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Few-Body Systems

, 60:39 | Cite as

Two-Pion Exchange Three-Nucleon Force Effects in Elastic Nucleon–Deuteron Scattering Cross Sections

  • Souichi IshikawaEmail author
Article
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Part of the following topical collections:
  1. Ludwig Faddeev Memorial Issue

Abstract

Differential cross sections for elastic nucleon–deuteron scattering at intermediate energies are calculated by solving the Faddeev equation in coordinate space using interaction models consisting of a two-nucleon potential and three-nucleon potentials based on the exchange of two pions among three nucleons. Attractive effects of the pion-exchange at medium range region in the three-nucleon potential are taken into account by using a larger cutoff mass parameter and by adding phenomenological repulsive three-nucleon potentials as a counterpart. It is shown that these effects increase the cross sections at backward angles, which tends to reduce discrepancies between theoretical calculations and experimental data.

Notes

References

  1. 1.
    J.-I. Fujita, H. Miyazawa, Pion theory of three-body forces. Prog. Thoer. Phys. 17, 360 (1957)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    S.A. Coon, M.D. Scadron, P.C. McNamee, B.R. Barrett, D.W.E. Blatt, B.H.J. McKellar, The two-pion-exchange three-nucleon potential and nuclear matter. Nucl. Phys. A 317, 242 (1979)ADSCrossRefGoogle Scholar
  3. 3.
    S.A. Coon, W. Glöckle, Two-pion-exchange three-nucleon potential: partial wave analysis in momentum space. Phys. Rev. C 23, 1790 (1981)ADSCrossRefGoogle Scholar
  4. 4.
    S.A. Coon, H.K. Han, Reworking the Tucson-Melbourne three-nucleon potential. Few Body Syst. 30, 131 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    H.T. Coelho, T.K. Das, M.R. Robilotta, Two-pion-exchange three-nucleon force and the \({}^{3}\)H and \({}^{3}\)He nuclei. Phys. Rev. C 28, 1812 (1983)ADSCrossRefGoogle Scholar
  6. 6.
    M.R. Robilotta, H.T. Coelho, Taming the two-pion exchange three-nucleon potential. Nucl. Phys. A 460, 645 (1986)ADSCrossRefGoogle Scholar
  7. 7.
    S. Ishikawa, M.R. Robilotta, Two-pion exchange three-nucleon potential: \(O(q^4)\) chiral expansion. Phys. Rev. C 76, 014006 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    H. Witała, W. Glöckle, D. Hüber, J. Golak, H. Kamada, The cross section minima in elastic \(Nd\) scattering: possible evidence for three nucleon force effects. Phys. Rev. Lett. 81, 1183 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    H. Witała, J. Golak, W. Glöckle, H. Kamada, Relativistic effects in neutron–deuteron elastic scattering. Phys. Rev. C 71, 054001 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    L.D. Faddeev, Scattering theory for a three-particle system. Zh. Eksp. Teor. Fiz. 39, 1459 (1961). [English transl.: Sov. Phys. JETP 12, 1014 (1961)]Google Scholar
  11. 11.
    T. Sasakawa, S. Ishikawa, Triton binding energy and three-nucleon potential. Few Body Syst. 1, 3 (1986)ADSCrossRefGoogle Scholar
  12. 12.
    S. Ishikawa, Method of continued fractions with application to three-nucleon problems. Nucl. Phys. A 463, 145c (1987)ADSCrossRefGoogle Scholar
  13. 13.
    S. Ishikawa, Low-energy proton–deuteron scattering with a Coulomb modified Faddeev equation. Few Body Syst. 32, 229 (2003)ADSGoogle Scholar
  14. 14.
    S. Ishikawa, Operation of the Faddeev kernel in configuration space. Few Body Syst. 40, 145 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    S. Ishikawa, Coordinate space proton–deuteron scattering calculations including Coulomb force effects. Phys. Rev. C 80, 054002 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    S. Ishikawa, Three-body calculations of the triple-\(\alpha \) reaction. Phys. Rev. C 87, 055804 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Accurate nucleon–nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    R. Machleidt, High-precision, charge-dependent Bonn nucleon–nucleon potential. Phys. Rev. C 63, 024001 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    S. Ishikawa, M. Tanifuji, Y. Iseri, Central and tensor components of three-nucleon forces in low-energy proton–deuteron scattering. Phys. Rev. C 67, 061001(R) (2003)ADSCrossRefGoogle Scholar
  20. 20.
    K. Sekiguchi et al., Complete set of precise deuteron analyzing powers at intermediate energies: comparison with modern nuclear force predictions. Phys. Rev. C 65, 034003 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    K. Ermisch et al., Systematic investigation of the elastic proton–deuteron differential cross section at intermediate energies. Phys. Rev. C 68, 051001(R) (2003)ADSCrossRefGoogle Scholar
  22. 22.
    H. Shimizu et al., Analyzing powers and cross sections in elastic \(p\)-\(d\) scattering at 65 MeV. Nucl. Phys. A 382, 242 (1982)ADSCrossRefGoogle Scholar
  23. 23.
    K. Sekiguchi et al., Resolving the discrepancy of 135 MeV pd elastic scattering cross sections and relativistic effects. Phys. Rev. Lett. 95, 162301 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    A. Ramazani-Moghaddam-Arani et al., Elastic proton–deuteron scattering at intermediate energies. Phys. Rev. C 78, 014006 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    K. Kuroda, A. Michalowicz, M. Poulet, Mesure de la section efficace differentielle de diffusion proton–deuton a 155 MeV. Phys. Lett. 13, 67 (1964)ADSCrossRefGoogle Scholar
  26. 26.
    K. Hatanaka et al., Cross section and complete set of proton spin observables in \(pd\) elastic scattering at 250 MeV. Phys. Rev. C 66, 044002 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    H.R. Amir-Ahmadi et al., Three-nucleon force effects in cross section and spin observables of elastic deuteron–proton scattering at 90 MeV/nucleon. Phys. Rev. C 75, 041001(R) (2007)ADSCrossRefGoogle Scholar
  28. 28.
    H. Postma, R. Wilson, Elastic scattering of 146-MeV polarized protons. Phys. Rev. 121, 1229 (1961)ADSCrossRefGoogle Scholar
  29. 29.
    G. Igo et al., Large-angle elastic scattering of deuterons from hydrogen: \(T_k\) = 433, 362 and 291 MeV. Nucl. Phys. A 195, 33 (1972)ADSCrossRefGoogle Scholar
  30. 30.
    P. Mermod et al., Search for three-body force effects in neutron–deuteron scattering at 95 MeV. Phys. Lett. B 597, 243 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    P. Mermod et al., Evidence of three-body force effects in neutron–deuteron scattering at 95 MeV. Phys. Rev. C 72, 061002(R) (2005)ADSCrossRefGoogle Scholar
  32. 32.
    E. Ertan et al., Cross sections for neutron–deuteron elastic scattering in the energy range 135–250 MeV. Phys. Rev. C 87, 034003 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    Y. Maeda et al., Differential cross section and analyzing power measurements for \(nd\) elastic scattering at 248 MeV. Phys. Rev. C 76, 014004 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    S. Binder et al., Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon–nucleon forces. Phys. Rev. C 98, 014002 (2018)ADSCrossRefGoogle Scholar
  35. 35.
    E. Epelbaum et al., Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces. arXiv:1807.02848 [nucl-th]
  36. 36.
    M. Piarulli et al., Light-nuclei spectra from chiral dynamics. Phys. Rev. Lett. 120, 052503 (2018)ADSCrossRefGoogle Scholar
  37. 37.
    B.S. Pudliner, V.R. Pandharipande, J. Carlson, R.B. Wiringa, Quantum Monte Carlo calculations of \(A \le 6\) nuclei. Phys. Rev. Lett. 74, 4396 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    S.C. Pieper, V.R. Pandharipande, R.B. Wiringa, J. Carlson, Realistic models of pion-exchange three-nucleon interactions. Phys. Rev. C 64, 014001 (2001)ADSCrossRefGoogle Scholar
  39. 39.
    S. Shimizu et al., Analyzing powers of \(p+d\) scattering below the deuteron breakup threshold. Phys. Rev. C 52, 1193 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    S. Ishikawa, Spin-dependent three-nucleon force effects on nucleon–deuteron scattering. Phys. Rev. C 75, 061002(R) (2007)ADSCrossRefGoogle Scholar
  41. 41.
    A. Kievsky, Phenomenological spin-orbit three-body force. Phys. Rev. C 60, 034001 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    L. Girlanda, A. Kievsky, M. Viviani, Subleading contributions to the three-nucleon contact interaction. Phys. Rev. C 84, 014001 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    K. Sagara et al., Energy dependence of analyzing power \(A_y\) and cross section for \(p + d\) scattering below 18 MeV. Phys. Rev. C 50, 576 (1994)ADSCrossRefGoogle Scholar
  44. 44.
    B.v Przewoski et al., Analyzing powers and spin correlation coefficients for \(p+d\) elastic scattering at 135 and 200 MeV. Phys. Rev. C 74, 064003 (2006)ADSCrossRefGoogle Scholar
  45. 45.
    R. Tamagaki, Universal short-range repulsion in the baryon system originating from the confinement approach in string-junction model. Prog. Theor. Phys. 119, 965 (2008)ADSCrossRefGoogle Scholar
  46. 46.
    T. Takatsuka, S. Nishizaki, R. Tamagaki, Three-body force as an “extra repulsion” suggested from hyperon-mixed neutron stars. Prog. Theor. Phys. Suppl. 174, 80 (2008)ADSCrossRefGoogle Scholar
  47. 47.
    Y. Yamamoto, T. Furumoto, N. Yasutake, ThA Rijken, Multi-Pomeron repulsion and the neutron-star mass. Phys. Rev. C 88, 022801(R) (2013)ADSCrossRefGoogle Scholar
  48. 48.
    Y. Yamamoto, T. Furumoto, N. Yasutake, ThA Rijken, Hyperon mixing and universal many-body repulsion in neutron stars. Phys. Rev. C 90, 045805 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Science Research CenterHosei UniversityChiyoda, TokyoJapan

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