A comprehensive analysis of 19F + 12C, 16O, 28;30Si, 40Ca, 54;56Fe, 208Pb, 232Th fusion reactions


  • Murat Aygun Bitlis Eren University
  • H. Cin Bitlis Eren University




Fusion reaction reaction, density distribution., optical model, double folding model


In this study, a lot of fusion experimental data are theoretically analyzed by using ten different density distributions of the 19F nucleus. The real potentials are obtained by means of the double folding model while the imaginary potentials are accepted as the Woods-Saxon potential. The theoretical results are compared with the results calculated over one-dimensional Wong formula as well as the experimental data. Thus, alternative density distributions are proposed for the analysis of the experimental data of the 19F fusion reactions. Additionally, the barrier positions and heights of all the analyzed fusion reactions are calculated for all the density distributions and new analytical expressions for these results are derived. Finally, new pocket formulas giving the imaginary potential depths for fusion cross-section calculations with 19F are obtained for the first time.


M. Aygun and Z. Aygun, A comprehensive analysis of 9Li +70 Zn fu- sion cross section by using proximity potentials, temperature dependent den- sity distributions and nuclear potentials, Rev. Mex. Fis. 65 (2019) 573, https://doi.org/10.31349/revmexfis.65.573.

G. Kocak, M. Aygun, A theoretical analysis of the cross sections of 18;19;20O +12 C fusion reactions by using different density distributions, Nucl. Phys. A 1003 (2020) 122015, https://doi.org/10.1016/j.nuclphysa.2020.122015.

R. M. Anjos et al., No evidence of break-up effects on the fusion of 9Be with medium-light nuclei, Phys. Lett. B 534 (2002) 45, https://doi.org/10.1016/S0370-2693(02)01554-X.

R. M. Anjos et al., Effect of the entrance channel mass asymmetry on the limitation of light heavy-ion fusion cross sections, Phys. Rev. C 42 (1990) 354, https://doi.org/10.1103/PhysRevC.42.354.

M. S. Chiou, M. W. Wu, N. Easwar and J. V. Maher, Complete fusion of 19F with Al and Si isotopes, Phys. Rev. C 24 (1981) 2507, https://doi.org/10.1103/PhysRevC.24.2507.

H. Funaki and E. Arai, Anomaly in the 15N, 16O, 19F +54;56 Fe fusion cross sections around the Coulomb barrier energy, Nucl. Phys. A 556 (1993) 307, https://doi.org/10.1016/0375-9474(93)90353-Y.

D. J. Hinde, A. C. Berriman, M. Dasgupta, J. R. Leigh, J. C. Mein, C. R. Morton and J. O. Newton, Limiting angular momentum for statistical model de- scription of fission, Phys. Rev. C 60 (1999) 054602, https://doi.org/10.1103/PhysRevC.60.054602.

S. Kailas et al., Fission fragment angular distributions for the system 19F+232Th, Phys. Rev. C 43 (1991) 1466, https://doi.org/10.1103/PhysRevC.43.1466.

Z. Gao-Long and L. Xiao-Yun, Double folding model calculation applied to fusion reactions, Chin. Phys. C 32 (2008) 812, https://doi.org/10.1088/1674-1137/32/10/009.

I. I. Gontchar, D. J. Hinde, M. Dasgupta and J. O. Newton, Double fold- ing nucleus-nucleus potential applied to heavyion fusion reactions, Phys. Rev. C 69 (2004) 024610, https://doi.org/10.1103/PhysRevC.69.024610.

M. Rashdan, Folding model description of 16O+154Sm fusion reaction, J. Phys. G: Nucl. Part. Phys. 22 (1996) 139, https://doi.org/10.1088/0954-3899/22/1/013.

M. Aygun, A Comprehensive Description of 19F Elastic Scattering by 12C, 16O, 66Zn, 159Tb, and 208Pb Target Nuclei, Braz. J. Phys. 49 (2019) 760, https://doi.org/10.1007/s13538-019-00680-7.

G. R. Satchler and W.G. Love, Folding model potentials from realistic in- teractions for heavy-ion scattering, Phys. Rep. 55 (1979) 183, https://doi.org/10.1016/0370-1573(79)90081-4.

J. Cook, DFPOT-a program for the calculation of double folded potentials, Commun. Comput. Phys. 25 (1982) 125.

I.J. Thompson, Coupled reaction channels calculations in nuclear physics, Comput. Phys. Rep. 7 (1988) 167.

L. C. Chamon et al., Toward a global description of the nucleusnucleus in- teraction, Phys. Rev. C 66 (2002) 014610, https://doi.org/10.1103/PhysRevC.66.014610.

W. M. Seif and H. Mansour, Systematics of nucleon density distributions and neutron skin of nuclei, Int. J. Mod. Phys. E 24 (2015) 1550083, https://doi.org/10.1142/S0218301315500834.

H. Schechter and L. F. Canto, Proximity formulae for folding potentials, Nucl. Phys. A 315 (1979) 470, https://doi.org/10.1016/0375-9474(79)90623-7.

S. A. Moszkowski, Energy dependence of the ion-ion potential with a simplified energy density method, Nucl. Phys. A 309 (1978) 273, https://doi.org/10.1016/0375-9474(78)90548-1.

C. W. De Jager, H. De Vries and C. De Vries, Nuclear chargeand magnetization-density-distribution parameters from elastic electron scattering, At. Data Nucl. Data Tables 14 (1974) 479, https://doi.org/10.1016/S0092-640X(74)80002-1.

C. Ngoˆ et al., Properties of heavy ion interaction potentials calculated in the energy density formalism, Nucl. Phys. A 252 (1975) 237, https://doi.org/10.1016/0375-9474(75)90614-4.

H. Ngo and C. Ng ˆ o, Calculation of the real part of the interaction potential between two heavy ions in the sudden approximation,Nucl. Phys. A 348 (1980) 140. https://doi.org/10.1016/0375-9474(80)90550-3.

R. K. Gupta, D. Singh and W. Greiner, Semiclassical and microscopic calculations of the spin-orbit density part of the Skyrme nucleus-nucleus interac- tion potential with temperature effects included, Phys. Rev. C 75 (2007) 024603, https://doi.org/10.1103/PhysRevC.75.024603.

O. N. Ghodsi and F. Torabi, Comparative study of fusion barriers using Skyrme interactions and the energy density functional, Phys. Rev. C 92 (2015) 064612, https://doi.org/10.1103/PhysRevC.92.064612.

R. K. Gupta, D. Singh, R. Kumar and W. Greiner, Universal functions of nuclear proximity potential for Skyrme nucleusnucleus interaction in a semiclassical approach, J. Phys. G: Nucl. Part. Phys. 36 (2009) 075104, https://doi.org/10.1088/09543899/36/7/075104.

E. Wesolowski, The RMS radii of the charge distribution in nuclei, J. Phys. G: Nucl. Part. Phys. 11 (1985) 1401, https://doi.org/10.1088/0305-4616/11/8/008.

N. K. Dhiman, Role of Different Model Ingredients in the Exotic Cluster- Decay of 56Ni, Ukr. J. Phys. 57 (2012) 796, https://doi.org/10.15407/ujpe57.8.796.


S. Goriely, M. Samyn, P.-H. Heenen, J. M. Pearson and F. Tondeur, Hartree-Fock mass formulas and extrapolation to new mass data, Phys. Rev. C 66 (2002) 024326, https://doi.org/10.1103/PhysRevC.66.024326.

M. Samyn, S. Goriely, P.-H. Heenen, J. M. Pearson and F. Tondeur, A Hartree-Fock-Bogoliubov mass formula, Nucl. Phys. A 700 (2002) 142, https://doi.org/10.1016/S0375-9474(01)01316-1.

V. Hnizdo, J. Szymakowski, K. W. Kemper, and J. D. Fox, Folding-model description of elastic and inelastic scattering of 9Be by 40;44Ca and 39K at 40 MeV, Phys. Rev. C 24 (1981) 1495, https://doi.org/10.1103/PhysRevC.24.1495.

M. El-Azab Farid and M. A. Hassanain, Density-independent folding anal- ysis of the 6;7Li elastic scattering at intermediate energies, Nucl. Phys. A 678 (2000) 39, https://doi.org/10.1016/S0375-9474(00)00313-4.

G. Kocak, M. Karakoc, I. Boztosun and A. B. Balantekin, Effects of ff-cluster potentials for the 16O +16 O fusion reaction and S factor, Phys. Rev. C 81 (2010) 024615, https://doi.org/10.1103/PhysRevC.81.024615.

S. Qing-biao, F. Da-chun and Z. Yi-zhong, Neutron relativistic phenomenological and microscopic optical potential, Phys. Rev. C 43 (1991) 2773, https://doi.org/10.1103/PhysRevC.43.2773.

H. F. Ehrenberg, R. Hofstadter, U. Meyer-Berkhout, D.G. Ravenhall and S. E. Sobottka, High-Energy Electron Scattering and the Charge Distribution of Carbon-12 and Oxygen-16, Phys. Rev. 113 (1959) 666, https://doi.org/10.1103/PhysRev.113.666.

S. Hossain, M. N. A. Abdullah, Md. Z. Rahman, A. K. Basak and F. B. Malik, Non-monotonic potentials for 6Li elastic scattering at 88 MeV, Phys. Scr. 87 (2013) 015201, https://doi.org/10.1088/0031-8949/87/01/015201.


C. Y. Wong, Interaction Barrier in Charged-Particle Nuclear Reactions, Phys. Rev. Lett. 31 (1973) 766, https://doi.org/10.1103/PhysRevLett.31.766.

A. B. Balantekin and N. Takigawa, Quantum tunneling in nuclear fusion, Rev. Mod. Phys. 70 (1998) 77, https://doi.org/10.1103/RevModPhys.70.77.

Q. Haider and F. B. Malik, Barrier penetration calculation of heavy-ion fusion cross sections in the above- and sub-barrier regions, J. Phys. G: Nucl. Phys. 12 (1986) 537, https://doi.org/10.1088/0305-4616/12/6/012.

L. F. Canto, P. R. S. Gomes, J. Lubian, L. C. Chamon and E. Crema, Dy- namic effects of breakup on fusion reactions of weakly bound nuclei, Nucl. Phys. A 821 (2009) 51, https://doi.org/10.1016/j.nuclphysa.2009.02.001.

H. C. Manjunatha and K. N. Sridhar, Fusion barrier characteristics of actinides, Nucl. Phys. A 971 (2018) 83, https://doi.org/10.1016/j.nuclphysa.2018.01.016.

P. R. Christensen and A. Winther, The evidence of the ion-ion potentials from heavy ion elastic scattering, Phys. Lett. B 65 (1976) 19, https://doi.org/10.1016/0370-2693(76)90524-4.

D. G. Kovar et al., Systematics of carbon- and oxygen-induced fusion on nuclei with 12 ≤ A ≤ 19, Phys. Rev. C 20 (1979) 1305, https://doi.org/10.1103/PhysRevC.20.1305.

M. Ismail and M. M. Osman, Real part of the ion-ion interaction potential by use of the Negele realistic nucleon-nucleon force, Phys. Rev. C 24 (1981) 458, https://doi.org/10.1103/PhysRevC.24.458.

H. C. Manjunatha and K. N. Sridhar, Semi empirical formula for fusion barriers of nuclei with 1 ≤ Z ≤ 20, Indian J. Phys. 95 (2021) 935, https://doi.org/10.1007/s12648-020-01756-w.

S. K. Gupta and S. Kailas, Rapid Communication Fusion barriers for heavy-ion systems, Phys. Rev. C 26 (1982) 747, https://doi.org/10.1103/PhysRevC.26.747.

M. Liu et al., Applications of Skyrme energy-density functional to fu- sion reactions spanning the fusion barriers, Nucl. Phys. A 768 (2006) 80, https://doi.org/10.1016/j.nuclphysa.2006.01.011.

A. K. Mohanty, S. V. S. Sastry, S. K. Kataria and V. S. Ramamurthy, Experimental determination of energy-dependent barriers for fusion, Phys. Rev. C 46 (1992) 2012, https://doi.org/10.1103/PhysRevC.46.2012.




How to Cite

M. Aygun and H. Cin, “A comprehensive analysis of 19F + 12C, 16O, 28;30Si, 40Ca, 54;56Fe, 208Pb, 232Th fusion reactions”, Rev. Mex. Fís., vol. 68, no. 3 May-Jun, pp. 031202 1–, May 2022.