Ranking and validation of spallation models for isotopic production cross sections of heavy residua

  • Sushil K. Sharma
  • Bogusław KamysEmail author
  • Frank Goldenbaum
  • Detlef Filges
Open Access
Regular Article - Theoretical Physics


The production cross sections of isotopically identified residual nuclei of spallation reactions induced by 136Xe projectiles at 500AMeV on hydrogen target were analyzed in a two-step model. The first stage of the reaction was described by the INCL4.6 model of an intranuclear cascade of nucleon-nucleon and pion-nucleon collisions whereas the second stage was analyzed by means of four different models; ABLA07, GEM2, GEMINI++ and SMM. The quality of the data description was judged quantitatively using two statistical deviation factors; the H-factor and the M-factor. It was found that the present analysis leads to a different ranking of models as compared to that obtained from the qualitative inspection of the data reproduction. The disagreement was caused by sensitivity of the deviation factors to large statistical errors present in some of the data. A new deviation factor, the A factor, was proposed, that is not sensitive to the statistical errors of the cross sections. The quantitative ranking of models performed using the A-factor agreed well with the qualitative analysis of the data. It was concluded that using the deviation factors weighted by statistical errors may lead to erroneous conclusions in the case when the data cover a large range of values. The quality of data reproduction by the theoretical models is discussed. Some systematic deviations of the theoretical predictions from the experimental results are observed.


  1. 1.
    A.Yu. Konobeyev et al., J. Korean Phys. Soc. 59, 927 (2011)CrossRefGoogle Scholar
  2. 2.
    S.K. Sharma, PhD Thesis, Jagiellonian University (2015)Google Scholar
  3. 3.
    S.K. Sharma, B. Kamys, F. Goldenbaum, D. Filges, Eur. Phys. J. A 52, 171 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    R.E.L. Green, R.G. Korteling, K.P. Jackson, Phys. Rev. C 29, 1806 (1984)ADSCrossRefGoogle Scholar
  5. 5.
    L. Giot, J.A. Alcántara-Núñez, J. Benlliure, D. Pérez-Loureiro, L. Audouin, A. Boudard, E. Casarejos, T. Enqvist, J.E. Ducret, B. Fernández-Dominguez, M. Fernández Ordóñez, F. Farget, A. Heinz, V. Henzl, D. Henzlova, A. Kelić-Heil, A. Lafriaskh, S. Leray, P. Napolitani, C. Paradela, J. Pereira, M.V. Ricciardi, C. Stéphan, K.-H. Schmidt, C. Schmitt, L. Tassan-Got, C. Villagrasa, C. Volant, O. Yordanov, Nucl. Phys. A 899, 116 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    A. Boudard, J. Cugnon, J.-C. David, S. Leray, D. Mancusi, Phys. Rev. C 87, 014606 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    A. Kelić, M.V. Ricciardi, K.-H. Schmidt, in Proceedings of the Joint ICTP-IAEA Advanced Workshop on Model Codes for Spallation Reactions, ICTP Trieste, Italy, 4-8 February 2008, edited by D. Filges (IAEA INDC(NDS)-530, Vienna, 2008) p. 181, and arXiv:0906.4193 [nucl-th]
  8. 8.
    S. Furihata, Nucl. Instrum. Methods B 171, 251 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    S. Furihata, T. Nakamura, J. Nucl. Sci. Technol. Suppl. 2, 758 (2002)CrossRefGoogle Scholar
  10. 10.
    R.J. Charity et al., Nucl. Phys. A 483, 371 (1988)ADSCrossRefGoogle Scholar
  11. 11.
    R.J. Charity, Phys. Rev. C 82, 014610 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    A.S. Botvina, A.S. Iljinov, I.N. Mishustin, Sov. J. Nucl. Phys. 42, 712 (1985)Google Scholar
  13. 13.
    A.S. Botvina, A.S. Iljinov, I.N. Mishustin, J.P. Bondorf, R. Donangelo, K. Sneppen, Nucl. Phys. A 475, 633 (1987)ADSCrossRefGoogle Scholar
  14. 14.
    A.S. Botvina, A.S. Iljinov, I.N. Mishustin, Nucl. Phys. A 507, 649 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257, 133 (1995)ADSCrossRefGoogle Scholar
  16. 16.
    Hongfei Xi, T. Odeh, R. Bassini, M. Begemann-Blaich, A.S. Botvina, S. Fritz, S.J. Gaff, C. Gross, G. Immé, I. Iori, U. Kleinevoss, G.J. Kunde, W.D. Kunze, U. Lynen, V. Maddalena, M. Mahi, T. Möhlenkamp, A. Moroni, W.F.J. Müller, C. Nociforo, B. Ocker, F. Petruzzelli, J. Pochodzalla, G. Raciti, G. Riccobene, F.P. Romano, Th. Rubehn, A. Saija, M. Schnittker, A. Schüttauf, C. Schwarz, W. Seidel, V. Serfling, C. Sfienti, W. Trautmann, A. Trzciński, G. Verde, A. Wörner, B. Zwiegliński, Z. Phys. A 359, 397 (1997)ADSCrossRefGoogle Scholar
  17. 17.
    K. Turzó, G. Auger, M.L. Begemann-Blaich, N. Bellaize, R. Bittiger, F. Bocage, B. Borderie, R. Bougault, B. Bouriquet, J.L. Charvet, A. Chbihi, R. Dayras, D. Durand, J.D. Frankland, E. Galichet, D. Gourio, D. Guinet, S. Hudan, G. Immé, P. Lautesse, F. Lavaud, A. Le Févre, R. Legrain, O. Lopez, J. Lukasik, U. Lynen, W.F.J. Müller, L. Nalpas, H. Orth, E. Plagnol, G. Raciti, E. Rosato, A. Saija, C. Schwarz, W. Seidel, C. Sfienti, B. Tamain, W. Trautmann, A. Trzciński, E. Vient, M. Vigilante, C. Volant, B. Zwiegliński, A.S. Botvina, Eur. Phys. J. A 21, 293 (2004)CrossRefGoogle Scholar

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© The Author(s) 2017

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Sushil K. Sharma
    • 1
  • Bogusław Kamys
    • 1
    Email author
  • Frank Goldenbaum
    • 2
  • Detlef Filges
    • 2
  1. 1.The Marian Smoluchowski Institute of PhysicsJagiellonian UniversityKrakówPoland
  2. 2.Institut fuer KernphysikForschungszentrum JuelichJuelichGermany

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