Brazilian Journal of Physics

, Volume 47, Issue 3, pp 321–332 | Cite as

Approximate Transmission Coefficients in Heavy Ion Fusion

  • A. J. Toubiana
  • L. F. Canto
  • M. S. Hussein
General and Applied Physics


In this paper, we revisit the one-dimensional tunneling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier shape by functional forms where the transmission coefficient is known analytically. Then, we consider Kemble’s approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of the different approximations considered in this paper by comparing their predictions for transmission coefficients and cross sections of three heavy ion systems with the corresponding quantum mechanical results.


Heavy ion reactions Fusion Quantum tunneling Transmission coefficients 



We are grateful to Raul Donangelo for critically reading the manuscript. Partial support from the Brazilian funding agencies, CNPq, FAPESP, and FAPERJ, is acknowledged. M. S. H. acknowledges support from the CAPES/ITA Senior Visiting Professor Fellowship Program.


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Copyright information

© Sociedade Brasileira de Física 2017

Authors and Affiliations

  • A. J. Toubiana
    • 1
    • 2
  • L. F. Canto
    • 3
    • 4
  • M. S. Hussein
    • 5
    • 6
    • 7
  1. 1.Departamento de Engenharia Nuclear, Escola PolitécnicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.École CentraleSupélecPlateau de MoulonGif-sur-YvetteFrance
  3. 3.Instituto de FísicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  4. 4.Instituto de FísicaUniversidade Federal FluminenseNiteróiBrazil
  5. 5.Departamento de Física Matemática, Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  6. 6.Instituto de Estudos AvançadosUniversidade de São PauloSão PauloBrazil
  7. 7.Departamento de Física, Instituto Tecnológico de AeronáuticaCTASão PauloBrazil

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