Velocity-in/dependent double folding analysis of 12C + 12C elastic scattering cross section at different energies

Authors

  • Sunday D. Olorunfunmi
    Department of Physics & Engineering Physics, Obafemi Awolowo University, Ile-Ife, 220005, Osun State, Nigeria
  • Armand Bahini
    Université de Caen Normandie, ENSICAEN, CNRS/IN2P3, LPC Caen UMR6534, F-14000 Caen, France
  • Samuel A. Adeojo
    Department of Physics & Engineering Physics, Obafemi Awolowo University, Ile-Ife, 220005, Osun State, Nigeria

Keywords:

Velocity–dependent potential

Abstract

This study investigates the elastic scattering cross sections for 12 C + 12 C over a wide range of incident energies from 78.85 to 420 MeV using the velocity–dependent São Paulo Potential version 2 (SPP2) and the velocity–independent Brazilian Nuclear Potential (BNP) within the optical-model-based double folding (DF) framework. Two different density distributions for 12C, experimental matter density (ED), and the Dirac-Hartree-Bogoliubov (DHB) theoretical matter density, were employed. The analysis compares the computed potentials, obtained by folding the density distributions, and evaluates the accuracy of the results through comparison with experimental data. Two approaches were explored to determine the depths of the potentials, highlighting their performance and sensitivity to energy and density distributions. Results indicate good agreement with experimental data, with SPP2 generally outperforming BNP. Analysis of volume integrals and reaction cross sections further elucidates the behavior of the potentials and their implications on scattering phenomena. Overall, this study provides insights into the dynamics of nuclear interactions at intermediate energies, contributing to the understanding of nuclear reactions.

Dimensions

[1] G. R. Satchler & W. G. Love, “Folding model potentials from realistic interactions for heavy-ion scattering”, Physics Reports 55 (1979) 183. https://doi.org/10.1016/0370-1573(79)90081-4.

[2] A. M. Kobos, B. A. Brown, P. E. Hodgson, G. R. Satchler & A. Budxanowski, “Folding model anallysis of α–particle elastic scattering with a semirealistic density–dependent effective interaction”, Nuclear Physics A 384 (1982) 65. https://doi.org/10.1016/0375-9474(82)90305-0.

[3] A. M. Kobos, B. A. Brown, R. Lindsay & G. R. Satchler, “Optical potentials for heavy-ion elastic scattering”, Nuclear Physics A 425 (1984) 205. https://doi.org/10.1016/0375-9474(84)90073-3.

[4] M. E. Farid & G. R. Satchler, “A density–dependent interaction in the folding model for heavy–ion potentials”, Nuclear Physics A 438 (1985) 525. https://doi.org/10.1016/0375-9474(85)90391-4.

[5] D. T. Khoa, W. von Oertzen & H. G. Bohlen, “Double–folding model for heavy-ion optical potential: revised and applied to study 12C and 16O elastic scattering ”, Physical Review C 49 (1994) 1652. https://doi.org/10.1103/PhysRevC.49.1652.

[6] D. T. Khoa, W. V. Oertzen, H. G. Bohlen, G. Bartnitzky, H. Clement, Y. Sugiyama, B. Gebauer, A. N. Ostrowski, T. Wilpert, M. Wilpert & C. Langner, “Equation of state for cold nuclear matter from refractive 16 O+16 O elastic scattering”, Physical Review Letters 74 (1995) 34. https://doi.org/10.1103/PhysRevLett.74.34.

[7] S. Hossain, M. N. A. Abdullah, K. M. Hasan, M. Asaduzzaman, M. A. R. Akanda, S. K. Das, A. S. B. Tariq, M. A. Uddin, A. K. Basak, S. Ali & F. B. Malik, “Shallow folding potential for 16 O + 12 C elastic scattering ”, Physics Letters B 636 (2006) 248. https://doi.org/10.1016/j.physletb.2006.03.071.

[8] D. T. Khoa, N. H. Phuc, D. T. Loan & B. M. Loc, “Nuclear mean field and double-folding model of the nucleus–nucleus optical potential ”, Physical Review C 94 (2016) 034612. http://link.aps.org/doi/10.1103/PhysRevC.94.

[9] M. E. Brandan & G. R. Satchler, “The interaction between light heavy-ions and what it tells us”, Physics Reports 285 (1997) 143. https://doi.org/10.1016/S0370-1573(96)00048-8.

[10] A. J. Cole, W. D. M. Rae, M. E. Brandan, A. Dacal, B. G. Harvey, R. Legrain, M. J. Murphy & R. G. Stokstad, “12 C+12 C reaction cross section between 70 and 290 MeV obtained from elastic scattering”, Physical Review Letters 47 (1981) 1705. https://doi.org/10.1103/PhysRevLett.47.1705.

[11] H. G. Bohlen, X. S. Chen, J. G. Cramer, P. Frobrich, B. Gebauer, H. Lettau, A. Miczaika, W. von Oertzen, R. Ulrich & T. Wilpert, “Refractive scattering and the nuclear rainbow in the interaction of 12,13C with 12 C at 20 MeV/N ”, Zeitschrift fũr Physik A Atoms and Nuclei 322 (1985) 241. https://doi.org/10.1007/BF01411889.

[12] E. Stiliaris, H. G. Bohlen, P. Frobrich, B. Gebaur, D. Kolbert, W. von Oertzen, M. Wilpert & Th. Wilpert, “Nuclear rainbow structures in the elastic scattering of 16 O on 16 O at EL = 350 MeV”,Physics Letters B 223 (1989) 291. https://doi.org/10.1016/0370-2693(89)91604-3.

[13] G. Bertsch, J. Borysowicz, H. McManus & W. G. Love, “Interactions for inelastic scattering derived form realistic potentials”, Nuclear Physics A 284 (1977) 399. https://doi.org/10.1016/0375-9474(77)90392-X.

[14] D. T. Khoa, N. H. Phuc, D. T. Loan & B. H. Loc, “Nuclear mean field and double–folding model of the nucleus–nucleus optical potential”, Physical Review C 94 (2016) 034612. https://doi.org/10.1103/PhysRevC.94.034612.

[15] N. Rowley, H. Doubre & C. Marty, “Low partial waves in 12 C+12 C elastic scattering”, Physics Letter B 69 (1977) 147. https://doi.org/10.1016/0370-2693(77)90630-X.

[16] Z.M.M. Mahmoud & M.A. Hassanien, “Analysis of 12 C+12 C elastic scattering for energy between 70 and 1440 MeV ”, Physics of Atomic Nuclei 82 (2019) 599. https://doi.org/10.1134/S1063778819060103.

[17] M. A. Hassanain, A. A. Ibraheem & M. E. Farid, “Double folding cluster potential for 12 C+12 C elastic scattering”, Physical Review C 77 (2008) 034601. https://doi.org/10.1103/PhysRevC.77.034601

[18] L. C. Chamon, B. V. Carlson & L. R. Gasques, “São Paulo potential version 2 (SPP2) and Brazilian nuclear potential (BNP) ”, Computer Physics Communications 267 (2021) 108061. https://doi.org/10.1016/j.cpc.2021.108061.

[19] A. A. Ibraheem & H. Al-Amri, “Analysis of 4,6,8 He+208 Pb elastic scattering at E = 22 MeV using various potentials”, Revista Mexicana de Fisica 68051201 (2022) 1. https://doi.org/10.31349/RevMexFis.68.051201.

[20] Sh. Hamada & A. A. Ibraheem, “Reanalysis of 6 Li+90 Zr angular distributions using different nuclear potentials”, Journal of Taibah University for Science 16 (2022) 163. https://doi.org/10.1080/16583655.2022.2036428.

[21] U. Umbelino, R. Lichtenthäler, O.C. Santos, K. C. Pires, A. S. Serra, V. Scarduelli, A. L. de Lara, E. O. Zevallos, J. C. Zamora, A. Lepine–Szily, J. M. B. Shorto, M. Assunifmmode & V. A. B. Zagatto, “Quasielastic scattering of light radioactive and stable projectiles on 9 Be” Physical Review C 106 (2022) 054602. https://doi.org/10.1103/PhysRevC.106.054602.

[22] S. D. Olorunfunmi & A. Bahini, “Reanalysis of 10 B+120 Sn Elastic Scattering Cross Section Using São Paulo Potential Version 2 and Brazilian Nuclear Potential”, Brazilan Journal of Physics 52 (2022) 11. https://doi.org/10.1007/s13538-021-01018-y.

[23] S. D. Olorunfunmi, S. A. Adeojo & A. Bahini, “Investigation of elastic scattering angular distributions of 12,13C + 90,91,92,94,96 Zr: a comparative analysis of different optical model potentials”, Indian Journal of Physics 98 (2024) 7. https://doi.org/10.1007/s12648-023-03025-y

[24] A. H. Amer, Z. M. M. Mahmoud & Yu. E. Penionzhkevich, “Double folding analysis of α+12 C elastic scattering using different effective interactions”, Nuclear Physics A (2022) 1020. https://doi.org/10.1016/j.nuclphysa.2022.122398.

[25] M. N. El-Hammamy, A. A. Ibraheem, M. E. Farid, E. F. Elshamy & S. Hamada, “Comprehensive examination of the elastic scattering angular distributions of 10 C+4 He, 27 Al, 58 Ni and 208 Pb using various potentials”, Revista Mexicana de Fisica 69 (2023) 031201. https://doi.org/10.31349/RevMexFis.69.031201.

[26] M. Nassurlla, N. Burtebayev, S. B. Sakuta, Sh. Hamada, S. V. Artemov, K. Rusek, N. Marzhan, N. Amangeldi, B. Mauyey, G. Yergaliuly, F. Ergashev, A. Sabidolda, R. Khojayev, Y. B. Mukanov, E. Piasecki & Awad A. Ibraheem, “Scattering of 10 B ions on 11 B nuclei at an energy of 41.3 MeV”, The European Physical Journal A 60 (2024) 30. https://doi.org/10.1140/epja/s10050-023-01220-3.

[27] L. C. Chamon, L. R. Gasques & B. V. Carlson, “Velocity–dependent model for the α–α interaction in the context of the double–folding potential”, Physical Review C 101 (2020) 034603. https://doi.org/10.1103/PhysRevC.101.034603.

[28] L. C. Chamon, L. R. Gasques & B. V. Carlson, “Approximate treatment of relativistic effects in the low-energy α+α scattering”, Physical Review C 84 (2011) 044607. https://doi.org/10.1103/PhysRevC.84.044607.

[29] H. De Vries, C.W. De Jager & C. De Vries, “Nuclear charge-density-distribution parameters from elastic electron scattering” Atomic Data and Nuclear Data Tables 36 (1987) 495. https://doi.org/10.1016/0092-640X(87)90013-1

[30] B.V. Carlson & D. Hirata, “Dirac-Hartree-Fock-Bogoliubov approximation for finite nuclei”, Physical Review C 62 (2000) 054310. https://doi.org/10.1103/PhysRevC.62.054310

[31] R. G. Stokstad, R. M. Wieland, G. R. Satchler, C. B. Fulmer, D. C. Hensley, S. Raman, L. D. Rickertsen, A. H. Snell & P. M. Stelson, ?Elastic and inelastic scattering of 12 C by 12 C from Ec.m. = 35 − 63 MeV?, Physical Review C 20 (1979) 655. https://link.aps.org/doi/10.1103/PhysRevC.20.655.

[32] C. C. Sahm, T. Murakarni, J. G. Cramer, A. J. Lazzarini, D. D. Leach, D. R. Tieger, R. A. Loveman, W. G. Lynch, M. B. Tsang & J. Van der Plicht, ?Total reaction cross section for 12 C on 12 C, 40 Ca, 90 Zr, and 208 Pb between 10 and 35 MeV/nucleon?, Physical Review C 34 (1986) 2165. https://link.aps.org/doi/10.1103/PhysRevC.34.2165.

[33] P. Mohr, Z. Fũlõp, G. Gyũrky, G. G. Kiss & T. Szũcs, “Successful prediction of total α–induced reaction cross sections at astrophysically relevant sub-Coulomb energies using a novel approach”, Physical Review Letters 124 (2020) 252701. https://doi.org/10.1103/PhysRevLett.124.252701.

[34] M. C. Mermaz, ''Phase shift analysis of heavy-ion elastic scattering measured at intermediate energies'', Zeitschrift fũr Physik A 321 (1985) 613 https://doi.org/10.1007/BF01432438.

[35] S. Kox, A. Gamp, C. Perrin, J. Arvieux, R. Bertholet, J. F. Bruandet, M. Buenerd, R. Cherkaoui, A. J. Cole, Y. El–Masri, N. Longequeue, J. Menet, F. Merchez & J. B.Viano, ?Trends of total reaction cross

sections for heavy ion collisions in the intermediate energy range?, Physical Review C 36 (1987) 1687. https://link.aps.org/doi/10.1103/PhysRevC.35.1678.

[36] M. Buenerd, A. Lounis, J. Chauvin, D. Lebrun, P. Martin, G. Duhamel, J.C. Gondrand, G. Duhamel, J.C. Gondrand & P. De Saintignon, ’Elastic and inelastic scattering of carbon ions at intermidiate energies’, Nuclear Physics A 424 (1984) 313. https://doi.org/10.1016/0375-9474(84)90186-6.

Published

2026-02-01

How to Cite

Velocity-in/dependent double folding analysis of 12C + 12C elastic scattering cross section at different energies. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 3028. https://doi.org/10.46481/jnsps.2026.3028

Issue

Volume 8, Issue 1, February 2026

Section

Physics & Astronomy
Copyright & Licensing

Copyright (c) 2026 Sunday D. Olorunfunmi, Armand Bahini, Samuel A. Adeojo (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Velocity-in/dependent double folding analysis of 12C + 12C elastic scattering cross section at different energies. (2026). Journal of the Nigerian Society of Physical Sciences, 8(1), 3028. https://doi.org/10.46481/jnsps.2026.3028

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