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Improved WKB approximation for quantum tunneling: Application to heavy-ion fusion

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Abstract.

In this paper we revisit the one-dimensional tunnelling problem. 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 this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum-mechanical results. We find that the extended Kemble’s approximation reproduces the results of quantum mechanics with great accuracy.

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References

  1. K. Hagino, N. Takigawa, Prog. Theor. Phys. 128, 1061 (2012)

    Article  ADS  Google Scholar 

  2. E.C. Kemble, Phys. Rev. 48, 549 (1935)

    Article  ADS  Google Scholar 

  3. D.L. Hill, J.A. Wheeler, Phys. Rev. 89, 1102 (1953)

    Article  ADS  Google Scholar 

  4. R.A. Broglia, A. Winther, Heavy Ion Reactions (Westview Press, 2004)

  5. G.F. Bertsch, J. Borysowicz, H. McManus, W.G. Love, Nucl. Phys. A 284, 399 (1977)

    Article  ADS  Google Scholar 

  6. L.F. Canto, M.S. Hussein, Scattering Theory of Molecules, Atoms and Nuclei (World Scientific Publishing Co. Pte. Ltd., 2013)

  7. G.H. Rawitscher, Phys. Rev. 135, B605 (1964)

    Article  ADS  Google Scholar 

  8. G.H. Rawitscher, Nucl. Phys. 85, 337 (1966)

    Article  Google Scholar 

  9. K. Hagino, N. Rowley, A.T. Kruppa, Comput. Phys. Commun. 123, 143 (1999)

    Article  ADS  Google Scholar 

  10. C.L. Jiang, B.B. Back, H. Esbensen, R.V.F. Janssens, K.E. Rehm, R.J. Charity, Phys. Rev. Lett. 110, 072701 (2013)

    Article  ADS  Google Scholar 

  11. N. Rowley, G.R. Satchler, P.H. Stelson, Phys. Lett. B 254, 25 (1991)

    Article  ADS  Google Scholar 

  12. K. Hagino, N. Rowley, Phys. Rev. C 69, 054610 (2004)

    Article  ADS  Google Scholar 

  13. M. Dasgupta, D. Hinde, N. Rowley, A. Stefanini, Annu. Rev. Nucl. Part. Sci. 48, 401 (1998)

    Article  ADS  Google Scholar 

  14. L.F. Canto, P.R.S. Gomes, R. Donangelo, M.S. Hussein, Phys. Rep. 424, 1 (2006)

    Article  ADS  Google Scholar 

  15. L.F. Canto, P.R.S. Gomes, R. Donangelo, J. Lubian, M.S. Hussein, Phys. Rep. 596, 1 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  16. C.Y. Wong, Phys. Rev. Lett. 31, 766 (1973)

    Article  ADS  Google Scholar 

  17. C.Y. Wong, Phys. Rev. C 86, 064603 (2012)

    Article  ADS  Google Scholar 

  18. N. Rowley, K. Hagino, Phys. Rev. C 91, 044617 (2015)

    Article  ADS  Google Scholar 

  19. E. Merzbacher, Quantum Mechanics, 3rd edition (John Wiley & Sons, Inc., 1998)

  20. C.J. Joachain, Quantum Collision Theory (North Holland, 1983)

  21. D.M. Brink, U. Smilansky, Nucl. Phys. A 405, 301 (1983)

    Article  ADS  Google Scholar 

  22. N. Fröman, P. Fröman, JWKB Approximation: Contributions to the Theory, 1st edition (North-Holland, Amsterdam, 1965)

  23. D.M. Brink, N. Takigawa, Phys. Rev. C 47, R2470 (1977)

    Google Scholar 

  24. S.Y. Lee, N. Takigawa, C. Marty, Nucl. Phys. A 308, 161 (1978)

    Article  ADS  Google Scholar 

  25. S.Y. Lee, N. Takigawa, Nucl. Phys. A 308, 189 (1978)

    Article  ADS  Google Scholar 

  26. E. Vigezzi, A. Winther, Ann. Phys. 192, 432 (1989)

    Article  ADS  Google Scholar 

Download references

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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. Paris Saclay, Espace Technologique, Bat. Discovery - RD 128 - 2e t., 91190, Saint-Aubin, France

    A. J. Toubiana

  4. Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, Rio de Janeiro, Brazil

    L. F. Canto

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

    L. F. Canto

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

    M. S. Hussein

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

    M. S. Hussein

  8. 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.

Additional information

Communicated by N. Alamanos

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Toubiana, A.J., Canto, L.F. & Hussein, M.S. Improved WKB approximation for quantum tunneling: Application to heavy-ion fusion. Eur. Phys. J. A 53, 34 (2017). https://doi.org/10.1140/epja/i2017-12225-6

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  • DOI: https://doi.org/10.1140/epja/i2017-12225-6

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