We report new measurements of the neutron–deuteron elastic scattering cross section at energies from 135 to 250 MeV and center-of-mass angles from 80° to 130°. Cross sections for neutron-proton elastic scattering were also measured with the same experimental setup for normalization purposes. Our nd cross section results are compared with predictions based on Faddeev calculations including three-nucleon forces, and with cross sections measured with charged particle and neutron beams at comparable energies

Akdogan, Taylan

Ertan, Erol

Kovash, Michael A.

Matthews, June L

Few-Body Systems

DSpace@MIT

Few-Body Syst (2013) 54:1339–1341DOI 10.1007/s00601-013-0638-9Erol Ertan · Taylan Akdogan · June L. Matthews ·Michael A. KovashCross Sections for Neutron–Deuteron Elastic Scatteringin the Energy Range 135–250 MeVReceived: 2 October 2012 / Accepted: 11 January 2013 / Published online: 8 February 2013© Springer-Verlag Wien 2013Abstract We report new measurements of the neutron–deuteron elastic scattering cross section at energiesfrom 135 to 250 MeV and center-of-mass angles from 80◦ to 130◦. Cross sections for neutron-proton elasticscattering were also measured with the same experimental setup for normalization purposes. Our nd crosssection results are compared with predictions based on Faddeev calculations including three-nucleon forces,and with cross sections measured with charged particle and neutron beams at comparable energies.1 IntroductionThe study of 3N systems has been enhanced by the growing database of precise measurements on two-nucleonsystems [1], and the ability of modern potential models to provide accurate predictions of nucleon–nucleonscattering observables [2–5]. Furthermore, modern computational techniques have made it possible to calculatescattering cross sections and spin observables in three-nucleon systems for any kinematical configuration usingthe Faddeev formalism [6], allowing the identification of experiments with strong sensitivity to the effects ofthree-nucleon forces (3NF).Most of the previous experiments have been carried out with charged particle beams, necessitating theconsideration of Coulomb effects on the cross section. Also, with the exception of the KVI work [7,8] andthe early work of Igo et al. [9], previous measurements have been performed at a single energy. Moreover,there are still some lingering uncertainties in the magnitude and shape of the differential cross section at 135MeV [10].These factors have motivated the present measurement: a study of the neutron–deuteron elastic scatteringcross section, at large angles where the sensitivity to 3NF is greatest, over a broad range of incident neutronenergies.Presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20–25 August, 2012, Fukuoka, Japan.E. Ertan (B) · T. AkdoganDepartment of Physics, Bogazici University, 34342 Bebek, Istanbul, TurkeyTel: +90-212-359 6604Fax: +90-212-287 2466E-mail: ertan.erol@gmail.com; erol.ertan@boun.edu.trJ.L. MatthewsDepartment of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology,Cambridge, MA 02139, USAM.A. KovashDepartment of Physics and Astronomy, University of Kentucky,Lexington, KY 40506, USA1340 E. Ertan et al.Since the absolute normalization of neutron scattering experiments can be a difficult problem, the npscattering cross section was also measured using the same experimental setup. The np data were then used tonormalize the measured nd cross sections.2 The ExperimentThe experiment was carried out at the Los Alamos Neutron Science Center (LANSCE) at the Los AlamosNational Laboratory, Los Alamos, New Mexico. Neutrons were produced as spallation products from an800 MeV H− beam incident on a bare tungsten target. The beam passes through a 238U foil fission ionizationchamber [11] that monitored the beam flux as a function of neutron energy. Approximately 1 m downstreamfrom the fission chamber, the beam impinged on a cryogenic target cell containing either liquid deuterium(LD2) or liquid hydrogen (LH2). Scattered neutrons and recoiling charged particles were observed in coinci-dence. Protons and deuterons were detected by five telescopes, each consisting of a thin E plastic scintillatorbacked by a pure CsI calorimeter. These detectors were positioned with their front faces 100 cm from thecenter of the target, at mean laboratory angles of θlab = 24◦, 30◦, 36◦, 42◦ and 48◦. The scattered neutronswere detected with five plastic scintillator bars, each 10 cm high × 10 cm thick × 200 cm wide which spanneda laboratory angle range from 34◦ to 108◦. Empty-target runs were interspersed throughout the experiment toprovide a measure of background. The target was filled with LD2 for the nd elastic scattering cross-sectionmeasurements and with LH2 for normalization purposes.3 Data AnalysisThe analysis was performed in two phases: neutron–proton and neutron–deutron elastic cross-section analysis.For the former, LH2 target was used and the data were analyzed with the proton-singles trigger. Thus, theneutron information was not used which eliminated any uncertainty in neutron detection efficiency. The back-ground subtraction was achieved using empty target data. Then the obtained cross-sections were normalizedFig. 1 The cross-section results. The experimental data and the theoretical work prior to this study is taken from [12,8,10,13,14,9,15,16] and [17,4,5,18], respectively.Cross Sections for Neutron–Deuteron Elastic Scattering 1341with respect to the SAID multi-energy partial wave analysis [1] to handle the uncertainties arising from targetthickness and unknown uranium fission cross-section. This normalization factor was later used in the deuteronanalysis for which the target is LD2. This time the coincidence data were used since the timing informationof the neutrons is crucial in order to get rid of the background. As a side note, the needed neutron efficienciesfor coincidence analysis was also measured using the experimental data and the measurements are in goodagreement with the Monte Carlo simulations. Lastly, the correction due to the weak polarization of the beamwas applied.4 ResultsThe results for 135, 150 and 250 MeV incident beam energy are presented in Fig. 1 along with the previousexperiments and theoretical predictions for the corresponding energies. In addition to the statistical errors,systematic errors varied from 16 to 24%. The latter were due to uncertainties in the np normalization, themeasured neutron detection efficiency, the polarization correction, and the interpolation procedure used toobtain the uranium fission cross-section.5 ConclusionIn this study, the differential cross section for nd elastic scattering was extracted in a continuous incident neu-tron energy range from 135 to 250 MeV, by detecting scattered neutrons and recoil deuterons in coincidence,with the aim of elucidating the contribution of three-nucleon forces (3NF), in particular the energy depen-dence of this effect. The current data are in good agreement with previous measurements. At angles near thecross section minimum, where the 3NF contribution is most important, our results generally favor calculationswhich include three-nucleon forces. The 3NF effect could be further tested by confronting the present datawith theoretical predictions for the differential cross section at fixed angles as a function of incident neutronenergy.References1. Arndt, R.A., Strakovsky, I.I., Workman, R.L.: Nucleon-nucleon elastic scattering to 3 gev. Phys. Rev. D 62, 034005 (2000)2. Stoks, V., de Swart, J.J.: Comparison of potential models with the pp scattering data below 350 (m)e(v). Phys. Rev.C 47, 761 (1993)3. Wiringa, R.B., Stoks, V.G.J., Schiavilla, R.: Accurate nucleon-nucleon potential with charge-independence breaking. Phys.Rev. C 51, 38 (1995)4. Machleidt, R.: High-precision, charge-dependent bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001)5. Deltuva, A., Machleidt, R., Sauer, P.U.: Realistic two-baryon potential coupling two- nucleon and nucleon–isobar states: Fitand applications to three-nucleon system. Phys. Rev. C 68, 024005 (2003)6. Glockle, W. et al.: The three-nucleon continuum: achievements, challenges and applications. Phys. Rep. 274, 107 (1996)7. Ermisch, K. et al.: Systematic investigation of the elastic proton-deuteron differential cross section at intermediate ener-gies. Phys. Rev. C 68, 051001(R) (2003)8. Ermisch, K. et al.: Systematic investigation of three-nucleon force effects in elastic scattering of polarized protons fromdeuterons at intermediate energies. Phys. Rev. C 71, 064004 (2005)9. Igo, G. et al.: Large-angle elastic scattering of deuterons from hydrogen: Tk = 433, 362, 291M eV. Nucl. Phys. A 195, 33–56 (1972)10. Ramazani-Moghaddam-Arani, A. et al.: Elastic proton-deuteron elastic scattering at intermediate energies. Phys. Rev.C 78, 014006 (2008)11. Wender, S.A. et al.: A fission ionization detector for neutron flux measurements at a spallation source. Nucl. Inst. MethodA 336, 226 (1993)12. Sakai, H. et al: Precise measurement of dp elastic scattering at 270 MeV and three- nucleon force effects. Phys. Rev. Lett.84(23) (2000)13. Palmieri, J.N.: Neutron-deuteron scattering at 152 MeV. Nucl. Phys. A 188 (1972)14. Postma, H., Wilson, R.: Elastic scattering of 146-mev polarized protons by deuterons. Phys. Rev. 121, 1229–1244 (1961)15. Hatanaka, A. et al.: Cross section and complete set of proton spin observables in pd elastic scattering at 250 MeV. Phys.Rev. C 66, 044002 (2002)16. Maeda, Y. et al.: Differential cross section and analyzing power measurements for nd elastic scattering at 248 MeV. Phys.Rev. C 76, 014004 (2007)17. Witala, H. et al.: Cross section minima in elastic nd scattering: Possible evidence for three- nucleon force effects. Phys. Rev.Lett. 81, 1183 (1998)18. Witala, H. et al.: Three-nucleon force in relativistic three-nucleon faddeev calculations. Phys. Rev. C 83, 044001 (2011)

Cross Sections for Neutron–Deuteron Elastic Scattering in the Energy Range 135–250 MeV

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Cross Sections for Neutron–Deuteron Elastic Scattering in the Energy Range 135–250 MeV

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