Skip to main content
SpringerLink
Log in

Reduction Methods for Total Reaction Cross Sections

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

The most frequently used methods to reduce fusion and total reaction excitation functions were investigated in a very recent paper Canto et al. (Phys Rev C 92:014626, 2015). These methods are widely used to eliminate the influence of masses and charges in comparisons of cross sections for weakly bound and tightly bound systems. This study reached two main conclusions. The first is that the fusion function method is the most successful procedure to reduce fusion cross sections. Applying this method to theoretical cross sections of single channel calculations, one obtains a system independent curve (the fusion function), that can be used as a benchmark to fusion data. The second conclusion was that none of the reduction methods available in the literature is able to provide a universal curve for total reaction cross sections. The reduced single channel cross sections keep a strong dependence of the atomic and mass numbers of the collision partners, except for systems in the same mass range. In the present work we pursue this problem further, applying the reduction methods to systems within a limited mass range. We show that, under these circumstances, the reduction of reaction data may be very useful.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Canto L.F., Mendes Junior D.R., Gomes P.R.S., Lubian J.: Reduction of fusion and reaction cross sections at near-barrier energies. Phys. Rev. C 92, 014626 (2015)

    Article  ADS  Google Scholar 

  2. Canto L.F., Gomes P.R.S., Donangelo R., Hussein M.S.: Fusion and breakup of weakly bound nuclei. Phys. Rep. 424, 1 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  3. Liang J.F., Signorini C.: Fusion induced by radioactive ion beams. Int. J. Mod. Phys. E 14, 1121 (2005)

    Article  ADS  Google Scholar 

  4. Keeley N., Raabe R., Alamanos N., Sida J.L.: Fusion and direct reactions of halo nuclei at energies around the coulomb barrier. Prog. Part. Nucl. Phys. 59, 579 (2007)

    Article  ADS  Google Scholar 

  5. Keeley N., Alamanos N., Kemper K.W., Rusek K.: Elastic scattering and reactions of light exotic beams. Prog. Part. Nucl. Phys. 63, 396 (2009)

    Article  ADS  Google Scholar 

  6. Hagino K., Takigawa N.: Subbarrier fusion reactions and many-particle quantum tunneling. Prog. Theor. Phys. 128, 1061 (2012)

    Article  ADS  Google Scholar 

  7. Back B.B., Esbensen H., Jiang C.L., Rehm K.E.: Recent developments in heavy-ion fusion reactions. Rev. Mod. Phys. 86, 317 (2014)

    Article  ADS  Google Scholar 

  8. Canto L.F., Gomes P.R.S., Donangelo R., Lubian J., Hussein M.S.: Recent developments in fusion and direct reactions with weakly bound nuclei. Phys. Rep. 596, 1 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. Raabe R., Sida J.L., Chavet J.L., Alamanos N., Angulo C. et al.: No enhancement of fusion probability by the neutron halo of 6He. Nature 431, 823 (2004)

    Article  ADS  Google Scholar 

  10. Aguilera E.F., Kolata J.J., Nunes F.M., Becchetti F.D., De Young P.A. et al.: Transfer and/or breakup modes in the 6He + 209 Bi reaction near the coulomb barrier. Phys. Rev. Lett. 84, 5058 (2000)

    Article  ADS  Google Scholar 

  11. Di Pietro A., Figuera P., Amorini F., Angulo C., Cardella G. et al.: Reactions induced by the halo nucleus 6 He at energies around the coulomb barrier. Phys. Rev. C 69, 044613 (2004)

    Article  ADS  Google Scholar 

  12. Navin A., Tripathi V., Blumenfeld Y., Nanal V., Simenel C. et al.: Direct and compound reactions induced by unstable helium beams near the coulomb barrier. Phys. Rev. C 70, 044601 (2004)

    Article  ADS  Google Scholar 

  13. Chatterjee A., Navin A., Shrivastava A., Bhattacharyya S., Rejmund M. et al.: 1n and 2n transfer with the borromean nucleus 6He near the coulomb barrier. Phys. Rev. Lett. 101, 032701 (2008)

    Article  ADS  Google Scholar 

  14. Lemasson A., Navin A., Keeley N., Rejmund M., Bhattacharyya S. et al.: Reactions with the double-borromean nucleus 8He. Phys. Rev. C 82, 044617 (2010)

    Article  ADS  Google Scholar 

  15. Penionzhkevich Y.E., Astabatyan R., Demekhina N., Gulbekian G., Kalpakchieva R. et al.: Excitation functions of fusion reactions and neutron transfer in the interaction of 6He with 197Au and 206Pb. Eur. Phys. J. A 31(2), 185 (2007)

    Article  ADS  Google Scholar 

  16. Acosta L., Sánchez-Benítez A.M., Gómez M.E., Martel I., Pérez-Bernal F. et al.: Elastic scattering and α-particle production in 6He + 208Pb collisions at 22 mev. Phys. Rev. C 84, 044604 (2011)

    Article  ADS  Google Scholar 

  17. Cubero M., Fernández-García J.P., Rodríguez-Gallardo M., Acosta L., Alcorta M. et al.: Do halo nuclei follow rutherford elastic scattering at energies below the barrier? The case of 11Li. Phys. Rev. Lett. 109, 262701 (2012)

    Article  ADS  Google Scholar 

  18. Canto L.F., Gomes P.R.S., Lubian J., Chamon L.C., Crema E.: Dynamic effects of breakup on fusion reactions of weakly bound nuclei. Nucl. Phys. A 821, 51 (2009)

    Article  ADS  Google Scholar 

  19. Canto L.F., Gomes P.R.S., Lubian J., Chamon L.C., Crema E.: Disentangling static and dynamic effects of low breakup threshold in fusion reactions. J. Phys. G Nucl. Part. Phys. 36, 015109 (2009)

    Article  ADS  Google Scholar 

  20. Wang B., Zhao W.J., Gomes P.R.S., Zhao E.G., Zhou S.G.: Systematic study of breakup effects on complete fusion at energies above the coulomb barrier. Phys. Rev. C 90, 034612 (2014)

    Article  ADS  Google Scholar 

  21. Santra S., Kailas S., Ramachandran K., Parkar V.V., Jha V. et al.: Reaction mechanisms involving weakly bound 6Li and 209Bi at energies near the coulomb barrier. Phys. Rev. C 83, 034616 (2011)

    Article  ADS  Google Scholar 

  22. Lubian J., Correa T., Paes B., Figueira J.M., Abriola D. et al.: 7Li breakup polarization potential at near barrier energies. Nucl. Phys. A 791, 24 (2007)

    Article  ADS  Google Scholar 

  23. Lubian J., Correa T., Gomes P.R.S., Canto L.F.: Effect of breakup on fusion cross sections of the 8B +  58Ni system by means of quasi-elastic angular distributions. Phys. Rev. C 78, 064615 (2008)

    Article  ADS  Google Scholar 

  24. Hussein M.S., Gomes P.R.S., Lubian J., Chamon L.C.: New manifestation of the dispersion relation: breakup threshold anomaly. Phys. Rev. C 73, 044610 (2006)

    Article  ADS  Google Scholar 

  25. Gomes P.R.S., Lubian J., Padrón I., Anjos R.M.: Uncertainties in the comparison of fusion and reaction cross sections of different systems involving weakly bound nuclei. Phys. Rev. C 71, 017601 (2005)

    Article  ADS  Google Scholar 

  26. Wong C.Y.: Interaction barrier in charged-particle nuclear reactions. Phys. Rev. Lett. 31, 766 (1973)

    Article  ADS  Google Scholar 

  27. Gasques L.R., Chamon L.C., Gomes P.R.S., Lubian J.: Comparison between heavy-ion reaction and fusion processes for hundreds of systems. Nucl. Phys. A 764, 135 (2006)

    Article  ADS  Google Scholar 

  28. Akyüz, O., Winther, A.: Nuclear structure of heavy ion reaction. In: Broglia, R.A., Dasso, C.H., Ricci, R.A. Proc. E. Fermi Summer School of Physics, North Holland, Amsterdam (1981)

  29. Leigh J.R., Dasgupta M., Hinde D.J., Mein J.C., Morton C.R. et al.: Barrier distributions from the fusion of oxygen ions with 144,148,154Sm and 186W. Phys. Rev. C 52, 3151 (1995)

    Article  ADS  Google Scholar 

  30. Barnett A., Lilley J.: Interaction of alpha particles in the lead region near the coulomb barrier. Phys. Rev. C 9, 2010 (1974)

    Article  ADS  Google Scholar 

  31. Martí G.V., Gomes P.R.S., Rodriguez M.D., Fernández Niello J.O., Capurro O.A. et al.: Fusion, reaction, and breakup cross sections of 9Be on a light mass target. Phys. Rev. C 71, 027602 (2005)

    Article  ADS  Google Scholar 

  32. Mukherjee A., Pramanik U., Sarkar M., Goswami A., Basu P. et al.: 7Li + 12C and 7Li + 13C fusion reactions at subbarrier energies. Nucl. Phys. A 596, 299 (1996)

    Article  ADS  Google Scholar 

  33. Mukherjee A., Dasgupta M., Hinde D.J., Timmers H., Butt R. et al.: Absence of fusion suppression due to breakup in the 12C + 7Li reaction. Phys. Lett. B 526, 295 (2002)

    Article  ADS  Google Scholar 

  34. Mazzocco M., Signorini C., Pierroutsakou D., Glodariu T., Boiano A. et al.: Reaction dynamics for the system 17F + 58Ni at near-barrier energies. Phys. Rev. C 82, 054604 (2010)

    Article  ADS  Google Scholar 

  35. Signorini C., Pierroutsakou D., Martin B., Mazzocco M., Glodariu T. et al.: Interaction of 17F with a 208Pb target below the coulomb barrier. Eur. Phys. J. A 44, 63 (2010)

    Article  ADS  Google Scholar 

  36. Benjamim E., Lépine-Sziy A., Junior D.M., Richtenthäler R., Guimarẽs V. et al.: Elastic scattering and total reaction cross section for the 6He + 27Al system. Phys. Lett. B 647, 30 (2007)

    Article  ADS  Google Scholar 

  37. Barioni A., Guimarães V., Lépine-Szily A., Lichtenthäler R., Mendes D.R. et al.: Elastic scattering and total reaction cross sections for the 8Li + 12C system. Phys. Rev. C 80, 034617 (2009)

    Article  ADS  Google Scholar 

  38. Pires K.C.C., Lichtenthäler R., Lépine-Szily A., Morcelle V.: Total reaction cross section for the 6He + 9Besystem. Phys. Rev. C 90, 027605 (2014)

    Article  ADS  Google Scholar 

  39. Kolata J.J., Aguilera E.F.: Interaction barriers for light, weakly bound projectiles. Phys. Rev. C 79, 027603 (2009)

    Article  ADS  Google Scholar 

  40. Aguilera E.F., Martinez-Quiroz E., Lizcano D., Gómez-Camacho A., Kolata J.J. et al.: Reaction cross sections for 8B, 7Be, and 6Li + 58Ni near the coulomb barrier: proton-halo effects. Phys. Rev. C 79, 021601 (2009)

    Article  ADS  Google Scholar 

  41. Aguilera E.F., Martel I., Sánchez-Benítez A.M., Acosta L.: Systematics of reactions with 4,6He: static and dynamic halo effects and evidence for core-halo decoupling. Phys. Rev. C 83, 021601 (2011)

    Article  ADS  Google Scholar 

  42. Shorto J.M.B., Gomes P.R.S., Lubian J., Canto L.F., Mukherjee S. et al.: Reaction functions for weakly bound systems. Phys. Lett. B 678, 77 (2009)

    Article  ADS  Google Scholar 

  43. Zamora J.C., Guimarães V., Barioni A., Lépine-Szily A., Lichtenthäler R. et al.: 7,9,10Be elastic scattering and total reaction cross sections on a 12C target. Phys. Rev. C 84, 034611 (2011)

    Article  ADS  Google Scholar 

  44. Lei J., Wang J.S., Mukherjee S., Wang Q., Wada R.: Phenomenological formula of total reaction cross sections for low-energy systems. Phys. Rev. C 86, 057603 (2012)

    Article  ADS  Google Scholar 

  45. Yang X.P., Zhang G.L., Zhang H.Q.: Systematic study of reaction functions of weakly bound nuclei. Phys. Rev. C 87, 014603 (2013)

    Article  ADS  Google Scholar 

  46. Pakou A., Pierroutsakou D., Mazzocco M., Acosta L., Aslanoglou X. et al.: Total reaction cross sections for 8Li + 64Zn at near-barrier energies. Eur. Phys. J. A 51, 55 (2015)

    Article  ADS  Google Scholar 

  47. Mukherjee S., Deshmukh N.N., Guimarães V., Lubian J., Gomes P.R.S. et al.: Total reaction cross-sections for light weakly bound systems. Eur. Phys. J. A 45, 23 (2010)

    Article  ADS  Google Scholar 

  48. de Faria P.N., Lichtenthäler R., Pires K.C.C., Moro A.M., Lépine-Szily A. et al.: Elastic scattering and total reaction cross section of 6He + 120Sn. Phys. Rev. C 81, 044605 (2010)

    Article  ADS  Google Scholar 

  49. Deshmukh N.N., Mukherjee S., Patel D., Singh N.L., Rath P.K. et al.: Breakup threshold anomaly in the near-barrier elastic scattering of 6Li + 116,112Sn. Phys. Rev. C 83, 024607 (2011)

    Article  ADS  Google Scholar 

  50. Morcelle V., Lichtenthäler R., Linares R., Morais M.C., Guimarães V. et al.: Elastic scattering and total reaction cross section for the 7Be + 27Al system at near-barrier energies. Phys. Rev. C 89, 044611 (2014)

    Article  ADS  Google Scholar 

  51. Crema, E.: Masters degree thesis, Universidade de São Paulo (1979). Unpublished

  52. Figueira J.M., Fernández Niello J.O., Abriola D., Arazi A., Capurro O. A., andde Barbará E. et al.: Breakup threshold anomaly in the elastic scattering of 6Li on 27Al. Phys. Rev. C 75, 017602 (2007)

    Article  ADS  Google Scholar 

  53. Figueira J.M., Abriola D., Fernández Niello J.O., Arazi A., Capurro O.A. O.A. et al.: Absence of the threshold anomaly in the elastic scattering of the weakly bound projectile 7Li on 27Al. Phys. Rev. C 73, 054603 (2006)

    Article  ADS  Google Scholar 

  54. Gomes P.R.S., Anjos R.M., Muri C., Lubian J., Padron I. et al.: Threshold anomaly with weakly bound projectiles: Elastic scattering of 9Be + 27Al. Phys. Rev. C 70, 054605 (2004)

    Article  ADS  Google Scholar 

  55. Gomes P.R.S., Rodriguez M.D., Martí G.V., Padrón I., Chamon L.C. et al.: Effect of the breakup on the fusion and elastic scattering of weakly bound projectiles on 64Zn. Phys. Rev. C 71, 034608 (2005)

    Article  ADS  Google Scholar 

  56. Morcelle V., Pires K.C.C., Rodríguez-Gallardo M., Lichtenthäler R., Lépine-Szily A. et al.: Four-body effects in the 6He + 58Ni scattering. Phys. Lett. B 732, 228 (2014)

    Article  ADS  Google Scholar 

  57. Moraes S.B., Gomes P.R.S., Lubian J., Alves J.J.S., Anjos R.M. et al.: Fusion and elastic scattering of 9Be +  64Zn: a search of the breakup influence on these processes. Phys. Rev. C 61, 064608 (2000)

    Article  ADS  Google Scholar 

  58. Tenreiro C., Acquadro J.C., Freitas P.A.B., Liguori Neto R., Ramirez G. et al.: Elastic and inelastic scattering of 16O + 64Zn at near-barrier energies. Phys. Rev. C 53, 2870 (1996)

    Article  ADS  Google Scholar 

  59. Alves J.J.S., Gomes P.R.S., Lubian J., Chamon L.C., Pereira D. et al.: Consistent analysis of peripheral reaction channels and fusion for the 16,18O + 58Ni systems. Nucl. Phys. A 748, 59 (2005)

    Article  ADS  Google Scholar 

  60. Di Pietro A., Scuderi V., Moro A.M., Acosta L., Amorini F. et al.: Experimental study of the collision 11Be +  64Zn around the coulomb barrier. Phys. Rev. C 85, 054607 (2012)

    Article  ADS  Google Scholar 

  61. Abriola D., DiGregorio D., Testoni J.E., Etchegoyen A., Etchegoyen M.C. et al.: Energy dependence of the optical potential for the 16O +  144Sm system near the coulomb barrier. Phys. Rev. C 39, 546 (1989)

    Article  ADS  Google Scholar 

  62. Figueira J.M., Niello J.O.F., Arazi A., Capurro O.A., Carnelli P. et al.: Energy dependence of the optical potential of weakly and tightly bound nuclei as projectiles on a medium-mass target. Phys. Rev. C 81, 024613 (2010)

    Article  ADS  Google Scholar 

  63. Maciel A.M.M., Gomes P.R.S., Lubian J., Anjos R.M., Cabezas R. et al.: Influence of the 6,7Li breakup process on the near barrier elastic scattering by heavy nuclei. Phys. Rev. C 59, 2103 (1999)

    Article  ADS  Google Scholar 

  64. Gomes P.R.S., Padrón I., Crema E., Capurro O.A., Niello J.O.F. et al.: Comprehensive study of reaction mechanisms for the 9Be + 144Sm system at near-and sub-barrier energies. Phys. Rev. C 73, 064606 (2006)

    Article  ADS  Google Scholar 

  65. Gomes P.R.S., Lubian J., Paes B., Garcia V.N., Monteiro D.S. et al.: Near-barrier fusion, breakup and scattering for the 9Be +  144Sm system. Nucl. Phys. A 828, 233 (2009)

    Article  ADS  Google Scholar 

  66. Fernández-García J.P., Alvarez M.A.G., Moro A.M., Rodríguez-Gallardo M.: Simultaneous analysis of elastic scattering and transfer/breakup channels for the 6He + 208Pb reaction at energies near the coulomb barrier. Phys. Lett. B 693, 310 (2010)

    Article  ADS  Google Scholar 

  67. Woolliscroft R.J., Fulton B.R., Cowin R.L., Dasgupta M., Hinde D.J. et al.: Elastic scattering and fusion of 9Be + 208Pb: Density function dependence of the double folding renormalization. Phys. Rev. C 69, 044612 (2004)

    Article  ADS  Google Scholar 

  68. Singh P., Kailas S., Chatterjee A., Kerekatte S., Navin A. et al.: Threshold anomaly in 16O + 209Bi system. Nucl. Phys. A 555, 606 (1993)

    Article  ADS  Google Scholar 

  69. Mazzocco M., Signorini C., Romoli M., Bonetti R., De Francesco A. et al.: Elastic scattering for the system 11Be + 209Bi at coulomb barrier energies. Eur. Phys. J. Spec. Top. 150(1), 37 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, Gragoatá, Niterói, RJ, 24210-340, Brazil

    P. R. S. Gomes, D. R. Mendes Junior, L. F. Canto, J. Lubian & P. N. de Faria

  2. Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, Rio de Janeiro, RJ, 21941-972, Brazil

    L. F. Canto

Authors
  1. P. R. S. Gomes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. R. Mendes Junior
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. F. Canto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Lubian
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. N. de Faria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. R. S. Gomes.

Additional information

The authors would like to thank CNPq, CAPES, FAPERJ and PRONEX for the partial financial support.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gomes, P.R.S., Mendes Junior, D.R., Canto, L.F. et al. Reduction Methods for Total Reaction Cross Sections. Few-Body Syst 57, 205–216 (2016). https://doi.org/10.1007/s00601-015-1042-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-015-1042-4

Keywords

Search

Navigation