Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English, Russian   Periodicity: 4 times per year   Open access peer reviewed journal

Full text (ua)

О. I. Davydovska, V. Yu. Denisov^*, V. O. Nesterov

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

^*Corresponding author. E-mail address: denisov@kinr.kiev.ua

Abstract: Effective nucleus-nucleus potential is studied within the framework of the double folding approach, where the contribution of the kinetic energy of the nucleons is taken into account additionally. The potentials of nucleus-nucleus interaction for the system ⁴⁰Сa + ⁴⁰Сa with and without the internal kinetic energy of the nucleons are obtained. It is shown that the accounting of the contribution of kinetic energy to the potential allows to simultaneously describe the experimental cross sections of the subbarrier fusion and elastic scattering.

Keywords: nucleus, interaction potential, nucleon distribution density, fusion cross-section, kinetic energy, elastic scattering.

1. R. Bass. Nuclear Reactions With Heavy Ions (Berlin: Springer-Verlag, 1980). Google books

2. G.R. Satchler. Direct Nuclear Reactions (Oxford University, Oxford, 1983). Google books

3. P. Frobrich, R. Lipperheide, Theory of Nuclear Reactions (Oxford: Clarendon Press, 1996). Google books

4. V.Yu. Denisov, V.A. Plujko. Problems of Nuclear Physics and Nuclear Reactions (Kyiv: Publishing and Printing Center “Kyiv University”, 2013). (Rus) Book

5. Dao 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. Phys. Rev. C 49 (1994) 1652. https://doi.org/10.1103/PhysRevC.49.1652

6. M.E. Brandan, G.R. Satchler, The interaction between light heavy-ions and what it tells us. Phys. Rep. 285 (1997) 143. https://doi.org/10.1016/S0370-1573(96)00048-8

7. Dao T. Khoa, W. von Oertzen, A nuclear matter study using the density dependent M3Y interaction. Phys. Lett. B 304 (1993) 8. https://doi.org/10.1016/0370-2693(93)91391-Y

8. V.B. Soubbotin et al. Pauli distorted double folded potential. Phys. Rev. C 64 (2001) 014601. https://doi.org/10.1103/PhysRevC.64.014601

9. A.A. Ogloblin et al. Pronounced Airy structure in elastic ¹⁶O + ¹²C scattering at E_lab = 132 MeV. Phys. Rev. C 57 (1998) 1797. https://doi.org/10.1103/PhysRevC.57.1797

10. A. Ogloblin et al. New measurement of the refractive, elastic ¹⁶O + ¹²C scattering at 132, 170, 200, 230, and 260 MeV incident energies. Phys. Rev. C 62 (2000) 044601. https://doi.org/10.1103/PhysRevC.62.044601

11. Dao T. Khoa et al. Study of diffractive and refractive structure in the elastic ¹⁶O + ¹⁶O scattering at incident energies ranging from 124 to 1120 MeV. Nucl. Phys. A 672 (2000) 387. https://doi.org/10.1016/S0375-9474(99)00856-8

12. T. Khoa Dao et al. Nuclear rainbow scattering and nucleus-nucleus potential. J. Phys. G 34 (2007) R111. https://doi.org/10.1088/0954-3899/34/3/R01

13. V.Yu. Denisov, V.A. Nesterov. Potential of interaction between nuclei and nucleon-density distribution in nuclei. Phys. Atom. Nucl. 69 (2006) 1472. https://doi.org/10.1134/S1063778806090067

14. K.A. Brueckner, J.R. Buchler, M.M. Kelly. New Theoretical Approach to Nuclear Heavy-Ion Scattering. Phys. Rev. C 173 (1969) 944. https://doi.org/10.1103/PhysRev.173.944

15. J. Blocki et al. Proximity forces. Ann. Phys. (N.Y.) 105 (1977) 427. https://doi.org/10.1016/0003-4916(77)90249-4

16. V.Yu. Denisov. Interaction potential between heavy ions. Phys. Lett. B 526 (2002) 315. https://doi.org/10.1016/S0370-2693(01)01513-1

17. V.Yu. Denisov, W. Norenberg, Entrance channel potentials in the synthesis of the heaviest nuclei. Eur. Phys. J. A 15 (2002) 375. https://doi.org/10.1140/epja/i2002-10039-3

18. V.Yu. Denisov. Nucleus-nucleus potential with shell-correction contribution. Phys. Rev. С 91 (2015) 024603. https://doi.org/10.1103/PhysRevC.91.024603

19. V.Yu. Denisov, V.A. Nesterov, Effect of the Pauli exclusion principle on the potential of nucleus-nucleus interaction. Phys. At. Nucl. 73 (2010) 1142. https://doi.org/10.1134/S1063778810070070

20. V.A. Nesterov, Effect of the Pauli exclusion principle and the polarization of nuclei on the potential of their interaction for the example of the ¹⁶O + ¹⁶O system. Phys. At. Nucl. 76 (2013) 577; https://doi.org/10.1134/S106377881304008X

21. S. Misicu, H. Esbensen. Signature of shallow potentials in deep sub-barrier fusion reactions Phys. Rev. C 75 (2007) 034606. https://doi.org/10.1103/PhysRevC.75.034606

22. T. Izumoto, S. Krewald, A. Faessler. Nuclear Matter Approach to the Heavy-Ion Optical Potential. Nucl. Phys. A 341 (1980) 319. https://doi.org/10.1016/0375-9474(80)90316-4

23. S. Hossain et al. Shallow folding potential for ¹⁶O + ¹²C elastic scattering. Phys. Lett. B 636 (2006) 248. https://doi.org/10.1016/j.physletb.2006.03.071

24. V.Yu. Denisov, O.I. Davidovskaya. Elastic scattering of heavy nuclei and nucleus-nucleus potential with repulsive core. Phys. At. Nucl. 73 (2010) 404. https://doi.org/10.1134/S1063778810030026

25. V.Yu. Denisov, O.I. Davidovskaya. Elastic scattering of ¹⁶О + ¹⁶О and nucleus-nucleus potential with repulsive core. Ukr. J. Phys. 54(7) (2009) 669. (Ukr) http://archive.ujp.bitp.kiev.ua/files/journals/54/7/540704p.pdf

26. V.Yu. Denisov, O.I. Davidovskaya, V.O. Nesterov. Nucleus-nucleus potential with repulsive core and elastic scattering. Part 1. Nucleus-nucleus interaction potential. Nucl. Phys. At. Energy 11(1) (2010) 25. http://jnpae.kinr.kiev.ua/11.1/Articles_PDF/jnpae-2010-11-0025-Davidovskaya_part1.pdf

27. V.Yu. Denisov, O.I. Davidovskaya, V.O. Nesterov. Nucleus-nucleus potential with repulsive core and elastic scattering. Part 2. The elastic scattering cross sections with and without core. Nucl. Phys. At. Energy 11(1) (2010) 33. http://jnpae.kinr.kiev.ua/11.1/Articles_PDF/jnpae-2010-11-0033-Davidovskaya_part2.pdf

28. V.Yu. Denisov, O.I. Davidovskaya. Elastic scattering of heavy ions and nucleus-nucleus potential with a repulsive core. Bull. Russ. Acad. Sci.: Physics 74 (2010) 572. https://doi.org/10.3103/S1062873810040325

29. V.Yu. Denisov, O.I. Davidovskaya. Elastic ¹⁶O + ¹⁶O scattering and nucleus-nucleus potential with repulsive core. Ukr. J. Phys. 55 (2010) 861. http://archive.ujp.bitp.kiev.ua/files/journals/55/8/550801p.pdf

30. O.I. Davidovskaya, V.Yu. Denisov, V.A. Nesterov, Effective nucleus-nucleus potential with the contribution of the kinetic energy of nucleons, and the cross-sections of elastic scattering and subbarrier fusion. Ukr. J. Phys. 62 (2017) 473.

31. M. Brack, C. Guet, H.B. Hakanson. Selfconsistent semiclassical description of average nuclear properties – a link between microscopic and macroscopic models. Phys. Rep. 123 (1985) 275. https://doi.org/10.1016/0370-1573(86)90078-5

32. M. Brack, R. K. Bhaduri. Semiclassical Physics (Addison-Wesley, 1997). Google books

33. V.Yu. Denisov, V.A. Nesterov. Binding energies of nuclei and their density distributions in a nonlocal extended Thomas - Fermi approximation. Phys. At. Nucl. 65 (2002) 814. https://doi.org/10.1134/1.1481472

34. T.H.R. Skyrme. The effective nuclear potential. Nucl. Phys. 9 (1959) 615. https://doi.org/10.1016/0029-5582(58)90345-6

35. O.B. Firsov. Interaction energy of atoms for small nuclear separations. JETP 5 (1957) 1192.

36. I.G. Kaplan. Introduction to the Theory of Intermolecular Interactions (Moskva: Nauka, 1982). (Rus) Google books

37. P. Ring, P. Schuck. The Nuclear Many-Body Problem (New York: Springer-Verlag, 1980). https://www.springer.com/us/book/9783540212065

38. J. Bartel et al. Towards a better parametrisation of Skyrme-like effective forces: a critical study of the SkM force. Nucl. Phys. A 386 (1982) 79. https://doi.org/10.1016/0375-9474(82)90403-1

39. K. Hagino, N. Rowley, A.T. Kruppa, A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions. Comput. Phys. Commun. 123 (1999) 143. https://doi.org/10.1016/S0010-4655(99)00243-X

40. B. Pritychenko et al. Tables of E2 transition probabilities from the first 2+ states in even-even nuclei. At. Data Nucl. Data Tabl. 107 (2016) 1. https://doi.org/10.1016/j.adt.2015.10.001

41. T. Kibedi, R.H. Spear. Reduced electric-octupole transition probabilities, B(E3; 0 → 3)-an update. At. Data Nucl. Data Tabl. 80 (2002) 35. https://doi.org/10.1006/adnd.2001.0871

42. G. Montagnoli et al. Fusion of ⁴⁰Ca + ⁴⁰Ca and other Ca + Ca systems near and below the barrier. Phys. Rev. C 85 (2012) 024607. https://doi.org/10.1103/PhysRevC.85.024607

43. H. Doubre et al. Elastic scattering of ⁴⁰Ca by ⁴⁰Ca. Phys. Rev. C 15 (1977) 693. https://doi.org/10.1103/PhysRevC.15.693