Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system

  • Ian J. Thompson
  • R. J. deBoer
  • P. DimitriouEmail author
  • S. Kunieda
  • M. T. Pigni
  • G. Arbanas
  • H. Leeb
  • Th. Srdinko
  • G. Hale
  • P. Tamagno
  • P. Archier


R-matrix theory is used to describe nuclear reactions in the resolved resonance region. It uses information on bound states and low energy resonances to accurately parametrize cross sections on the resonances as well as the non-resonant background. Since the seminal work of Lane and Thomas (1958), the approach has been widely used to analyze experimental cross-section data in a broad range of fields spanning nuclear reaction dynamics, nuclear astrophysics, ion beam analysis and their applications. Different R-matrix codes have been developed and used in these different applications with very little communication among the developers or practitioners on the capabilities, achievements or limitations of the codes. A limited comparison among three R-matrix codes on neutron-induced reactions was performed by the International Atomic Energy Agency (IAEA) International Evaluation of Neutron Cross Section Standards project (2007). Since then, significant progress has been made in their implementation of the R-matrix algorithms, and R-matrix codes have enhanced capabilities. In this paper we present, for the first time, the results of a comprehensive effort to verify the most widely used R-matrix codes in the various fields of nuclear science and applications: AMUR, AZURE2, CONRAD, EDA, FRESCO, GECCCOS, and SAMMY. In addition to the description of the capabilities of the codes and their specifications, we discuss the results of a joint exercise which was coordinated by the International Atomic Energy Agency. The aim of the exercise was to compare calculations of charged-particle reaction cross sections for the light composite system 7Be. The calculations were performed by the codes using identical input R-matrix parameters and other specifications and were limited to charged-particle channels.


  1. 1.
    Technical Report IAEA TECDOC-1780, International Atomic Energy Agency, Vienna, Austria (2015)Google Scholar
  2. 2.
    Technical Report IAEA TECDOC-1822, International Atomic Energy Agency, Vienna, Austria (2017)Google Scholar
  3. 3.
    Ion beam analysis nuclear data library,, IAEA, Vienna, Austria
  4. 4.
    P. Dimitriou, V. Semkova, V. Zerkin, EPJ Web of Conferences 146, 09014 (2017)CrossRefGoogle Scholar
  5. 5.
    A. Gurbich, Nucl. Instrum. Methods Phys. Res. B 371, 27 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    S. Simakov, Q.Y. van den Berg, Nucl. Data Sheets 139, 190 (2017)ADSCrossRefGoogle Scholar
  7. 7.
    C. Angulo, M. Arnould, M. Rayet, P. Descouvemont, D. Baye, C. Leclercq-Willain, A. Coc, S. Barhoumi, P. Aguer, C. Rolfs et al., Nucl. Phys. A 656, 3 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    Y. Xu, K. Takahashi, S. Goriely, M. Arnould, M. Ohta, H. Utsunomiya, Nucl. Phys. A 918, 61 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    R.H. Cyburt, A.M. Amthor, R. Ferguson, Z. Meisel, K. Smith, S. Warren, A. Heger, R.D. Hoffman, T. Rauscher, A. Sakharuk et al., Astrophys. J. Suppl. 189, 240 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Xu, S. Goriely, A. Jorissen, G.L. Chen, M. Arnould, Astron. Astrophys. 549, A106 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    I. Dillmann, R. Plag, F. Käppeler, T. Rauscher, KADoNiS v0.3 - The third update of the “Karlsruhe Astrophysical Database of Nucleosynthesis in Stars” (2010)Google Scholar
  12. 12.
    Computational Infrastructure for Nuclear Astrophysics,
  13. 13.
    P. Dimitriou, R.J. deBoer, S. Kunieda, H. Leeb, M. Paris, T. Srdinko, I.J. Thompson, Technical Report INDC(NDS)-0703, International Atomic Energy Agency, Vienna, Austria (2016)
  14. 14.
    H. Leeb, P. Dimitriou, I.J. Thompson, Technical Report INDC(NDS)-0726, International Atomic Energy Agency, Vienna, Austria (2017)
  15. 15.
    H. Leeb, P. Dimitriou, I.J. Thompson, Technical Report INDC(NDS)-0737, International Atomic Energy Agency, Vienna, Austria (2017)
  16. 16.
    H. Leeb, P. Dimitriou, I.J. Thompson, Technical Report INDC(NDS)-0767, International Atomic Energy Agency, Vienna, Austria (2018)
  17. 17.
    Technical Report STI/PUB/1291, International Atomic Energy Agency, Vienna, Austria (2007)Google Scholar
  18. 18.
    A.M. Lane, R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    P. Descouvemont, D. Baye, Rep. Prog. Phys. 73, 036301 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    C.R. Brune, Phys. Rev. C 66, 044611 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    C.W. Reich, M.S. Moore, Phys. Rev. 111, 929 (1958)ADSCrossRefGoogle Scholar
  22. 22.
    F. Froehner, JEFF Report 18 (2001), see eq. (196)Google Scholar
  23. 23.
    G. Arbanas, V. Sobes, A. Holcomb, P. Ducru, M. Pigni, D. Wiarda, EPJ Web of Conferences 146, 12006 (2017)CrossRefGoogle Scholar
  24. 24.
    S. Kunieda, EPJ Web of Conferences 146, 12029 (2017)CrossRefGoogle Scholar
  25. 25.
    E.P. Wigner, L. Eisenbud, Phys. Rev. 72, 29 (1947)ADSCrossRefGoogle Scholar
  26. 26.
    T. Kawano, H. Matsunobu, T. Murata, A. Zukeran, Y. Nakajima, M. Kawai, O. Iwamoto, K. Shibata, T. Nakagawa, T. Ohsawa et al., J. Nucl. Sci. Technol. 37, 327 (2000)CrossRefGoogle Scholar
  27. 27.
    R.E. Azuma, E. Uberseder, E.C. Simpson, C.R. Brune, H. Costantini, R.J. de Boer, J. Görres, M. Heil, P.J. LeBlanc, C. Ugalde et al., Phys. Rev. C 81, 045805 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    E. Uberseder, R.J. deBoer, AZURE2 User Manual (2015) azure.nd.eduGoogle Scholar
  29. 29.
    R.J. deBoer, J. Görres, M. Wiescher, R.E. Azuma, A. Best, C.R. Brune, C.E. Fields, S. Jones, M. Pignatari, D. Sayre et al., Rev. Mod. Phys. 89, 035007 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    The GSL Team, GSL 2.5 Documentation (2018)
  31. 31.
    N. Michel, Comput. Phys. Commun. 176, 232 (2007)ADSCrossRefGoogle Scholar
  32. 32.
  33. 33.
    G. D’Agostini, Nucl. Instrum. Methods Phys. Res. A 346, 306 (1994)ADSCrossRefGoogle Scholar
  34. 34.
    L. Wolfenstein, Annu. Rev. Nucl. Sci. 6, 43 (1956)ADSCrossRefGoogle Scholar
  35. 35.
    R. Newton, Scattering Theory of Waves and Particles, Dover Books on Physics (Dover Publications, 2002)Google Scholar
  36. 36.
    I.J. Thompson, Comput. Phys. Rep. 7, 167 (1988)ADSCrossRefGoogle Scholar
  37. 37.
    Fresco coupled reaction channels calculations (2006)
  38. 38.
    Scattering code FRESCO for coupled-channels calculations (2017)
  39. 39.
    A. Koning, S. Hilaire, S. Goriely, TALYS - A nuclear reaction program (2015)
  40. 40.
    I. Thompson, A. Barnett, Comput. Phys. Commun. 36, 363 (1985)ADSCrossRefGoogle Scholar
  41. 41.
    B. Adams, L. Bauman, W. Bohnhoff, K. Dalbey, M. Ebeida, J. Eddy, M. Eldred, P. Hough, K. Hu, J. Jakeman, DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.4 User’s Manual, Sandia Technical Report SAND2010-2183 (2009), updated April 2013Google Scholar
  42. 42.
    N.M. Larson, Technical Report ORNL/TM-9179/R8, Oak Ridge National Laboratory (2008)Google Scholar
  43. 43.
    P. Archier, C. De Saint Jean, O. Litaize, G. Noguère, L. Berge, E. Privas, P. Tamagno, Nucl. Data Sheets 118, 488 (2014)ADSCrossRefGoogle Scholar
  44. 44.
    J. Raynal, Technical Report CEA-N-2772, pp. 1--145, Commissariat à l’Énergie Atomique, Saclay, France (1994)Google Scholar
  45. 45.
    B. Habert, C. De Saint Jean, G. Noguère, L. Leal, Y. Rugama, Nucl. Sci. Eng. 166, 276 (2010)CrossRefGoogle Scholar
  46. 46.
    M. Herman, A. Trkov, ENDF-6 Formats Manual, (Brookhaven National Laboratory, 2009) bNL-90365-2009Google Scholar
  47. 47.
    B. Beck, C. Mattoon, Technical Report, Lawrence Livermore National Laboratory (2014) lLNL-PROC-648476Google Scholar
  48. 48.
    C. Mattoon, B. Beck, N. Patel, N. Summers, G. Hedstrom, D. Brown, Nucl. Data Sheets 113, 3145 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    F. Barker, Aust. J. Phys. 25, 341 (1972)ADSCrossRefGoogle Scholar
  50. 50.
    N. Otuka, E. Dupont, V. Semkova, B. Pritychenko, A. Blokhin, M. Aikawa, S. Babykina, M. Bossant, G. Chen, S. Dunaeva et al., Nucl. Data Sheets 120, 272 (2014)ADSCrossRefGoogle Scholar
  51. 51.
    R.J. Spiger, T.A. Tombrello, Phys. Rev. 163, 964 (1967)ADSCrossRefGoogle Scholar
  52. 52.
    A. Barnard, C. Jones, G. Phillips, Nucl. Phys. 50, 629 (1964)CrossRefGoogle Scholar
  53. 53.
    T.A. Tombrello, P.D. Parker, Phys. Rev. 130, 1112 (1963)ADSCrossRefGoogle Scholar
  54. 54.
    J.A. McCray, Phys. Rev. 130, 2034 (1963)ADSCrossRefGoogle Scholar
  55. 55.
    A.J. Elwyn, R.E. Holland, C.N. Davids, L. Meyer-Schützmeister, F.P. Mooring, W. Ray, Phys. Rev. C 20, 1984 (1979)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Ian J. Thompson
    • 1
  • R. J. deBoer
    • 2
    • 3
  • P. Dimitriou
    • 4
    Email author
  • S. Kunieda
    • 5
  • M. T. Pigni
    • 6
  • G. Arbanas
    • 6
  • H. Leeb
    • 7
  • Th. Srdinko
    • 7
  • G. Hale
    • 8
  • P. Tamagno
    • 9
  • P. Archier
    • 9
  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA
  2. 2.The Joint Institution of Nuclear AstrophysicsUniversity Notre DameNotre DameUSA
  3. 3.Department of PhysicsUniversity Notre DameNotre DameUSA
  4. 4.Division of Physical and Chemical SciencesInternational Atomic Energy AgencyViennaAustria
  5. 5.Japan Atomic Energy AgencyTokaiJapan
  6. 6.Oak Ridge National LaboratoryOak RidgeUSA
  7. 7.AtominstitutTechnische Universität WienViennaAustria
  8. 8.Los Alamos National Laboratory, Theoretical DivisionLos AlamosUSA
  9. 9.CEA-DEN Cadarache, DER/SPRC/LEPhSaint-Paul-lez-DuranceFrance

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