Ramazani-Moghaddam-Arani, Ahmad

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Proceedings - University of Groningen

   University of GroningenCross-section and analyzing-power measurements in three and four-nucleon scatteringRamazani-Moghaddam-Arani, AhmadIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2009Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Ramazani-Moghaddam-Arani, A. (2009). Cross-section and analyzing-power measurements in three andfour-nucleon scattering. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 03-06-2022Chapter 1IntroductionThe most fundamental questions in nuclear physics are related to the forces which bindnucleons, protons and neutrons, together to form the building blocks of matter, nuclei.Already in 1935, Yukawa successfully proposed to describe the nucleon-nucleon (NN)force with an exchange of a particle [1], similar to the electromagnetic interaction whichcan be represented by an exchange of a photon. Later, this particle, the pion, was discov-ered [2–4] and its mass was found to be close to the mass predicted by Yukawa. Mean-while, and for a large part inspired by the original idea of Yukawa, various phenomeno-logical NN potentials have been derived [5–9], which are allab e to fit the proton-protonand proton-neutron scattering data with extremely high precision. In some of these mod-els, the longest-range, attractive two-nucleon force (2NF) is described by the exchangeof pions and the repulsive shorter ranges by the exchange of two pions and heaviermesons [10]. More recently, NN potentials have become availble which are derived fromthe basic symmetry properties of the fundamental theory of Quantum Chromodynamics(QCD) [11, 12]. These so-called chiral-perturbation (χPT) driven models construct sys-tematically a NN potential from a low-energy expansion of the most general Lagrangianwith only the Goldstone bosons, e.g. pions, as exchange particles.Although much has been learned about the interaction between two nucleons, it re-mains questionable whether this knowledge is sufficient to describe the interaction be-tween more than two nucleons. Already for the simplest three-nucleon system, the triton,an exact solution of the three-nucleon Faddeev equations employing 2NFs clearly under-estimates the experimental binding energy [13], showing that 2NFs are not sufficient todescribe the three-nucleon system accurately. In a three-nucl on system, the interactionbetween two of the nucleons may be influenced by the presence of the third nucleon.This extra effect comes from a force which is beyond the two-nucleon interaction andwill be referred to as three-nucleon force in this thesis (3NF). A well-known example ofsuch a force is the Fujita-Miyazawa force [14] in which all three nucleons interact via a2π-exchange mechanism with an intermediate∆ xcitation of one of the nucleons.12 Chapter 1. Introduction1.1 Three-nucleon force studies in three-nucleon scatter-ing processesTo provide a better understanding of 3NF effects, differential cross sections and po-larization observables have been measured extensively in proton-deuteron and neutron-deuteron scattering systems. The data have been compared tothe predictions of rigorousFaddeev calculations which are based on the modern NN potentials including the vari-ous models for the 3NF effects. One of the “smoking guns” was the discrepancy foundwith the measured angular distributions in elastic nucleon-deuteron scattering, in particu-lar at scattering angles for which the total cross section isat ts minimum. Furthermore,the three-body break-up channel has been predicted to be an ide l probe to study 3NFeffects. At low incident beam energies, up to 30 MeV, the differential cross sections,tensor-analyzing powers and spin-transfer coefficients innucleon-deuteron scattering aredescribed rather well using solely two-nucleon potentials. Here, the effect of the 3NF ispredicted to be small. In contrast, the description of the analyzing power fails leading tothe well-knownAy puzzle. At intermediate energies, 50-200 MeV/nucleon, theeffect ofthe 3NF becomes significant and grows with increasing bombarding energy. Generally,including 3NF effects to the modern potentials improves thecomparison with differentialcross-section data [15–27]. However, a comparison betweentheory predictions and datafor the polarization observables revealed various large discrepancies [16–18, 22, 28–34],which demonstrated that spin-dependent parts of the 3NFs are poorly understood.Apart from disagreements between data and the predictions by theory, some of theexperimental data are not consistent with each other. One ofthe worst cases is the dis-agreements in the differential cross section of the elastic~p+d reaction atElabp =135 MeV.Figure 1.1 represents these cross section data as a function of the centr-of-mass an-gle, θc.m.. The open triangles are data from Ref. [19] and the open squares data fromRef. [17, 18]. The solid curve represents the results of a coupled-channel calculation bythe Hanover-Lisbon theory group and is based on the CD-Bonn potential including theCoulomb interaction and an intermediate∆-isobar. The results of a similar calculationexcluding the∆-isobar and accounting only for the 2NF, shown as a dotted curve. Theobserved inconsistency for the differential cross section, as shown in Fig.1.1, initiateda discussion within the nuclear-physics community on the reliability of the experimentaldata and on how to interpret the data in terms of underlying physics, such as 3NF effects.It is, therefore, of importance to review these observations with respect to three-nucleonscattering data taken at other energies and in other channels. I this thesis, we present theresults of an independent measurement of the cross section using the BINA setup installedat the KVI. Furthermore, a systematic analysis of the discrepancy is made including datataken at other laboratories as well.1.2 Three-nucleon force studies in four-nucleon systems 30 30 60 90 120 150 180c.m.[deg]10-125125102d/d[mb/sr]CD-Bonn+C+CD-Bonn+CKVI [17,18]RIKEN [19]Figure 1.1: The differential cross section of the elastic~p+d reaction atElabp =135 MeV asa function of the center-of-mass angle,θc.m.. The open squares are data from Ref. [17,18]and the open triangles are data from Ref. [19]. The solid curverepresents the results ofa coupled-channel calculation by the Hanover-Lisbon theory group and are based on theCD-Bonn potential including the Coulomb interaction and an intermediate∆-isobar. Theresults of a similar calculation excluding the∆-isobar and accounting only for 2NF areshown as a dotted curve.1.2 Three-nucleon force studies in four-nucleon systemsThe 3NF effects are in general very small in the three-nucleon system, which requires sta-tistically high-precision data and - moreover - a good contrl of systematic uncertainties.For some observables the effects reveal themselves at specific configurations or towardshigher incident energies. Another complementary approachis to look into systems forwhich the 3NF effects are significantly enhanced in magnitude. For this, it was proposedto study the four-nucleon system. Naively, one might expecttha the 3NF effects in-crease by the argument that the number of three-nucleon combinations with respect totwo-nucleon combinations gets larger with increasing number of nucleons. We, however,note that the saturation of 3NF effects sets in very quickly for large nuclei as well). Thissimple counting rule is supported by a comparison between prdictions and data for thebinding energies of light nuclei [35], which is depicted in Fig. 1.2. Here, the predictions of4 Chapter 1. Introductiona Green’s function MonteCarlo calculation based on the Argonne V18 [6] NN interaction(AV18) and the Illinois-2 (IL2) 3NF [36, 37] are compared to exp rimental data. Whilea calculation which only includes the AV18 NN potential deviates significantly from theexperimental results, a calculation which includes as wella 3NF compares much betterto the data, especially for the first few light nuclei. Note that the effect of the 3NF onthe binding energy for the triton is∼0.5 MeV, whereas the effect increases significantlyfor the four-nucleon system,4He, to∼4 MeV. For heavier nuclei, even adding the 3NFas modeled in the present calculations, is not enough to resolve the discrepancy betweenthe theoretical predictions and the measurements. One might ar ue that the discrepanciesfor the binding energies of the heavier nuclei stem from four-n cleon force (4NF) effects.These higher-order many-body potentials are, however, predicted byχPT approaches [38]to be negligible compared to 3NF effects. Therefore, the large discrepancies cannot likelybe explained by a missing 4NF or even higher-order nuclear-force effects.-70-65-60-55-50-45-40-35-30-25-20-15-10-50Energy (MeV) α+d α+tα+α α+2n  6He+2n 7Li+n 8Li+n 8Be+n 9Li+n  9Be+n 6Li+αAV18IL2 Exp1+2H1/2+3H0+4He1+0+2+6He 1+3+2+6Li3/2−1/2−7/2−5/2−7Li1+0+2+8He0+2+1+3+4+(0,1)+8Li0+2+4+1+3+8Be5/2−7/2−3/2−1/2−(5/2−)9Li9/2−3/2−5/2−1/2−7/2−9Be1+2+?10Li3+4+0+2+(2+,3+)10Be3+1+2+4+10B3+1+2+4+Argonne v18With Illinois-2GFMC Calculations 6 November 2002Figure 1.2: Binding energies of the ground and excited statesof light nuclei. The ex-perimental results are compared with the predictions of a Green’s function MonteCarlocalculation based on the AV18 and AV18+IL2.The importance of understanding in detail the forces which play a role in the four-nucleon system becomes also evident in a recent observationof charge-symmetry break-ing (CSB) by the IUCF experimental group via a non-zero measurement of the cross sec-tion of the reaction,d+ d→ α+π0 [39]. The total cross section for neutral-pion produc-tion was reported to be12.7± 2.2 pb at a beam energy of 228.5 MeV and15.1± 3.1 pb at1.3 Outline of the thesis 5231.8 MeV. The theory of the strong interaction between quarks, QCD, is approximatelyinvariant under what is called charge symmetry. In other words, if we swap an up quarkwith a down quark, then the strong interaction will look almost the same. This symmetryis related to the concept of “isospin”. Aside from trivial Coul mb effects, the CSB mech-anism is responsible for the mass difference between protons and neutrons. Hence, theobservation by the IUCF group in principle allows one to determine the mass differencebetween the up and down quark. For an unambiguous determination it is crucial to under-stand the underlying reaction dynamics, such as initial-state interactions. Following theCSB experiment, the IUCF group performed a set of angular distribution measurementsof the cross sections and analyzing powers for~d+d elastic scattering at 231.8 MeV. Thesedata could be used to check the four-nucleon calculations used to describe the entrancechannel in the theoretical treatment of the CSB reaction. Thetheoretical formalism usedto describe the data is so far developed in an approximate wayusing the lowest-orderterms in a Born series expansion of the Yakubovsky equations [40] developed for thefour-nucleon system [41]. This approximation is expected to be valid for deuteron bom-barding energies larger than 100 MeV and for low momentum transfers. Large deviationsbetween calculations and data from IUCF are observed, which hinders the extraction ofthe up-down quark mass difference [42].The experimental database in the four-nucleon system is presently poor in comparisonwith the three-nucleon system. Most of the available data were taken at very low energies,in particular below the three-body break-up threshold of 2.2 MeV. Also, theoretical devel-opments are evolving rapidly at low energies [43–46], but lag behind at higher energies.The experimental database at these energies is very limited[47–49]. This situation callsfor extensive four-nucleon studies at intermediate energies. This thesis describes a com-prehensive measurement of cross sections and spin observables in variousd+d scatteringprocesses at 65 MeV/nucleon, namely the elastic and three-body break-up channels. Withthese data, we have drastically enriched the four-nucleon scattering database. The exten-sive database of spin and cross section observables in various deuteron-deuteron scatteringprocesses as presented in this thesis together with preciseand ab-initio calculations canpotentially reveal many details of 3NF effects.1.3 Outline of the thesisThe theoretical background of this work is given in the next chapter. The scattering for-malism for a two-, three-, and four-body system and a description of the cross section andanalyzing powers are discussed briefly.Chapter3 is devoted to introduce the experimental setups which were used for theexperiments discussed in this thesis. The procedure of producing polarized beams ofprotons and deuterons is given. The different components ofthe detection system, BINA,are introduced as well.The analysis procedure, results, and the discussion of the~d + p elastic scattering at65 MeV/nucleon and~p+ d elastic scattering at 135 MeV are presented in Ch.4.6 Chapter 1. IntroductionChapter5 contains the analysis procedure of the~d+ d scattering at 65 MeV/nucleon.The identification of the elastic and break-up channels and the measurement of the beampolarization are discussed in detail. Results and the discussion for the elastic and three-body break-up channels are presented in Ch.6. Finally, the summary, conclusions, andoutlook of this work are presented in Ch.7.

Cross-section and analyzing-power measurements in three and four-nucleon scattering

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Cross-section and analyzing-power measurements in three and four-nucleon scattering

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