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Approximate Transmission Coefficients in Heavy Ion Fusion

  • General and Applied Physics
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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Departamento de Engenharia Nuclear, Escola Politécnica, Universidade Federal do Rio de Janeiro, C.P. 68529, 21941-909, Rio de Janeiro, RJ, Brazil

    A. J. Toubiana

  2. École CentraleSupélec, Plateau de Moulon, 3 rue Joliot-Curie, 91192, Gif-sur-Yvette, France

    A. J. Toubiana

  3. Instituto de Física, Universidade Federal do Rio de Janeiro, CP 68528, 21941-972, Rio de Janeiro, RJ, Brazil

    L. F. Canto

  4. Instituto de Física, Universidade Federal Fluminense, Av. Litoranea s/n, Gragoatá, Niterói, R.J., 24210-340, Brazil

    L. F. Canto

  5. Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, C.P. 66318, 05314-970, São Paulo, SP, Brazil

    M. S. Hussein

  6. Instituto de Estudos Avançados, Universidade de São Paulo, C.P. 72012, 05508-970, São Paulo, SP, Brazil

    M. S. Hussein

  7. Departamento de Física, Instituto Tecnológico de Aeronáutica, CTA, São José dos Campos, São Paulo, SP, Brazil

    M. S. Hussein

Authors
  1. A. J. Toubiana
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  2. L. F. Canto
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  3. M. S. Hussein
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Corresponding author

Correspondence to M. S. Hussein.

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Toubiana, A.J., Canto, L.F. & Hussein, M.S. Approximate Transmission Coefficients in Heavy Ion Fusion. Braz J Phys 47, 321–332 (2017). https://doi.org/10.1007/s13538-017-0499-7

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  • DOI: https://doi.org/10.1007/s13538-017-0499-7

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