Skip to main content
SpringerLink
Log in

Multidimensional harmonic oscillator model of subbarrier fusion

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

The new coupled-reaction channel model for the subbarrier fusion of heavy ions is presented. The low-energy surface vibrational states of both nuclei are described in the harmonic oscillator approach. The coupling channel potentials are evaluated numerically using the harmonic oscillator wave functions and the expressions for the potential energy. The approximate solution of the coupled reaction channel equations is obtained using the diagonalization at the barrier. All one- and two-phonon channels related to the \(2^+\) and \(3^-\) states in both nuclei are taken into account. The experimental data for the heavy-ion fusion reactions \(^{64}\)Ni+\(^{64}\)Ni, \(^{48}\)Ti+\(^{58}\)Fe, and \(^{54}\)Fe+\(^{58}\)Ni are well described in the model. The dressed and bare heavy-ion potentials are discussed in detail. It is shown that dressed potential is smaller than the bare one around the barrier, which leads to the enhancements of the barrier transmission. The manifestations of the shell effects on both the nucleus-nucleus potential and subbarrier fusion are discussed in detail.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study. The experimental data described in this study have been published in refereed papers.]

References

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

    Article  ADS  Google Scholar 

  2. C.H. Dasso, S. Landowne, A. Winther, Nucl. Phys. A 405, 381 (1983)

    Article  ADS  Google Scholar 

  3. C.H. Dasso, S. Landowne, A. Winther, Nucl. Phys. A 407, 221 (1983)

    Article  ADS  Google Scholar 

  4. C.H. Dasso, S. Landowne, Phys. Lett. B 183, 141 (1987)

    Article  ADS  Google Scholar 

  5. P.M. Jacobs, U. Smilansky, Phys. Lett. B 127, 313 (1983)

    Article  ADS  Google Scholar 

  6. M. Dasgupta et al., Nucl. Phys. A 539, 351 (1992)

    Article  ADS  Google Scholar 

  7. D. Ackermann et al., Nucl. Phys. A 609, 91 (1996)

    Article  ADS  Google Scholar 

  8. M. Dasgupta et al., Annu. Rev. Nucl. Part. Sci. 48, 401 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. VYu. Denisov, Eur. Phys. J. A 7, 87 (2000)

    Article  ADS  Google Scholar 

  11. C.L. Jiang et al., Phys. Rev. Lett. 93, 012701 (2004)

    Article  ADS  Google Scholar 

  12. H. Esbensen, Phys. Rev. C 72, 054607 (2005)

    Article  ADS  Google Scholar 

  13. S. Misicu, H. Esbensen, Phys. Rev. C 75, 034606 (2007)

    Article  ADS  Google Scholar 

  14. B.B. Back et al., Rev. Mod. Phys. 86, 317 (2014)

    Article  ADS  Google Scholar 

  15. VYu. Denisov, Phys. Rev. C 89, 044604 (2014)

    Article  ADS  Google Scholar 

  16. A.M. Stefanini et al., Phys. Rev. C 92, 64607 (2015)

    Article  ADS  Google Scholar 

  17. G. Montagnoli, A.M. Stefanini, Eur. Phys. J. A 53, 169 (2017)

    Article  ADS  Google Scholar 

  18. C.L. Jiang et al., Eur. Phys. J. A 54, 218 (2018)

    Article  ADS  Google Scholar 

  19. VYu. Denisov, IYu. Sedykh, Eur. Phys. J. A 55, 153 (2019)

    Article  ADS  Google Scholar 

  20. C.L. Jiang et al., Eur. Phys. J. A 57, 235 (2021)

    Article  ADS  Google Scholar 

  21. Vijay et al., Phys. Rev. C 103, 024607 (2021)

    Article  ADS  Google Scholar 

  22. O.I. Davydovska, VYu. Denisov, V.A. Nesterov, Nucl. Phys. A 1018, 122372 (2022)

    Article  Google Scholar 

  23. V.Yu. Denisov, V.A. Plujko, Problems of physics of atomic nucleus and nuclear reactions (Publishing and Polygraphic Centre ”The University of Kyiv”, Kiev, 2013) (in Russian)

  24. S. Hofmann, Radiochim. Acta 107, 879 (2019)

    Article  Google Scholar 

  25. Y.T. Oganessian, A. Sobiczewski, G.M. Ter-Akopian, Phys. Scr. 92, 023003 (2017)

    Article  ADS  Google Scholar 

  26. VYu. Denisov, IYu. Sedykh, Chinese Phys. C 45, 044106 (2021)

    Article  ADS  Google Scholar 

  27. G.R. Satchler, Direct Nuclear Reactions (Clarendon Press, Oxford, 1983)

    Google Scholar 

  28. P. Frobrich, R. Lipperheide, Theory of Nuclear Reactions (Clarendon Press, Oxford, 1996)

  29. A. Bohr, B. Mottelson, Nuclear Structure, vol. 2 (W. A. Benjamin, Reading, 1975)

    MATH  Google Scholar 

  30. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1972)

  31. VYu. Denisov, N.A. Pilipenko, Phys. Rev. C 76, 014602 (2007)

    Article  ADS  Google Scholar 

  32. VYu. Denisov, IYu. Sedykh, Eur. Phys. J. A 57, 129 (2021)

    Article  ADS  Google Scholar 

  33. P. Moller, J.R. Nix, Nucl. Phys. A272, 502 (1976)

    Article  ADS  Google Scholar 

  34. VYu. Denisov, Phys. Rev. C 88, 044608 (2013)

    Article  ADS  Google Scholar 

  35. VYu. Denisov, T.O. Margitych, IYu. Sedykh, Nucl. Phys. A 958, 101 (2017)

    Article  ADS  Google Scholar 

  36. VYu. Denisov, IYu. Sedykh, Nucl. Phys. A 963, 15 (2017)

    Article  ADS  Google Scholar 

  37. D.A. Varshalovich, A.N. Moskalev, V.K. Khersonsky, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988)

    Book  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. M. Ismail, I.A.M. Abdul-Magead, Nucl. Phys. A 922, 168 (2012)

    Article  ADS  Google Scholar 

  40. VYu. Denisov, Sov. J. Nucl. Phys. 49, 399 (1989)

    Google Scholar 

  41. VYu. Denisov, Phys. Atom. Nucl. 59, 981 (1996)

    Google Scholar 

  42. B.V. Derjaguin, Kolloid-Zeitschrift 69, 155 (1934)

    Article  Google Scholar 

  43. J. Blocki et al., Ann. Phys. 105, 427 (1977)

    Article  ADS  Google Scholar 

  44. VYu. Denisov, Phys. Rev. C 91, 024603 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  45. I. Dutt, R.K. Puri, Phys. Rev. C 81, 064609 (2010)

    Article  ADS  Google Scholar 

  46. VYu. Denisov, Phys. Lett. B 526, 315 (2002)

    Article  ADS  Google Scholar 

  47. V.M. Strutinsky, Sov. J. Nucl. Phys. 3, 449 (1966)

    Google Scholar 

  48. V.M. Strutinsky, Nucl. Phys. A 95, 420 (1967)

    Article  ADS  Google Scholar 

  49. V.M. Strutinsky, Nucl. Phys. A 122, 1 (1968)

    Article  ADS  Google Scholar 

  50. M. Brack et al., Rev. Mod. Phys. 44, 320 (1972)

    Article  ADS  Google Scholar 

  51. W.J. Huang et al., Chin. Phys. C 45, 030003 (2021)

    Article  Google Scholar 

  52. B. Pritychenko et al., At. Data Nucl. Data Tabl. 107, 1 (2016)

    Article  ADS  Google Scholar 

  53. T. Kibedi, R.H. Spear, At. Data Nucl. Data Tables 80, 35 (2002)

    Article  ADS  Google Scholar 

  54. R.O. Akyuz, A. Winther, Proc. Enrico Fermi Int. School of Physics, 1979, ”Nuclear structure and heavy-ion reactions”, ed. by R.A. Broglia, C.H. Dasso, R. Ricci (North-Holland, Amsterdam, 1981) p. 491

  55. H. Feshbach, Theoretical Nuclear Physics: Nuclear Reactions (Wiley, New York, 1992)

    Google Scholar 

Download references

Acknowledgements

The author strongly thanks the support of Professors Fabiana Gramegna, Enrico Fioretto, Giovanna Montagloli, and Alberto Stefanini. The author thanks for the support to Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro of Istituto Nazionale di Fisica Nucleare, the National Academy of Sciences of Ukraine and Taras Shevchenko National University of Kiev.

Author information

Authors and Affiliations

  1. INFN Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020, Legnaro, Italy

    V. Yu. Denisov

  2. Institute for Nuclear Research, Prospect Nauki 47, 03028, Kiev, Ukraine

    V. Yu. Denisov

  3. Faculty of Physics, Taras Shevchenko National University of Kiev, Prospect Glushkova 2, 03022, Kiev, Ukraine

    V. Yu. Denisov

Authors
  1. V. Yu. Denisov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Yu. Denisov.

Additional information

Communicated by Alexis Diaz-Torres.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Denisov, V.Y. Multidimensional harmonic oscillator model of subbarrier fusion. Eur. Phys. J. A 58, 91 (2022). https://doi.org/10.1140/epja/s10050-022-00746-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-022-00746-2

Search

Navigation