(θp)√24).Thus, the shapes of the experimental ratios (1) are described by thefunction g(φ) + h(φ). Such dependencies were fitted to the data — seeFig. 1 (left panel). The vector and tensor analyzing power values at theselected θp angles were taken (in the absence of the experimental data) fromcalculations with the CD-Bonn and TM99 forces.216 A. Biegun et al.From the fits the values of the vector Pz and tensor Pzz polarizationswere obtained. The results for the tensor beam polarization are independentof the analyzed θp (see Fig. 1, right panel), what confirms the right shapeof the theoretically predicted functions T22(θp) and T20(θp). The resultingmean values in the two used states are Pzz = −1.346 ± 0.012 and Pzz =+0.542 ± 0.011, respectively. Vector polarization for these states is close tozero (Pz = −0.060 ± 0.007 and Pz = +0.016 ± 0.006).Fig. 1. Left: ratios fθpP (φ) for two pure tensor beam polarization states (nominalpolarizations shown in the panel), for one chosen proton polar angle θp = 17◦ ±0.5◦; Right: tensor polarizations Pzz obtained for the same two states at severalangles θp, with the resulting mean values.4. Breakup analyzing powers T22The determined above values of the beam polarizations were used toobtain the tensor analyzing powers T22 for the breakup reaction.In the first step, the kinematical spectra E1 versus E2 were built (asdescribed in [8]) and the events along the kinematical curve were divided intoarclength bins with the width of ∆S = 16MeV. The variable S representsthe distance, measured along the kinematical curve, from the point of mini-mal E2 value. For every bin in S in the selected angular configuration(θ1, θ2, φ12), the number of the breakup events NSP (φ) was obtained asa function of the azimuthal angle φ of the “first” proton. Similar ratiosas for the elastic scattering (in Eq. (1) the variable θp is replaced by ξ ≡(θ1, θ2, φ12, S), defining a point in the final phase space) were constructed.Again, the ratios can be described by a function g(φ) + h(φ) withg(φ) = + iT11(ξ)Pz√3(sinφ+ cosφ) ,h(φ) = −T22(ξ)Pzz√32(sin 2φ+ cos 2φ)− T20(ξ)Pzz√24,which was fitted to the breakup data.Three-Nucleon Force Effects in the Analyzing Powers of the . . . 217From the fit it is, in principle, possible to obtain the experimental valuesof the analyzing powers iT11, T22 and T20 as functions of S in the selectedconfigurations (θ1, θ2, φ12). However, in the discussed piece of analysis,Pz ≈ 0 and the sensitivity to iT11 is suppressed. In addition, even thoughT20 and T22 are always fitted simultaneously, we focus here on T22 only,relying rather on the shape of the φ distribution than on the absolute valueof the ratios. Obtained T22 values for the two beam polarization states havebeen found consistent with each other and the weighted averages of thoseresults were calculated. The examples of T22 distributions are presentedin Fig. 2.-0.100.10.260 90 120 15060 90 120 150-0.100.10.2T2260 90 120S (MeV)θ1, θ2 = 20°, 15° θ1, θ2 = 25°, 15°θ1, θ2 = 15°, 15°φ12 = 100° φ12 = 100° φ12 = 100°Fig. 2. The breakup analyzing powers T22 for 3 kinematical configurations, indi-cated in the individual panels. The error bars represent the statistical uncertainties.In the upper part the results are compared to the predictions based on the realisticNN potentials only (light-grey bands) and with the calculations in which the TM993NF has been included (dark-grey bands). The results obtained within the coupled-channel framework with the CD-Bonn+∆ potential are shown as the dashed lines.In the lower part the same data are compared to the predictions obtained withinthe ChPT approach at NNLO: the complete 3N calculations (dark-grey bands)and the results for the NN contributions only (light-grey bands).218 A. Biegun et al.5. Comparison with theoretical predictionsThe experimental results of T22 have been compared with various ap-proaches to the theoretical treatment of the 3N scattering problem: thepredictions based on the realistic NN (CD-Bonn, AV18, Nijm I and Nijm II)potentials only and with the TM99 3NF model included, the results of thecoupled-channel calculations with the CD-Bonn+∆ potential, and the pre-dictions obtained within the ChPT framework at NNLO.Searches for the 3NF effects are particularly well founded in a situationwhen the data are properly described in the regions of consistency betweenall the models. Therefore, our studies of T22 started in the angular rangewhere the theoretical predictions are very similar in all the approaches (seeexamples in Fig. 2). The bands of the theoretical predictions are narrowfor both, pure NN and NN + 3NF calculations, and the discrepancies be-tween results of these two approaches are small. In the case of the ChPTcalculations at NNLO (Fig. 2, lower part), the bands representing the un-certainties of the ChPT predictions have widths comparable with the 3NFeffects predicted at this order of calculations.In two of the three presented configurations the data are very well re-produced by the theoretical predictions. For the configuration θ1=θ2=15◦,φ12=100◦ the theories fail in describing the data. In order to trace eventualregularities of the discrepancies a large number of the experimental pointswill be analyzed, similarly to the cross section case [8]. In the next step ofthe data evaluation also T20 will be extracted, for which large 3NF effects arepredicted in some regions. Establishing patterns of (dis)agreements acrossthe phase space for all analyzing powers might help in locating weak pointsin the present-day understanding of the 3N system dynamics.REFERENCES[1] R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C51, 38 (1995).[2] R. Machleidt, F. Sammarruca, Y. Song, Phys. Rev. C53, R1483 (1996);R. Machleidt, Phys. Rev. C63, 024001 (2001).[3] V.G.J. Stoks et al., Phys. Rev. C49, 2950 (1994).[4] S.A. Coon et al., Nucl. Phys. A317, 242 (1979); S.A. Coon, H.K. Han, Few-Body Syst. 30, 131 (2001).[5] B.S. Pudliner et al., Phys. Rev. C56, 1720 (1997).[6] A. Deltuva, K. Chmielewski, P.U. Sauer, Phys. Rev. C67, 034001 (2003);A. Deltuva, R. Machleidt, P.U. Sauer, Phys. Rev. C68, 024005 (2003).[7] E. Epelbaum et al., Phys. Rev. C66, 064001 (2002).[8] St. Kistryn et al., Phys. Rev. C68, 054004 (2003); St. Kistryn et al., Phys.Rev. C72, 044006 (2005).

Three-nucleon force effects in the analyzing powers of the dp breakup at 130 MeV

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Three-nucleon force effects in the analyzing powers of the dp breakup at 130 MeV

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