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   Periodicity: 4 times per year   Open access peer reviewed journal

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V. O. Nesterov^*

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

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

Abstract: Nucleon distribution densities and nucleus-nucleus interaction potentials for the ¹⁶O nucleus and ^{112,114,116,118,120,122,124}Sn isotopes were calculated within the framework of the modified Thomas - Fermi method, taking into account all terms to the second-order of ħ in the quasiclassical expansion of kinetic energy. Skyrme forces dependent on the nucleon density were used as nucleon-nucleon interaction. A successful parameterization was found for the obtained potential, which allows to present it in an analytical form.

Keywords: nucleon density, Skyrme forces, nucleus-nucleus potential, repulsive core, analytical representation.

1. R. Bass. Nuclear Reactions with Heavy Ions (Berlin, Heidelberg: Springer, 1980) 410 p. https://link.springer.com/book/9783540096115

2. G.R. Satchler. Direct Nuclear Reactions (Clarendon Press, 1983) 833 p. Google books

3. P. Fröbrich, R. Lipperheide. Theory of Nuclear Reactions (Clarendon Press, 1996) 476 p. https://doi.org/10.1093/oso/9780198537830.001.0001

4. V.Yu. Denisov, V.A. Plujko. Problems of the Physics of the Atomic Nucleus and Nuclear Reactions (Kyiv: Kyiv University, 2013) 430 p. (Rus) https://inis.iaea.org/collection/NCLCollectionStore/_Public/45/091/45091761.pdf

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

6. W.D. Myers, W.J. Swiatecki. Nucleus-nucleus proximity potential and superheavy nuclei. Phys. Rev. C 62 (2000) 044610. https://doi.org/10.1103/PhysRevC.62.044610

7. 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

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

9. H.J. Krappe, J.R. Nix, A.J. Sierk. Unified nuclear potential for heavy-ion elastic scattering, fusion, fission, and ground state masses and deformations. Phys. Rev. C 20 (1979) 992. https://doi.org/10.1103/PhysRevC.20.992

10. 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

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

12. A. Winther. Dissipation, polarization and fluctuation in grazing heavy-ion collisions and the boundary to the chaotic regime. Nucl. Phys. A 594 (1995) 203. https://doi.org/10.1016/0375-9474(95)00374-A

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

14. V.Yu. Denisov, O.I. Davidovskaya. Repulsive core potential and elastic heavy-ion collisions. Ukr. J. Phys. 54 (2009) 669. http://archive.ujp.bitp.kiev.ua/files/journals/54/7/540704p.pdf

15. K.A. Brueckner, J.R. Buchler, M.M. Kelly. New theoretical approach to nuclear heavy-ion scattering. Phys. Rev. 173 (1968) 944. https://doi.org/10.1103/PhysRev.173.944

16. J. Fleckner, U. Mosel. Antisymmetrization effects in heavy ion potentials. Nucl. Phys. A 277 (1977) 170. https://doi.org/10.1016/0375-9474(77)90268-8

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

18. V.Yu. Denisov, O.I. Davidovskaya. Elastic scattering of heavy ions and nucleus-nucleus potential with repulsive core. Izvestiya Rossiyskoy Akademii Nauk. Seriya Fizicheskaya 74(4) (2010) 611. (Rus) https://doi.org/10.3103/S1062873810040325

19. 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. https://doi.org/10.15407/ujpe62.06.0473

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. Atom. Nucl. 76 (2013) 577. https://doi.org/10.1134/S106377881304008X

21. O.I. Davidovskaya, V.Yu. Denisov. Elastic ¹⁶O + ¹⁶O scattering and nucleus-nucleus potential with a repulsive core. Ukr. J. Phys. 55 (2010) 861. https://kinr.kyiv.ua/data/departments/NStrD/Denisov/Davydovska_Denisov-UJP55-861-engl.pdf

22. О.I. Davydovska, V.Yu. Denisov, V.O. Nesterov. Nucleus-nucleus potential, the elastic scattering and subbarrier fusion cross sections for the system ⁴⁰Сa + ⁴⁰Сa. Nucl. Phys. At. Energy 19 (2018) 203. (Ukr) https://doi.org/10.15407/jnpae2018.03.203

23. O.I. Davydovska, V.Yu. Denisov, V.A. Nesterov. Comparison of the nucleus-nucleus potential evaluated in the double-folding and energy density approximations and the cross-sections of elastic scattering and fusion of heavy ions. Nucl. Phys. A 989 (2019) 214. https://doi.org/10.1016/j.nuclphysa.2019.06.004

24. V.O. Nesterov, O.I. Davydovska, V.Yu. Denisov. Calculation of the cross-sections of sub-barrier fusion and elastic scattering of heavy ions using the modified Thomas - Fermi approach with the Skyrme force. Nucl. Phys. At. Energy 20(4) (2019) 349. (Ukr) https://doi.org/10.15407/jnpae2019.04.349

25. P. Ring, P. Schuck. The Nuclear Many-Body Problem (New York: Springer-Verlag, 1980) 718 p. https://doi.org/10.1007/978-3-642-61852-9

26. M. Brack, C. Guet, H.B. Hakanson. Self-consistent 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

27. M. Brack, R.K. Bhaduri, Semiclassical Physics (Massachusetts: Addison-Wesley Publ. Co, Reading, 1997) 462 p. Google books

28. V.M. Strutinsky, A.G. Magner, V.Yu. Denisov. Density distributions in nuclei. Z. Phys. A 322 (1985) 149. https://doi.org/10.1007/BF01412028

29. J. Dobaczewski, W. Nazarewicz, P.G. Reinhard. Pairing interaction and self-consistent densities in neutron-rich nuclei. Nucl. Phys. A 693 (2001) 361. https://doi.org/10.1016/S0375-9474(01)00993-9

30. D. Vautherin, D.M. Brink. Hartree-Fock Calculations with Skyrme’s Interaction. I. Spherical Nuclei. Phys. Rev. C 5 (1972) 626. https://doi.org/10.1103/PhysRevC.5.626

31. 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

32. S.A. Fayans et al. Nuclear isotope shifts within the local energy density functional approach. Nucl. Phys. A 676 (2000) 49. https://doi.org/10.1016/S0375-9474(00)00192-5

33. J.W. Negele. The mean-field theory of nuclear structure and dynamics. Rev. Mod. Phys. 54 (1982) 913. https://doi.org/10.1103/RevModPhys.54.913

34. O.I. Davydovska, V.A. Nesterov, V.Yu. Denisov. The nucleus-nucleus potential within the extended Thomas-Fermi method and the cross-sections of subbarrier fusion and elastic scattering for the systems ¹⁶O + ^58,60,62,64Ni. Nucl. Phys. A 1002 (2020) 121994. https://doi.org/10.1016/j.nuclphysa.2020.121994

35. V.A. Nesterov, O.I. Davydovska, V.Yu. Denisov. Elastic scattering cross-sections obtained on the basis of the potential of the modified Thomas-Fermi method and taking the core into account. Ukr. J. Phys. 67(9) (2022) 645. https://doi.org/10.15407/ujpe67.9.645

36. A. Mukherjee et al. Failure of the Woods-Saxon nuclear potential to simultaneously reproduce precise fusion and elastic scattering measurements. Phys. Rev. C 75 (2007) 044608. https://doi.org/10.1103/PhysRevC.75.044608

37. C.R. Morton e al. Coupled-channels analysis of the ¹⁶O + ²⁰⁸Pb fusion barrier distribution. Phys. Rev. C 60 (1999) 044608. https://doi.org/10.1103/PhysRevC.60.044608

38. M. Dasgupta et al. Beyond the Coherent Coupled Channels Description of Nuclear Fusion. Phys. Rev. Lett. 99 (2007) 192701. https://doi.org/10.1103/PhysRevLett.99.192701

39. S.Ya. Goroshenko, A.V. Nesterov, V.A. Nesterov. The interaction energy of two uniformly charged spheroids. Example of deformed nuclei. Nucl. Phys. At. Energy 21 (2020) 13. https://doi.org/10.15407/jnpae2020.01.013