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Journal of Fusion Energy

, Volume 35, Issue 6, pp 816–822 | Cite as

Fusion Cross Section of \({\mathrm{T(d,n)}}^{4}{\mathrm{He}}\) and \({}^{3}{\mathrm{He(d,p)}}^{4}{\mathrm{He}}\) Reactions by Four Parameters Formula

  • T. Koohrokhi
  • A. M. Izadpanah
  • S. K. Hosseini
Original Research
  • 152 Downloads

Abstract

Fusion cross sections of light nuclei are calculated by a complex potential and taking into account of conservation of angular momentum and parity. The nuclear potential is assumed to be as simple as a spherical complex square well with a rigid core. Then the nuclear phase shift is extracted from continuity condition of inverse of the logarithmic derivative of the wave functions as a complex quantity. The quantum tunneling probability and cross section are obtained via real and complex components of nuclear phase shift. The obtained results for the two most important light nuclei reactions, \({\mathrm{T(d,n)}}^{4}{\mathrm{He}}\), \({}^{3}{\mathrm{He(d,p)}}^{4}{\mathrm{He}}\) are compared with other theoretical formulas and experimental data. Despite that the theory is simplified as much as possible and the complexities and details of nuclear interactions has been ignored, excellent agreements with experimental data are achieved.

Keywords

Complex potential Nuclear phase shift Quantum tunneling probability Fusion cross section 

References

  1. 1.
    M. Razavy, Quantum Theory of Tunneling (World Scientific Publishing Co. Pte. Ltd., Singapore, 2003)CrossRefMATHGoogle Scholar
  2. 2.
    C. Iliadis, Nuclear Physics of Stars (WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim, 2007)CrossRefGoogle Scholar
  3. 3.
    G.Z. Gamov, Physics 51, 204 (1928)CrossRefGoogle Scholar
  4. 4.
    E.M. Burbidge, G.R. Burbidge, W.A. Fowler, F. Hoyle, Rev. Mod. Phys. 29, 547 (1957)ADSCrossRefGoogle Scholar
  5. 5.
    D.D. Clyton, Principles of Stellar Evolution And Nucleosynthesis (Mcgraw-Hill, New York, 1968)Google Scholar
  6. 6.
    J.G. Brennan, Phys. Rev. III, 1592 (1958)CrossRefGoogle Scholar
  7. 7.
    B.H. Duane, Fusion cross section theory. In Annual Report on CTR Technology (1972), ed. W.C. Wolkenhauer, Rep. BNWL-1685, Battelle Pacific Northwest Laboratory, Richland (1972)Google Scholar
  8. 8.
    J.D. Huba, NRL Plasma Formulary (Naval Research Laboratory, Washington DC, 2013), p. 44. (revised)Google Scholar
  9. 9.
    H.S. Bosch, G.M. Hale, Nucl. Fusion 32, 611–631 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    X.Z. Li, J. Tian, M.Y. Mei, C.X. Li, Sub-barrier fusion and selective resonant tunneling. Phys. Rev. C 61, 024610 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    X.Z. Li, Nuclear fusion for nuclear fusion. Fusion Sci. Tech. 41, 63 (2002)Google Scholar
  12. 12.
    X.Z. Li, B. Liu, S. Chen, Q.M. Wei, H. Hora, Fusion cross sections for inertial fusion energy. Laser Part. Beams 22, 469 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    X.Z. Li, Q.M. Wei, B. Liu, A new simple formula for fusion cross-sections of light nuclei. Nucl. Fusion 48, 125003 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    X.Z. Li, Z.M. Dong, C.L. Liang, J. Fusion Energ. 31, 432–436 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    T. Koohrokhi, R. Azadifar, J. Fusion Energ. 35, 493–497 (2016)CrossRefGoogle Scholar
  16. 16.
    O.N. Ghodsi, V. Zanganeh, The effect of the nuclear state equation on the surface diffuseness parameter of the Woods-Saxon potential in the heavy ion fusion reactions. Nucl. Phys. A 846, 40–50 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1964)MATHGoogle Scholar
  18. 18.
    D.R. Tilley, C.M. Cheves, J.L. Godwin, G.M. Hale, H.M. Hofmann, J.H. Kelley, C.G. Sheu, H.R. Weller, Nucl. Phys. A 708, 3 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    C.L. Dunford, Data retrieved from the Cross Section Information Storage and Retrieval System (CSISRS) data base (1996). http://www.nndc.bnl.gov. (EXFORC0023001) plot produced using the code BNL 325. National Nuclear Data Center, Brookhaven National Laboratory
  20. 20.
    D.M. Brink, Semi-Classical Methods for Nucleus–Nucleus Scattering (Cambridge University Press, Cambridge, 2009)MATHGoogle Scholar
  21. 21.
    I.J. Thompson, F.M. Nunes, Nuclear Reactions For Astrophysics (Cambridge University Press, Cambridge, 2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • T. Koohrokhi
    • 1
  • A. M. Izadpanah
    • 1
  • S. K. Hosseini
    • 1
  1. 1.Faculty of SciencesGolestan UniversityGorganIran

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