The São Paulo Potential and the 3He Breakup Reaction at 130 MeV on 93Nb and 197Au


Nuclear reactions induced by weakly bound nuclei often result in the emission of light particles as products of the projectile breakup. The incident particle is expected to fragment before reaching the interior of the target nuclei, a characteristic that tends to favor forward angular emission. Although the first models developed for such reactions were proposed many decades ago by Udagawa and Tamura, Ichimura, Austern, Vincent, and Kasano, and Hussein and McVoy, to this date most of the attention has been dedicated to the breakup of the deuteron and other very weakly bound systems, while more strongly bound projectiles have not been fully explored. Here, we describe the production of protons and deuterons from the breakup of 3He. The breakup of 3He on two heavy targets, 93Nb and 197Au, is analyzed in this study. However, the incoming energy involved is much larger than that of the standard phenomenological optical potentials available in the literature for the 3He entrance channel. We have overcome this difficulty by using the São Paulo potential and adjusting the nuclear diffusivity. The deuteron inclusive spectra were calculated at several angles and compared well with the experimental data. Theoretical proton emission predictions are also given for future reference, since no inclusive measurements were performed for the targets under study. One of our goals is to verify the description of deuteron emission from fast projectiles, for which many partial waves contribute to the scattering process.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4


  1. 1.

    S.M. Qaim, F. Tárkányi, R. Capote. Nuclear data for the production of therapeutic radionuclides. Technical Reports Series (International Atomic Energy Agency, Vienna, 2012)

    Google Scholar 

  2. 2.

    G.B. Saha. Physics and radiobiology of nuclear medicine (Springer Verlag, New York, 2013)

    Google Scholar 

  3. 3.

    J.E. Escher, J.T. Burke, F.S. Dietrich, N.D. Scielzo, I.J. Thompson, W. Younes, Compound-nuclear reaction cross sections from surrogate measurements. Rev. Mod. Phys. 84, 353–397 (2012)

    ADS  Article  Google Scholar 

  4. 4.

    J. Lei, A.M. Moro, Reexamining closed-form formulae for inclusive breakup: Application to deuteron- and 6Li -induced reactions. Phys. Rev. C. 92, 044616 (2015)

    ADS  Article  Google Scholar 

  5. 5.

    A Di Pietro, A.M. Moro, J. Lei, R de Diego, Insights into the dynamics of breakup of the halo nucleus 11be on a 64zn target. Physics Letters B. 798, 134954 (2019)

    Article  Google Scholar 

  6. 6.

    N. Matsuoka, A. Shimizu, K. Hosono, T. Saito, M. Kondo, H. Sakaguchi, A. Goto, F. Ohtani, Angular correlation of (3he, pd) reactions at 90 mev and elastic break-up of 3he particles. Nucl. Phys. A. 337(2), 269–284 (1980)

    ADS  Article  Google Scholar 

  7. 7.

    A. Djaloeis, J. Bojowald, S. Gopal, W. Oelert, N.G. Puttaswamy, P. Turek, C Mayer-Böricke, Breakup of 3He projectiles at an incident energy of 43.3 mev/nucleon. Phys. Rev. C. 27, 2389–2392 (1983)

    ADS  Article  Google Scholar 

  8. 8.

    E.H.L. Aarts, R.A.R.L. Malfliet, R.J. De Meijer, S.Y. Van der Werf, Reaction mechanisms in 3he projectile breakup at 52 mev on 12c, 28si and 58ni. Nucl. Phys. A. 425, 23–92 (1984)

    ADS  Article  Google Scholar 

  9. 9.

    R. Serber, The production of high energy neutrons by stripping. Phys. Rev. 72, 1008 (1947)

    ADS  Article  Google Scholar 

  10. 10.

    N. Austern, C.M. Vincent, Inclusive breakup reactions. Phys. Rev. C. 23, 1847–1853 (1981)

    ADS  Article  Google Scholar 

  11. 11.

    T. Udagawa, T. Tamura, Derivation of breakup-fusion cross sections from the optical theorem. Phys. Rev. C. 24, 1348–1349 (1981)

    ADS  Article  Google Scholar 

  12. 12.

    A. Kasano, M. Ichimura, A new formalism of inclusive breakup reactions and validity of the surface approximation. Physics Letters B. 115(2), 81–85 (1982)

    ADS  Article  Google Scholar 

  13. 13.

    M. Ichimura, N. Austern, C.M. Vincent, Equivalence of post and prior sum rules for inclusive breakup reactions. Phys. Rev. C. 32, 431–439 (1985)

    ADS  Article  Google Scholar 

  14. 14.

    M.S. Hussein, K. McVoy, Inclusive projectile fragmentation in the spectator model. Nucl. Phys. A. 445, 124–139 (1985)

    ADS  Article  Google Scholar 

  15. 15.

    M. Ichimura, Relation among theories of inclusive breakup reactions. Phys. Rev. C. 41, 834–840 (1990)

    ADS  Article  Google Scholar 

  16. 16.

    J. Lei, A.M. Moro, Numerical assessment of post-prior equivalence for inclusive breakup reactions. Phys. Rev. C. 92, 061602(R) (2015)

    ADS  Article  Google Scholar 

  17. 17.

    B.V. Carlson, R. Capote, M. Sin, Inclusive proton emission spectra from deuteron breakup reactions. Few-Body Syst. 57, 307–314 (2016)

    ADS  Article  Google Scholar 

  18. 18.

    G. Potel, F.M. Nunes, I.J. Thompson, Establishing a theory for deuteron-induced surrogate reactions. Phys. Rev. C. 92, 034611 (2015)

    ADS  Article  Google Scholar 

  19. 19.

    G. Potel, G. Perdikakis, B. V. Carlson, Toward a complete theory for predicting inclusive deuteron breakup away from stability. Eur. Phys. J. A. 53, 178 (2017)

    ADS  Article  Google Scholar 

  20. 20.

    P.J.A. Buttle, L.J.B. Goldfarb, Finite range effects in deuteron stripping processes. Proc. Phys. Soc. 83(5), 701–717 (1964)

    ADS  Article  Google Scholar 

  21. 21.

    A.J. Koning, J.P. Delaroche, Local and global nucleon optical models from 1 kev to 200 mev. Nucl. Phys. A. 713(3), 231–310 (2003)

    ADS  Article  Google Scholar 

  22. 22.

    Y. Han, Y. Shi, Q. Shen, Deuteron global optical model potential for energies up to 200 mev. Phys. Rev. C. 74, 044615 (2006)

    ADS  Article  Google Scholar 

  23. 23.

    J.F.D. Becchetti, G.W. Greenlees, Annual Report of J. H. Williams Laboratory, University of Minnesota (1969)

  24. 24.

    L.C. Chamon, B.V. Carlson, L.R. Gasques, D. Pereira, C. De Conti, M.A.G. Alvarez, M.S. Hussein, M.A. Cândido Ribeiro, E.S. Rossi, C.P. Silva, Toward a global description of the nucleus-nucleus interaction. Phys. Rev. C. 66, 014610 (2002)

    ADS  Article  Google Scholar 

  25. 25.

    L.C. Chamon, The São Paulo potential. Nucl. Phys. A. 787(1), 198–205 (2007). Proceedings of the Ninth International Conference on Nucleus-Nucleus Collisions

    ADS  Article  Google Scholar 

  26. 26.

    I.J. Thompson, F.M. Nunes. Nuclear reactions for astrophysics: Principles, calculation and applications of low-energy reactions (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  27. 27.

    B.V. Carlson, T. Frederico, M.S. Hussein, Inclusive breakup of three-fragment weakly-bound nuclei. Physics Letters B. 767, 53–57 (2017)

    ADS  Article  Google Scholar 

Download references


BVC received support from grant 2017/05660-0 of the São Paulo Research Foundation (FAPESP) and grant 306433/2017-6 of the CNPq. EVC received support from grants 2016/07398-8 and 2017/13693-5 of the São Paulo Research Foundation (FAPESP). LAS received support from grant 2019/07767-1 of the São Paulo Research Foundation (FAPESP). All of the authors received the support of the INCT-FNA project 464898/2014-5. This work is performed in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 with support from LDRD project 19-ERD-017.

Author information



Corresponding author

Correspondence to E. V. Chimanski.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chimanski, E.V., Souza, L.A. & Carlson, B.V. The São Paulo Potential and the 3He Breakup Reaction at 130 MeV on 93Nb and 197Au. Braz J Phys 51, 323–327 (2021).

Download citation


  • Breakup
  • SP potential
  • Inclusive emissions
  • Nuclear reactions