We report on a first measurement of tensor analyzing powers in quasi-elastic
electron-deuteron scattering at an average three-momentum transfer of 1.7
fm$^{-1}$. Data sensitive to the spin-dependent nucleon density in the deuteron
were obtained for missing momenta up to 150 MeV/$c$ with a tensor polarized
$^2$H target internal to an electron storage ring. The data are well described
by a calculation that includes the effects of final-state interaction,
meson-exchange and isobar currents, and leading-order relativistic
contributions.Comment: 4 pages, 3 figure

A. Bianconi

B. Adeva

C. Bochna

C. E. Carlson

C. Gaulard

C. W. de Jager

D. J. de Lange

D. Nikolenko

D. W. Higinbotham

E. E. W. Bruins

E. Konstantinov

E. Passchier

E. Six

F. Klein

H. Arenhövel

H. de Vries

H. J. Bulten

H. R. Poolman

I. Passchier

I. Rachek

I. The

J. A. Caballero

J. Comfort

J. E. Belz

J. F. J. van den Brand

J. J. M. Steijger

J. L. Forest

J. Lang

K. Abe

L. L. Frankfurt

M. A. Miller

M. Anghinolfi

M. Bernheim

M. Bouwhuis

M. Ferro-Luzzi

M. Ripani

M. Taiuti

N. Papadakis

N. Vodinas

O. Unal

R. Alarcon

R. Ent

R. van Bommel

S. Choi

S. G. Popov

S. Gilad

S. J. Brodsky

S. M. Dolfini

S. Platchkov

T. Botto

T. de Forest, Jr.

T. Eden

W. Leidemann

Z.-L. Zhou

English

arXiv

We report on a first measurement of tensor analyzing powers in quasielastic electron-deuteron scattering at an average three-momentum transfer of 1.7 fm(-1). Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150 MeV/c with a tensor polarized H-2 target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions

Zhou, Z.L.

Bouwhuis, M.

Ferro-Luzzi, M.

Passchier, E.

Alarcon, R.

Anghinolfi, M.

Arenhovel, H.

van Bommel, R.

Botto, T.

van den Brand, J.F.J.

Bulten, H.J.

Choi, S.

Comfort, J.

Dolfini, S.M.

Ent, R.

Gaulard, C.

Higinbotham, D.W.

de Jager, C.W.

Konstantinov, E.

Lang, J.

Leidemann, W.

de Lange, D.J.

Miller, M.A.

Nikolenko, D.

Papadakis, N.

Passchier, I.

Poolman, H.R.

Popov, S.G.

Rachek, I.

Ripani, M.

Six, E.

Steijger, J.J.M.

Taiuti, M.

Unal, O.

Vodinas, N.

de Vries, H.

Maastricht University Research Portal

Tensor analyzing powers for quasielastic electron scattering from deuterium

Ferro Luzzi, M.M.E.

VU Research Portal

VU Research PortalTensor analyzing powers for quasielastic electron scattering from deuteriumZhou, Z.L.; Ferro Luzzi, M.M.E.; van Bommel, R.; Botto, T.; van den Brand, J.F.J.; Bulten,H.J.; Passchier, I.; Poolman, H.R.published inPhysical Review Letters1999DOI (link to publisher)10.1103/PhysRevLett.82.687document versionPublisher's PDF, also known as Version of recordLink to publication in VU Research Portalcitation for published version (APA)Zhou, Z. L., Ferro Luzzi, M. M. E., van Bommel, R., Botto, T., van den Brand, J. F. J., Bulten, H. J., Passchier, I.,& Poolman, H. R. (1999). Tensor analyzing powers for quasielastic electron scattering from deuterium. PhysicalReview Letters, 82, 687-690. https://doi.org/10.1103/PhysRevLett.82.687General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal ?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.E-mail address:vuresearchportal.ub@vu.nlDownload date: 23. May. 2021VOLUME 82, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 25 JANUARY 1999Tensor Analyzing Powers for Quasielastic Electron Scattering from DeuteriumZ.-L. Zhou,1,* M. Bouwhuis,2 M. Ferro-Luzzi,2,3 E. Passchier,2 R. Alarcon,4 M. Anghinolfi,5 H. Arenhövel,6R. van Bommel,2 T. Botto,2 J. F. J. van den Brand,1,7 H. J. Bulten,1,7 S. Choi,4 J. Comfort,4 S. M. Dolfini,4 R. Ent,8C. Gaulard,4 D. W. Higinbotham,9 C. W. de Jager,2,† E. Konstantinov,10 J. Lang,3 W. Leidemann,11 D. J. de Lange,2M. A. Miller, 1,‡ D. Nikolenko,10 N. Papadakis,2 I. Passchier,2 H. R. Poolman,2 S. G. Popov,10,§ I. Rachek,10 M. Ripani,5E. Six,4 J. J. M. Steijger,2 M. Taiuti,5 O. Unal,1 N. Vodinas,2 and H. de Vries21Department of Physics, University of Wisconsin, Madison, Wisconsin 537062NIKHEF, P.O. Box 41882, NL-1009 DB Amsterdam, The Netherlands3Institut für Teilchenphysik, Eidgenössische Technische Hochschule, CH-8093 Zürich, Switzerland4Department of Physics, Arizona State University, Tempe, Arizona 852875Istituto Nazionale di Fisica Nucleare (INFN), I-16146 Genova, Italy6Institut für Kernphysik, Johannes Gutenberg Universität, D-55099 Mainz, Germany7Department of Physics and Astronomy, Vrije Universiteit, NL-1081 HV Amsterdam, The Netherlands8TJNAF, Newport News, Virginia 23606,and Department of Physics, Hampton University, Hampton, Virginia 236689Department of Physics, University of Virginia, Charlottesville, Virginia 2290110Budker Institute for Nuclear Physics, Novosibirsk, 630090 Russian Federation11Dipartimento di Fisica and INFN (gruppo collegato di Trento), Università di Trento, I-38050 Povo (Trento), Italy(Received 18 September 1998)We report on a first measurement of tensor analyzing powers in quasielastic electron-deuteronscattering at an average three-momentum transfer of1.7 m21. Data sensitive to the spin-dependentnucleon density in the deuteron were obtained for missing momenta up to150 MeVyc with a tensorpolarized2H target internal to an electron storage ring. The data are well described by a calculationthat includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-orderrelativistic contributions. [S0031-9007(98)08241-6]PACS numbers: 25.30.Fj, 21.45.+v, 24.70.+s, 29.25.Pjr-n-thator].tictneamThe deuteron is often used as a benchmark to testclear theory, since reliable calculations can be performin both nonrelativistic and relativistic models. Observables such as its binding energy, static magnetic dipand charge quadrupole moment, asymptoticDyS ratio,and the elastic electromagnetic form factors place stroconstraints on models for the nuclear interaction. Futhermore, the deuteron is one of the few nuclear systefor which predictions based on quantum chromodynamics have been made and tested [1–4]. The understandof the deuteron has progressed to a level which allothe deuteron to be used as an effective neutron targestudies of the electromagnetic form factors of the neutr[5–8] and the spin structure functions of the neutrondeep inelastic scattering [9–11].Quasielastic scattering has been applied to determthe momentum distribution of the proton in the deutero[12] with necessary corrections for the interaction effec[13] and to study these, e0pd reaction mechanism itself[14]: the necessity of including relativistic correctionhas been demonstrated by determining the longitudintransverse interference structure function; details of telectromagnetic coupling to the nuclear currents habeen studied by performing longitudinal-transverse seprations and polarization transfer measurements, andinfluence of final-state interaction (FSI) effects has beisolated by studying the fifth structure function. Howeve0031-9007y99y82(4)y687(4)$15.00nu-ed-olengr-ms-ingwst inonininentssal-hevea-theenr,all of these measurements were performed with unpolaized deuterons. The use of polarized deuterium is advatageous, since one can select polarization observablesare sensitive to small amplitudes that are related to, fexample, the charge form factor of the neutron, or theD-wave admixture in the ground-state wave function [15Here, we report on the first measurement of quasielaselectron scattering from polarized deuterium.It is well known that the tensor force has an importaninfluence on deuteron structure. It introducesD-statecomponents into the predominantlyS-wave ground-statewave function and hence leads to a density distributiothat depends on the spin projectionmz . Because of thetensor part of the nucleon-nucleon interaction and threpulsive core at short distances, the deuteron exhibitstoroidal shape formz ­ 0 and a dumbbell shape formz ­61 (see, e.g., [16]). The spin-dependent momentudensity distributionrmz can be written asr0spd4p­ fR0 1p2 R2d20,0sudg2 1 3fR2d21,0sudg2,r61spd4p­"R0 21p2R2d20,0sud#2198R22s1 2 cos4 ud ,(1)with R0spd andR2spd the usual radial wave functions fororbital angular momentumL ­ 0 andL ­ 2 in momen-tum space, respectively,djm,m0 the rotation functions, and© 1999 The American Physical Society 687VOLUME 82, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 25 JANUARY 1999sonhetothetailonnlymanofoo-ne-omnethec-5tumpe,rr.heralr.ers–ofhels,dntc-g-isthef-4],ramer-hefordu the angle between the polarization axis and the relatmomentump of the two nucleons.The spin-dependent density distribution can be probby quasielastic electron scattering from tensor-polarizdeuterium targets, which yields data complementarythe elastic channel [17–19] where thetotal nuclear cur-rent (i.e., nucleon and meson contributions) is probed.plane-wave impulse approximation (PWIA), thes , e0pdcross section for unpolarized electrons factorizes inpart depending on the off-shell electron-proton cross setion and a part containing the spin-dependent momentdistribution as shown in Eq. (1) [20]. In that case threlative nucleon momentump can be related to the miss-ing momentum of the reaction, defined aspm ­ q 2 p0,with q the momentum transferred in the electron scatteing process andp0 the momentum of the knocked-out proton. In a cross section measurement with tensor-polarizdeuterons one can define the tensor analyzing powerATd :ATd ­s12s1spmd 1 s2spmd 2 2s0spmds1spmd 1 s2spmd 1 s0spmdPWIA­ 22R0spdR2spd 1q12 R22spdR20spd 1 R22spdd20,0sud , (2)with s0 (s6) the cross section measured withmz ­ 0(mz ­ 61) andd20,0 ­32 cos2 u 212 . In the limit whereR2 ø R0, ATd directly relates to the ratioR2yR0. Further-more, in PWIA whenR0 ­ 2p2 R2, thens0 ­ 0 andATdis maximum with a value of1q12 for u ­ 0. Even whenFSI and all other effects are included, the cross sectionexpected to be small for electron scattering from deuterowith mz ­ 0. Similarly, whenR0 ­q12 R2, the PWIAcross section for deuterons withmz ­ 61 vanishes andATd reaches a minimum of2p2.The experiment was performed with a polarized gtarget [21] internal to the AmPS electron storage rinat NIKHEF. A beam current of 120 mA was injectedThe 565 MeV electron beam had a lifetime of abou15 min. An atomic beam source was used to injectflux of 1.1 3 1016 atomsys with two hyperfine states intoa T -shaped storage cell, which was cooled to 100 Korder to further increase the target density. The dawere obtained with Teflon-coated aluminum cells (wathickness25 mm) with diameters of 15 or 20 mm anda length of 400 mm. The resulting target thicknesamounted up to2 3 1013 s2H atomsdycm2. The tensorpolarization of the targetPzz (­ 1 2 3n0, with n0 thefraction of deuterons withmz ­ 0) was varied every10 s betweenP1zz ­ 10.488 6 0.014 6 0.03 and P2zz ­20.893 6 0.027 6 0.052, where the first (second) errorrepresents the statistical (systematic) uncertainty. Ttensor polarization of the deuterium atoms was measuin situ by a polarimeter [22] that analyzes the fractioof the target gas that has been ionized by the traverselectron beam. Two electromagnets were used to gene688iveededtoInac-umer--edisnsasg.taintallsheredningratea magnetic field in the interaction region that allowone to orient the target polarization axis in the electrscattering plane, either parallel or perpendicular to tmomentum transfer. A set of scrapers was employedintercept the halo of the electron beam and thus reduceamount of background from the cell wall.The experimental setup has been described in dein Refs. [21,23], and results for elastic electron-deuterscattering have been presented previously [18]; here oa brief overview is given. Electrons scattered frothe tensor-polarized deuterium gas were detected inelectromagnetic calorimeter, consisting of six layersCsI(Tl) blocks covering a solid angle of 180 msr. Twplastic scintillators, one in front of the CsI(Tl) blocksand one positioned between the first two layers, prvided the electron trigger. The total energy resolutioobtained (about 22 MeV) was sufficient to distinguish btween events from quasielastic scattering and events frpion electroproduction. Two sets of wire chambers, oadjacent to the scattering chamber and one in front offirst trigger scintillator, were used for track reconstrution. The central angle of the electron detector was 3±corresponding to an average transferred three momenof jqj ø 1.7 fm21.The ejected protons were detected in a range telescoconsisting of 15 layers of 1 cm thick plastic scintillatopreceded by a layer of 2 mm thick plastic scintillatoThe trigger was formed by a coincidence between tfirst two layers. The detector was positioned at a centangle of 80± and covered a solid angle of nearly 300 msThe range telescope was preceded by two wire chambfor track reconstruction. Protons in the range of 30100 MeV were detected with an energy resolutionabout 1.5 MeV.Calibration measurements were performed with tkinematically overdetermined reaction1Hse, e0pd. Sincethe calorimeter excludes the pion-production channethe fivefold differential cross section can be obtaineby measuring the electron scattering anglesue, fe, theangles of the ejected protonup , fp, and the energyof the proton. This procedure resulted in an excellemissing-momentum resolution, for a nonmagnetic detetor setup, of6.2 MeVyc as demonstrated in Fig. 1 (toppanel). In the bottom panel of the figure, the missinmomentum spectrum for scattering from deuteriumshown. The data are in reasonable agreement withresult of a Monte Carlo calculation that includes the ofshell electron-proton cross section of de Forest, Jr. [2momentum densities from Bernheimet al. [12], and amodel for the detector phase space. The shaded histogrepresents the background contribution which was detmined by scattering from an empty cell. It is seen that tbackground contributes significantly to the data takenmissing momenta above150 MeVyc.Figure 2 shows the measured asymmetry,ATd , as a func-tion of the angleus between the polarization axis anVOLUME 82, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 25 JANUARY 1999lldf-tatstaford,FIG. 1. Top panel: Missing-momentum spectrum for thkinematically overcomplete reaction1Hse, e0pd. Bottom panel:Missing-momentum spectrum for scattering from deuteriumThe shaded histogram indicates the background from the cwall. The solid histogram shows a Monte Carlo prediction.the missing momentum. Results of measurements wthe polarization axis parallel and perpendicular to the mmentum transfer were combined in this figure. The daare compared to predictions [15] for the Paris potentiThe dashed curve in Fig. 2 represents the results forplane-wave Born approximation (PWBA) which includethe coupling to the neutron, whereas in the solid curve teffects of final-state interaction, meson-exchange (MEandD-isobar (IC) currents, and relativistic corrections aincluded. The spread in kinematics in each bin has betaken into account by applying a Monte Carlo code thinterpolated between a dense grid of calculations that coered the full acceptance of our setup. It is observed ththe calculations describe the data well. Since in PWthe asymmetry is proportional tod20,0 [see Eq. (2)], thezero crossings of the asymmetry are predicted to becosus ­ 6q13 (ø0.58), while without a D-state com-ponent to the ground-state wave function the asymmevanishes. The results for PWBA differ slightly from thisprediction, indicating that for our kinematics the couplinto the neutron is not completely negligible. Furthermorit is demonstrated that FSI effects modify the asymmetmainly for positive values of cosus.e.ellitho-taal.thesheC)reenatv-atIAattryge,ryθ-0.6-0.4-0.200.20.4-1 -0.5 0 0.5 1FIG. 2. ATd as a function of cosus. The dashed curverepresents the result for PWBA, the solid curve for the fucalculation including FSI, MEC, and IC contributions anrelativistic corrections.Figure 3 showsATd as a function of missing momentumin approximately parallel kinematics, i.e., the center-omass angle betweenp0 andq has been restricted (ucmpq ,13±). The results of the full calculation describe the dawell. The inclusion of spin-dependent rescattering effecimproves the description at the lowest missing momenθ-1-0.8-0.6-0.4-0.200.20 50 100 150 200FIG. 3. ATd as a function ofpm for parallel kinematics (i.e.,ucmpq , 13±). The short-dashed curve represents the resultPWBA; in the long-dashed curve FSI effects are also includeand the solid curve represents the full calculation.689VOLUME 82, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 25 JANUARY 1999,(pm . 50 MeVyc), whereD-state contributions are small.Note that the tensor analyzing power is sizable, even atrelatively small missing momenta addressed in the presexperiment. This is due to the fact that an interferenbetween the smallD-state amplitude and the dominanS-state amplitude is probed [see Eq. (2)], whereas in tunpolarized cross section only the sum of the squaresthe S-state andD-state amplitudes enter. Note that sincthe statistical uncertainties dominate, only those are shoin both Figs. 2 and 3.We have investigated the influence of the choicof nucleon-nucleon potential on the calculated tensanalyzing powers. The results forATd calculated with theParis, Bonn, Nijmegen, and Argonne potentials differ bless than 1% for missing momenta below150 MeVyc andtherefore do not influence our conclusions. In additiowe studied the influence of relativistic effects in thcurrent operator.ATd changes by less than 2% when thmodel is modified to not include third- and fourth-ordeterms in pyMp in the current operator and to negleccontributions from the boost operator that translates tinitial-state wave function from the laboratory frame tthe center-of-mass frame.In summary, a polarized deuterium target has succefully been utilized in quasielastic electron scattering. Tesor analyzing powers have been measured for missmomenta up to150 MeVyc. The data are well describedby the present model [15], using the Paris potential, athe tensor analyzing power is dominated by the effecof the D-state contribution. We have shown that thinternal-target technique allows for novel measurementsquasifree scattering from the deuteron, which in the futushould be extended to higher missing momenta, in thegion where the tensor analyzing powers are predictedstrongly depend on the details of the deuteron spin struture [16,25,26].We gratefully acknowledge discussions with SJeschonnek and T. W. Donnelly on factorization issuof the spin-dependentse, e0pd cross section. This workwas supported in part by the Stichting voor FundamenteOnderzoek der Materie (FOM), which is financiallysupported by the Nederlandse Organisatie voor Weteschappelijk Onderzoek (NWO), the Swiss National Foudation, the National Science Foundation under GranNo. PHY-9316221 (Wisconsin), No. PHY-9200435 (Arizona State), and No. HRD-9154080 (Hampton), NW690theentcetheofewneoryn,eertheoss-n-ingndtseofrere-toc-.eseln-n-ts-OGrant No. 713-119, and HCM Grants No. ERBCHBICT-930606 and No. ERB4001GT931472.*Present address: Laboratory for Nuclear ScienceMassachusetts Institute of Technology, Cambridge, MA02139.†Present address: TJNAF, Newport News, VA 23606.‡Present address: University of Illinois, Urbana-Champaign, IL 61801.§Deceased.[1] S. J. Brodsky and G. L. Farrar, Phys. Rev. Lett.31, 1153(1973).[2] J. E. Belzet al., Phys. Rev. Lett.74, 646 (1995).[3] C. E. Carlson, Nucl. Phys.A508, 481c (1990).[4] C. Bochnaet al., Phys. Rev. Lett.81, 4533 (1998).[5] S. Platchkovet al., Nucl. Phys.A510, 740 (1990).[6] T. Edenet al., Phys. Rev. C50, R1749 (1994).[7] F. Klein et al., Nucl. Phys.A623, 323c (1997).[8] E. E. W. Bruinset al., Phys. Rev. Lett.75, 21 (1995).[9] B. Adevaet al., Phys. Lett. B302, 533 (1993).[10] K. Abe et al., Phys. Rev. Lett.75, 25 (1995).[11] HERMES Collaboration, K. Ackerstaffet al., DESYReport No. DESY-PRC-93-06, 1993 (unpublished).[12] M. Bernheimet al., Nucl. Phys.A365, 349 (1981).[13] H. Arenhövel, Nucl. Phys.A384, 287 (1982).[14] S. Gilad, W. Bertozzi, and Z.-L. Zhou, Nucl. Phys.A631,276c (1998), and references therein.[15] H. Arenhövel, W. Leidemann, and E. L. Tomusiak, Phys.Rev. C52, 1232 (1995).[16] J. L. Forestet al., Phys. Rev. C54, 646 (1996).[17] I. The et al., Phys. Rev. Lett.67, 173 (1991).[18] M. Ferro-Luzziet al., Phys. Rev. Lett.77, 2630 (1996).[19] TJNAF experiment E94-018, S. Kox and E. J. Beise,spokespersons.[20] J. A. Caballero, T. W. Donnelly, and G. I. Poulis, Nucl.Phys.A555, 709 (1993).[21] Z.-L. Zhou et al., Nucl. Instrum. Methods. Phys. Res.,Sect. A378, 40 (1996).[22] Z.-L. Zhou et al., Nucl. Instrum. Methods. Phys. Res.,Sect. A379, 211 (1996).[23] E. Passchieret al., Nucl. Instrum. Methods. Phys. Res.,Sect. A387, 471 (1997).[24] T. de Forest, Jr., Nucl. Phys.A392, 232 (1983).[25] L. L. Frankfurt and M. I. Strikman, Nucl. Phys.A405, 557(1983).[26] A. Bianconi, S. Jeschonnek, N. N. Nikolaev, and B. G.Zakharov, Phys. Rev. C53, 576 (1996).

We report on a first measurement of tensor analyzing powers in quasielastic electron-deuteron scattering at an average three-momentum transfer of 1.7fm-1. Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150MeV/c with a tensor polarized 2H target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions

Z. L. Zhou

M. Ferro Luzzi

H. Arenhövel

J. van den Brand

H. Bulten

S. Dolfini

D. Higinbotham

C. de Jager

D. de Lange

M. Miller

H. Poolman

S. Popov

J. Steijger

TAIUTI, MAURO GINO

Archivio istituzionale della ricerca - Università di Genova

Tensor Analyzing Powers for Quasielastic Electron Scattering from Deuterium

Crossref

We report on a first measurement of tensor analyzing powers in quasi-elastic electron-deuteron scattering at an average three-momentum transfer of 1.7 fm{sup -1}. Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150 MeV/c with a tensor polarized {sup 2}H target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions

Zhou, Z.-L.

Arenhoevel, H.

Bommel, R. van

Brand, J.F.J. van den

ger, C.W. de Ja

Lange, D.J. de

lenko, D. Niko

i, M. Ripan

Vries, H. de

UNT (University of North Texas) Digital Library

VOLUME 82, NUMBER 4 PHY S I CA L REV I EW LE T T ER S 25 JANUARY 1999Tensor Analyzing Powers for Quasielastic Electron Scattering from DeuteriumZ.-L. Zhou,1,* M. Bouwhuis,2 M. Ferro-Luzzi,2,3 E. Passchier,2 R. Alarcon,4 M. Anghinolfi,5 H. Arenhövel,6R. van Bommel,2 T. Botto,2 J. F. J. van den Brand,1,7 H. J. Bulten,1,7 S. Choi,4 J. Comfort,4 S.M. Dolfini,4 R. Ent,8C. Gaulard,4 D.W. Higinbotham,9 C.W. de Jager,2,† E. Konstantinov,10 J. Lang,3 W. Leidemann,11 D. J. de Lange,2M.A. Miller,1,‡ D. Nikolenko,10 N. Papadakis,2 I. Passchier,2 H.R. Poolman,2 S.G. Popov,10,§ I. Rachek,10 M. Ripani,5E. Six,4 J. J.M. Steijger,2 M. Taiuti,5 O. Unal,1 N. Vodinas,2 and H. de Vries21Department of Physics, University of Wisconsin, Madison, Wisconsin 537062NIKHEF, P.O. Box 41882, NL-1009 DB Amsterdam, The Netherlands3Institut für Teilchenphysik, Eidgenössische Technische Hochschule, CH-8093 Zürich, Switzerland4Department of Physics, Arizona State University, Tempe, Arizona 852875Istituto Nazionale di Fisica Nucleare (INFN), I-16146 Genova, Italy6Institut für Kernphysik, Johannes Gutenberg Universität, D-55099 Mainz, Germany7Department of Physics and Astronomy, Vrije Universiteit, NL-1081 HV Amsterdam, The Netherlands8TJNAF, Newport News, Virginia 23606,and Department of Physics, Hampton University, Hampton, Virginia 236689Department of Physics, University of Virginia, Charlottesville, Virginia 2290110Budker Institute for Nuclear Physics, Novosibirsk, 630090 Russian Federation11Dipartimento di Fisica and INFN (gruppo collegato di Trento), Università di Trento, I-38050 Povo (Trento), Italy(Received 18 September 1998)We report on a first measurement of tensor analyzing powers in quasielastic electron-deuteronscattering at an average three-momentum transfer of 1.7 fm21. Data sensitive to the spin-dependentnucleon density in the deuteron were obtained for missing momenta up to 150 MeVyc with a tensorpolarized 2H target internal to an electron storage ring. The data are well described by a calculationthat includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-orderrelativistic contributions. [S0031-9007(98)08241-6]PACS numbers: 25.30.Fj, 21.45.+v, 24.70.+s, 29.25.PjThe deuteron is often used as a benchmark to test nu-clear theory, since reliable calculations can be performedin both nonrelativistic and relativistic models. Observ-ables such as its binding energy, static magnetic dipoleand charge quadrupole moment, asymptotic DyS ratio,and the elastic electromagnetic form factors place strongconstraints on models for the nuclear interaction. Fur-thermore, the deuteron is one of the few nuclear systemsfor which predictions based on quantum chromodynam-ics have been made and tested [1–4]. The understandingof the deuteron has progressed to a level which allowsthe deuteron to be used as an effective neutron target instudies of the electromagnetic form factors of the neutron[5–8] and the spin structure functions of the neutron indeep inelastic scattering [9–11].Quasielastic scattering has been applied to determinethe momentum distribution of the proton in the deuteron[12] with necessary corrections for the interaction effects[13] and to study the se, e0pd reaction mechanism itself[14]: the necessity of including relativistic correctionshas been demonstrated by determining the longitudinal-transverse interference structure function; details of theelectromagnetic coupling to the nuclear currents havebeen studied by performing longitudinal-transverse sepa-rations and polarization transfer measurements, and theinfluence of final-state interaction (FSI) effects has beenisolated by studying the fifth structure function. However,0031-9007y99y82(4)y687(4)$15.00all of these measurements were performed with unpolar-ized deuterons. The use of polarized deuterium is advan-tageous, since one can select polarization observables thatare sensitive to small amplitudes that are related to, forexample, the charge form factor of the neutron, or the D-wave admixture in the ground-state wave function [15].Here, we report on the first measurement of quasielasticelectron scattering from polarized deuterium.It is well known that the tensor force has an importantinfluence on deuteron structure. It introduces D-statecomponents into the predominantly S-wave ground-statewave function and hence leads to a density distributionthat depends on the spin projection mz . Because of thetensor part of the nucleon-nucleon interaction and therepulsive core at short distances, the deuteron exhibits atoroidal shape for mz ­ 0 and a dumbbell shape for mz ­61 (see, e.g., [16]). The spin-dependent momentumdensity distribution rmz can be written asr0spd4p­ fR0 1p2 R2d20,0sudg2 1 3fR2d21,0sudg2,r61spd4p­"R0 21p2R2d20,0sud#2198R22s1 2 cos4 ud ,(1)with R0spd and R2spd the usual radial wave functions fororbital angular momentum L ­ 0 and L ­ 2 in momen-tum space, respectively, djm,m0 the rotation functions, and© 1999 The American Physical Society 687VOLUME 82, NUMBER 4 PHY S I CA L REV I EW LE T T ER S 25 JANUARY 1999u the angle between the polarization axis and the relativemomentum p of the two nucleons.The spin-dependent density distribution can be probedby quasielastic electron scattering from tensor-polarizeddeuterium targets, which yields data complementary tothe elastic channel [17–19] where the total nuclear cur-rent (i.e., nucleon and meson contributions) is probed. Inplane-wave impulse approximation (PWIA), the se, e0pdcross section for unpolarized electrons factorizes in apart depending on the off-shell electron-proton cross sec-tion and a part containing the spin-dependent momentumdistribution as shown in Eq. (1) [20]. In that case therelative nucleon momentum p can be related to the miss-ing momentum of the reaction, defined as pm ­ q 2 p0,with q the momentum transferred in the electron scatter-ing process and p0 the momentum of the knocked-out pro-ton. In a cross section measurement with tensor-polarizeddeuterons one can define the tensor analyzing power ATd :ATd ­s12s1spmd 1 s2spmd 2 2s0spmds1spmd 1 s2spmd 1 s0spmdPWIA­ 22R0spdR2spd 1q12 R22spdR20spd 1 R22spdd20,0sud , (2)with s0 (s6) the cross section measured with mz ­ 0(mz ­ 61) and d20,0 ­ 32 cos2 u 2 12 . In the limit whereR2 ¿ R0, ATd directly relates to the ratio R2yR0. Further-more, in PWIA when R0 ­ 2p2 R2, then s0 ­ 0 and ATdis maximum with a value of 1q12 for u ­ 0. Even whenFSI and all other effects are included, the cross section isexpected to be small for electron scattering from deuteronswith mz ­ 0. Similarly, when R0 ­q12 R2, the PWIAcross section for deuterons with mz ­ 61 vanishes andATd reaches a minimum of 2p2.The experiment was performed with a polarized gastarget [21] internal to the AmPS electron storage ringat NIKHEF. A beam current of 120 mA was injected.The 565 MeV electron beam had a lifetime of about15 min. An atomic beam source was used to inject aflux of 1.1 3 1016 atomsys with two hyperfine states intoa T -shaped storage cell, which was cooled to 100 K inorder to further increase the target density. The datawere obtained with Teflon-coated aluminum cells (wallthickness 25 mm) with diameters of 15 or 20 mm anda length of 400 mm. The resulting target thicknessamounted up to 2 3 1013 s2H atomsdycm2. The tensorpolarization of the target Pzz (­ 1 2 3n0, with n0 thefraction of deuterons with mz ­ 0) was varied every10 s between P1zz ­ 10.488 6 0.014 6 0.03 and P2zz ­20.893 6 0.027 6 0.052, where the first (second) errorrepresents the statistical (systematic) uncertainty. Thetensor polarization of the deuterium atoms was measuredin situ by a polarimeter [22] that analyzes the fractionof the target gas that has been ionized by the traversingelectron beam. Two electromagnets were used to generate688a magnetic field in the interaction region that allowsone to orient the target polarization axis in the electronscattering plane, either parallel or perpendicular to themomentum transfer. A set of scrapers was employed tointercept the halo of the electron beam and thus reduce theamount of background from the cell wall.The experimental setup has been described in detailin Refs. [21,23], and results for elastic electron-deuteronscattering have been presented previously [18]; here onlya brief overview is given. Electrons scattered fromthe tensor-polarized deuterium gas were detected in anelectromagnetic calorimeter, consisting of six layers ofCsI(Tl) blocks covering a solid angle of 180 msr. Twoplastic scintillators, one in front of the CsI(Tl) blocksand one positioned between the first two layers, pro-vided the electron trigger. The total energy resolutionobtained (about 22 MeV) was sufficient to distinguish be-tween events from quasielastic scattering and events frompion electroproduction. Two sets of wire chambers, oneadjacent to the scattering chamber and one in front of thefirst trigger scintillator, were used for track reconstruc-tion. The central angle of the electron detector was 35–corresponding to an average transferred three momentumof jqj ø 1.7 fm21.The ejected protons were detected in a range telescope,consisting of 15 layers of 1 cm thick plastic scintillatorpreceded by a layer of 2 mm thick plastic scintillator.The trigger was formed by a coincidence between thefirst two layers. The detector was positioned at a centralangle of 80– and covered a solid angle of nearly 300 msr.The range telescope was preceded by two wire chambersfor track reconstruction. Protons in the range of 30–100 MeV were detected with an energy resolution ofabout 1.5 MeV.Calibration measurements were performed with thekinematically overdetermined reaction 1Hse, e0pd. Sincethe calorimeter excludes the pion-production channels,the fivefold differential cross section can be obtainedby measuring the electron scattering angles ue, fe, theangles of the ejected proton up , fp, and the energyof the proton. This procedure resulted in an excellentmissing-momentum resolution, for a nonmagnetic detec-tor setup, of 6.2 MeVyc as demonstrated in Fig. 1 (toppanel). In the bottom panel of the figure, the missing-momentum spectrum for scattering from deuterium isshown. The data are in reasonable agreement with theresult of a Monte Carlo calculation that includes the off-shell electron-proton cross section of de Forest, Jr. [24],momentum densities from Bernheim et al. [12], and amodel for the detector phase space. The shaded histogramrepresents the background contribution which was deter-mined by scattering from an empty cell. It is seen that thebackground contributes significantly to the data taken formissing momenta above 150 MeVyc.Figure 2 shows the measured asymmetry, ATd , as a func-tion of the angle us between the polarization axis andVOLUME 82, NUMBER 4 PHY S I CA L REV I EW LE T T ER S 25 JANUARY 1999FIG. 1. Top panel: Missing-momentum spectrum for thekinematically overcomplete reaction 1Hse, e0pd. Bottom panel:Missing-momentum spectrum for scattering from deuterium.The shaded histogram indicates the background from the cellwall. The solid histogram shows a Monte Carlo prediction.the missing momentum. Results of measurements withthe polarization axis parallel and perpendicular to the mo-mentum transfer were combined in this figure. The dataare compared to predictions [15] for the Paris potential.The dashed curve in Fig. 2 represents the results for theplane-wave Born approximation (PWBA) which includesthe coupling to the neutron, whereas in the solid curve theeffects of final-state interaction, meson-exchange (MEC)and D-isobar (IC) currents, and relativistic corrections areincluded. The spread in kinematics in each bin has beentaken into account by applying a Monte Carlo code thatinterpolated between a dense grid of calculations that cov-ered the full acceptance of our setup. It is observed thatthe calculations describe the data well. Since in PWIAthe asymmetry is proportional to d20,0 [see Eq. (2)], thezero crossings of the asymmetry are predicted to be atcos us ­ 6q13 (ø0.58), while without a D-state com-ponent to the ground-state wave function the asymmetryvanishes. The results for PWBA differ slightly from thisprediction, indicating that for our kinematics the couplingto the neutron is not completely negligible. Furthermore,it is demonstrated that FSI effects modify the asymmetrymainly for positive values of cos us.θ-0.6-0.4-0.200.20.4-1 -0.5 0 0.5 1FIG. 2. ATd as a function of cos us. The dashed curverepresents the result for PWBA, the solid curve for the fullcalculation including FSI, MEC, and IC contributions andrelativistic corrections.Figure 3 shows ATd as a function of missing momentumin approximately parallel kinematics, i.e., the center-of-mass angle between p0 and q has been restricted (ucmpq ,13–). The results of the full calculation describe the datawell. The inclusion of spin-dependent rescattering effectsimproves the description at the lowest missing momentaθ-1-0.8-0.6-0.4-0.200.20 50 100 150 200FIG. 3. ATd as a function of pm for parallel kinematics (i.e.,ucmpq , 13–). The short-dashed curve represents the result forPWBA; in the long-dashed curve FSI effects are also included,and the solid curve represents the full calculation.689VOLUME 82, NUMBER 4 PHY S I CA L REV I EW LE T T ER S 25 JANUARY 1999(pm . 50 MeVyc), where D-state contributions are small.Note that the tensor analyzing power is sizable, even at therelatively small missing momenta addressed in the presentexperiment. This is due to the fact that an interferencebetween the small D-state amplitude and the dominantS-state amplitude is probed [see Eq. (2)], whereas in theunpolarized cross section only the sum of the squares ofthe S-state and D-state amplitudes enter. Note that sincethe statistical uncertainties dominate, only those are shownin both Figs. 2 and 3.We have investigated the influence of the choiceof nucleon-nucleon potential on the calculated tensoranalyzing powers. The results for ATd calculated with theParis, Bonn, Nijmegen, and Argonne potentials differ byless than 1% for missing momenta below 150 MeVyc andtherefore do not influence our conclusions. In addition,we studied the influence of relativistic effects in thecurrent operator. ATd changes by less than 2% when themodel is modified to not include third- and fourth-orderterms in pyMp in the current operator and to neglectcontributions from the boost operator that translates theinitial-state wave function from the laboratory frame tothe center-of-mass frame.In summary, a polarized deuterium target has success-fully been utilized in quasielastic electron scattering. Ten-sor analyzing powers have been measured for missingmomenta up to 150 MeVyc. The data are well describedby the present model [15], using the Paris potential, andthe tensor analyzing power is dominated by the effectsof the D-state contribution. We have shown that theinternal-target technique allows for novel measurements ofquasifree scattering from the deuteron, which in the futureshould be extended to higher missing momenta, in the re-gion where the tensor analyzing powers are predicted tostrongly depend on the details of the deuteron spin struc-ture [16,25,26].We gratefully acknowledge discussions with S.Jeschonnek and T.W. Donnelly on factorization issuesof the spin-dependent se, e0pd cross section. This workwas supported in part by the Stichting voor FundamenteelOnderzoek der Materie (FOM), which is financiallysupported by the Nederlandse Organisatie voor Weten-schappelijk Onderzoek (NWO), the Swiss National Foun-dation, the National Science Foundation under GrantsNo. PHY-9316221 (Wisconsin), No. PHY-9200435 (Ari-zona State), and No. HRD-9154080 (Hampton), NWO690Grant No. 713-119, and HCM Grants No. ERBCHBICT-930606 and No. ERB4001GT931472.*Present address: Laboratory for Nuclear Science,Massachusetts Institute of Technology, Cambridge, MA02139.†Present address: TJNAF, Newport News, VA 23606.‡Present address: University of Illinois, Urbana-Champaign, IL 61801.§Deceased.[1] S. J. Brodsky and G. L. Farrar, Phys. Rev. Lett. 31, 1153(1973).[2] J. E. Belz et al., Phys. Rev. Lett. 74, 646 (1995).[3] C. E. Carlson, Nucl. Phys. A508, 481c (1990).[4] C. Bochna et al., Phys. Rev. Lett. 81, 4533 (1998).[5] S. Platchkov et al., Nucl. Phys. A510, 740 (1990).[6] T. Eden et al., Phys. Rev. C 50, R1749 (1994).[7] F. Klein et al., Nucl. Phys. A623, 323c (1997).[8] E. E.W. Bruins et al., Phys. Rev. Lett. 75, 21 (1995).[9] B. Adeva et al., Phys. Lett. B 302, 533 (1993).[10] K. Abe et al., Phys. Rev. Lett. 75, 25 (1995).[11] HERMES Collaboration, K. Ackerstaff et al., DESYReport No. DESY-PRC-93-06, 1993 (unpublished).[12] M. Bernheim et al., Nucl. Phys. A365, 349 (1981).[13] H. Arenhövel, Nucl. Phys. A384, 287 (1982).[14] S. Gilad, W. Bertozzi, and Z.-L. Zhou, Nucl. Phys. A631,276c (1998), and references therein.[15] H. Arenhövel, W. Leidemann, and E. L. Tomusiak, Phys.Rev. C 52, 1232 (1995).[16] J. L. Forest et al., Phys. Rev. C 54, 646 (1996).[17] I. The et al., Phys. Rev. Lett. 67, 173 (1991).[18] M. Ferro-Luzzi et al., Phys. Rev. Lett. 77, 2630 (1996).[19] TJNAF experiment E94-018, S. Kox and E. J. Beise,spokespersons.[20] J. A. Caballero, T.W. Donnelly, and G. I. Poulis, Nucl.Phys. A555, 709 (1993).[21] Z.-L. Zhou et al., Nucl. Instrum. Methods. Phys. Res.,Sect. A 378, 40 (1996).[22] Z.-L. Zhou et al., Nucl. Instrum. Methods. Phys. Res.,Sect. A 379, 211 (1996).[23] E. Passchier et al., Nucl. Instrum. Methods. Phys. Res.,Sect. A 387, 471 (1997).[24] T. de Forest, Jr., Nucl. Phys. A392, 232 (1983).[25] L. L. Frankfurt and M. I. Strikman, Nucl. Phys. A405, 557(1983).[26] A. Bianconi, S. Jeschonnek, N.N. Nikolaev, and B.G.Zakharov, Phys. Rev. C 53, 576 (1996).

Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

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Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from
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Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

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