• Українська
  • English

< | >

Current issue   Ukr. J. Phys. 2017, Vol. 62, N 6, p.473-480
https://doi.org/10.15407/ujpe62.06.0473    Paper

Davidovskaya O.I., Denisov V.Yu., Nesterov B.A.

Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
(47, Nauky Ave., Kyiv 03028, Ukraine; e-mail: denisov@kinr.kiev.ua)

Effective Nucleus-Nucleus Potential with Regard for the Con-tribution of the Kinetic Energy of Nucleons, and the Cross-Sections of Elastic Scattering and Subbarrier Fusion

Section: Nuclei and Nuclear Reactions
Original Author's Text: Ukrainian

Abstract: The microscopic double folding approach to the calculation of the nucleus-nucleus interaction has been discussed in detail. The nucleus-nucleus interaction potentials for the 16O + 208Pb system with and without the contribution of the kinetic energy of nucleons in the nuclei are constructed, and the cross-sections of elastic scattering and subbarrier fusion are calculated. The experimental values of those cross-sections are shown to be described well, if the contribution of nucleons’ kinetic energy is taken into account.

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

References:

  1. G.R. Satchler. Direct Nuclear Reactions (Oxford Univ. Press, 1983) [ISBN: 0198512694 9780198512691].
  2. P. Frobrich, R. Lipperheide. Theory of Nuclear Reactions (Clarendon Press, 1996) [ISBN: 0198537832].
  3. R. Bass. Nuclear Reactions with Heavy Ions (Springer, 1980) [ISBN: 978-3-540-09611-5].
  4. V.Yu. Denisov, V.A. Plyuyko. Problems of Nuclear Physics and Physics of Nuclear Reactions (Kyiv University Publ. Center, 2013) (in Russian) [ISBN: 978-966-439-673-5].
  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, 1652 (1994).
    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, 143 (1997).
    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. 304, 8 (1993).
    https://doi.org/10.1016/0370-2693(93)91391-Y
  8. V.B. Soubbotin, W. von Oertzen, X. Vi˜nas, K.A. Gridnev, H.G. Bohlen. Pauli distorted double folded potential. Phys. Rev. C 64, 014601 (2001).
    https://doi.org/10.1103/PhysRevC.64.014601
  9. A.A. Ogloblin, T. Khoa Dao, Y. Kond¯o, Yu. A. Glukhov, A.S. Dem'yanova, M.V. Rozhkov, G.R. Satchler, S.A. Goncharov. Pronounced Airy structure in elastic 16O + 12C scattering at Elab = 132 MeV. Phys. Rev. C 57, 1797 (1998).
    https://doi.org/10.1103/PhysRevC.57.1797
  10. A.A. Ogloblin, Yu.A. Glukhov, W.H. Trzaska, A.S. Dem'yanova, S.A. Goncharov, R. Julin, S.V. Klebnikov, M. Mutterer, M.V. Rozhkov, V.P. Rudakov, G.P. Tiorin, D.T. Khoa, G.R. Satchler. New measurement of the refractive, elastic 16O + 12C scattering at 132, 170, 200, 230, and 260 MeV incident energies. Phys. Rev. C 62, 044601 (2000).
    https://doi.org/10.1103/PhysRevC.62.044601
  11. Dao T. Khoa, W. von Oertzen, H.G. Bohlen, F. Nuoffer. 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, 387 (2000).
    https://doi.org/10.1016/S0375-9474(99)00856-8
  12. T. Khoa Dao, W. von Oertzen, H.G. Bohlen, S. Ohkubo. Nuclear rainbow scattering and nucleus–nucleus potential. J. Phys. G 34, R111 (2007).
    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, 1472 (2006).
    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, 944 (1968).
    https://doi.org/10.1103/PhysRev.173.944
  15. J. Blocki, J. Randrup, W.J. Swiatecki, C.F. Tsang. Proximity forces. Ann. Phys. (N.Y.) 105, 427 (1977).
    https://doi.org/10.1016/0003-4916(77)90249-4
  16. V.Yu. Denisov. Interaction potential between heavy ions. Phys. Lett. B 526, 315 (2002).
    https://doi.org/10.1016/S0370-2693(01)01513-1
  17. V.Yu. Denisov, W. N¨orenberg. Entrance channel potentials in the synthesis of the heaviest nuclei. Eur. Phys. J. A 15, 375 (2002).
    https://doi.org/10.1140/epja/i2002-10039-3
  18. V.Yu. Denisov. Nucleus-nucleus potential with shell-correction contribution. Phys. Rev. C 91, 024603 (2015).
    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. Atom. Nucl. 73, 1142 (2010).
    https://doi.org/10.1134/S1063778810070070
  20. ¸S. Mi¸sicu, H. Esbensen. Signature of shallow potentials in deep sub-barrier fusion reactions. Phys. Rev. C 75, 034606 (2007).
    https://doi.org/10.1103/PhysRevC.75.034606
  21. T. Izumoto, S. Krewald, A. Faessler. Nuclear matter approach to the heavy-ion optical potential. Nucl. Phys. A 341, 319 (1980).
    https://doi.org/10.1016/0375-9474(80)90316-4
  22. 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 16O + 12C elastic scattering. Phys. Lett. B 636, 248 (2006).
    https://doi.org/10.1016/j.physletb.2006.03.071
  23. V.Yu. Denisov, O.I. Davidovskaya. Repulsive core potential and elastic heavy-ion collisions. Yad. Fiz. 73, 429 (2010).
  24. V.Yu. Denisov, O.I. Davidovskaya. Repulsive core potential and elastic heavy-ion collisions. Ukr. J. Phys. 54, 669 (2009).
  25. O.I. Davidovskaya, V.Yu. Denisov, V.O. Nesterov. Nucleus-nucleus potential with repulsive core and elastic scattering. Part 1. Nucleus-nucleus interaction potential. Yad. Fiz. Energet. 11, No. 1, 25 (2010) (in Ukrainian).
  26. O.I. Davidovskaya, V.Yu. Denisov, V.O. Nesterov. Nucleus-nucleus potential with repulsive core and elastic scattering. Part 2. The elastic scattering cross sections with and without core. Yad. Fiz. Energet. 11, No. 1, 33 (2010) (in Ukrainian).
  27. V.Yu. Denisov, O.I. Davidovskaya. Elastic scattering of heavy ions and nucleus-nucleus potential with a repulsive core. Izv. Ross. Akad. Nauk Ser. Fiz. 74, 611 (2010) (in Russian).
    https://doi.org/10.3103/S1062873810040325
  28. V.Yu. Denisov, O.I. Davidovskaya. Elastic 16O + 16O scattering and nucleus-nucleus potential with a repulsive core. Ukr. Fiz. Zh. 55, 861 (2010).
  29. M. Brack, C. Guet, H.B. H˚akanson. Selfconsistent semiclassical description of average nuclear properties – a link between microscopic and macroscopic models. Phys. Rep. 123, 275 (1985).
    https://doi.org/10.1016/0370-1573(86)90078-5
  30. M. Brack, R.K. Bhaduri. Semiclassical Physics (AddisonWesley, 1997) [ISBN: 0-201-48351-3].
  31. V.Yu. Denisov, V.A. Nesterov. The binding energy and the density distribution of atomic nuclei in the framework of modified Thomas–Fermi method. Yad. Fiz. 65, 814 (2002) (in Russian).
  32. T.H.R. Skyrme. The effective nuclear potential. Nucl. Phys. 9, 615 (1959).
    https://doi.org/10.1016/0029-5582(58)90345-6
  33. O.B. Firsov. Scattering of ions by atoms. Zh. Eksp. Teor. ` Fiz. 34, 447 (1958) (in Russian).
  34. I.G. Kaplan, Theory of Molecular Interactions (Elsevier, 1986) [ISBN: 9780444426963].
  35. H. de Vries, C.W. de Jager, C. de Vries. Nuclear chargedensity-distribution parameters from elastic electron scattering. At. Data Nucl. Data Tabl. 36, 495 (1987).
    https://doi.org/10.1016/0092-640X(87)90013-1
  36. P. Ring, P. Schuck. The Nuclear Many-Body Problem (Springer, 1980) [ISBN: 978-3-540-21206-5].
    https://doi.org/10.1007/978-3-642-61852-9
  37. I. Angeli, K.P. Marinova. Table of experimental nuclear ground state charge radii: An update. At. Data Nucl. Data Tabl. 99, 69 (2013).
    https://doi.org/10.1016/j.adt.2011.12.006
  38. K. Hagino, N. Rowley, A.T. Kruppa. A program for coupled-channel calculations with all order couplings for heavyion fusion reactions. Comput. Phys. Commun. 1 23, 143 (1999).
  39. B. Pritychenko, M. Birch, B. Singh, M. Horoi. Tables of E2 transition probabilities from the first 2 + image states in even–even nuclei. At. Data Nucl. Data Tabl. 107, 1 (2016).
    https://doi.org/10.1016/j.adt.2015.10.001
  40. T. Kib’edi, R.H. Spear. Reduced electric-octupole transition probabilities, B(E3; 0+1 → 3−1) – an update. At. Data Nucl. Data Tabl. 80, 35 (2002).
    https://doi.org/10.1006/adnd.2001.0871
  41. C.R. Morton, A.C. Berriman, M. Dasgupta, D.J. Hinde, J.O. Newton, K. Hagino, I.J. Thompson. Coupled-channels analysis of the 16O + 208Pb fusion barrier distribution. Phys. Rev. C 60, 044608 (1999).
    https://doi.org/10.1103/PhysRevC.60.044608
  42. V.P. Rudakov, K.P. Artemov, Yu.A. Glukhov, S.A. Goncharov, A.S. Demyanova, A.A. Ogloblin, V.V. Paramonov, M.V. Rozhkov. Elastic 12C + 208Pb and 16O + 208Pb scattering and the form of the potential barrier. Bull. Rus. Acad. Sci. Phys. 65, 57 (2001).