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Incorporating self-consistent single-particle potentials into the microscopic-macroscopic method

  • G. G. Adamian
  • L. A. Malov
  • N. V. Antonenko
  • H. Lenske
  • Kun Wang
  • Shan-Gui Zhou
Regular Article - Theoretical Physics

Abstract.

Effective single-particle potentials obtained by self-consistent HFB calculations from the established non-relativistic and relativistic nuclear EDF approaches are incorporated into the microscopic-macroscopic method, a widely and successfully used approach for superheavy nuclei. We determine the Schrödinger-equivalent central and spin-orbit potentials incorporating effective mass effects. The method can be applied to non-relativistic and relativistic mean-fields. A parametrization in terms of the Wood-Saxon form is introduced to derive the proton and neutron potentials, appropriate for the microscopic-macroscopic method. As the first application, the extended microscopic-macroscopic approach is used to calculate the shell corrections in the heaviest nuclei. Constraints on parameters sets for central and spin-orbit potentials are derived for which the shell effects are amplified towards \( Z=120\) .

References

  1. 1.
    V.M. Strutinsky, Sov. J. Nucl. Phys. 3, 449 (1966) Nucl. Phys. A 95Google Scholar
  2. 2.
    S.G. Nilsson, C.F. Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, I.-L. Lamm, P. Möller, B. Nilsson, Nucl. Phys. A 131, 1 (1969)ADSGoogle Scholar
  3. 3.
    V.A. Chepurnov, Yad. Fiz. 6, 955 (1967)Google Scholar
  4. 4.
    A. Bohr, B. Mottelson, Nuclear Structure, Vols. I, II (Benjamin, NY, 1975)Google Scholar
  5. 5.
    V.G. Soloviev, Theory of Complex Nuclei (Pergamon Press, Oxford, 1976)Google Scholar
  6. 6.
    S.P. Ivanova, A.L. Komov, L.A. Malov, V.G. Soloviev, Phys. Part. Nucl. 7, 450 (1976)Google Scholar
  7. 7.
    V.G. Soloviev, A.V. Sushkov, N.Yu. Shirikova, Phys. Part. Nucl. 25, 157 (1994)Google Scholar
  8. 8.
    V.G. Soloviev, A.V. Sushkov, N.Yu. Shirikova, Phys. Part. Nucl. 27, 667 (1996)Google Scholar
  9. 9.
    J. Maruhn, W. Greiner, Z. Phys. A 251, 431 (1972)Google Scholar
  10. 10.
    P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995)ADSGoogle Scholar
  11. 11.
    J. Dudek, Z. Szymanski, T. Werner, A. Fäßler, C. Lima, Phys. Rev. C 26, 1712 (1982)ADSGoogle Scholar
  12. 12.
    I. Muntian, Z. Patyk, A. Sobiczewski, Acta. Phys. Pol. B 32, 691 (2001)ADSGoogle Scholar
  13. 13.
    I. Muntian, Z. Patyk, A. Sobiczewski, Acta. Phys. Pol. B 34, 2141 (2003)ADSGoogle Scholar
  14. 14.
    I. Muntian, S. Hofmann, Z. Patyk, A. Sobiczewski, Acta. Phys. Pol. B 34, 2073 (2003)ADSGoogle Scholar
  15. 15.
    I. Muntian, S. Hofmann, Z. Patyk, A. Sobiczewski, Phys. At. Nucl. 66, 1015 (2003)Google Scholar
  16. 16.
    A. Parkhomenko, I. Muntian, Z. Patyk, A. Sobiczewski, Acta. Phys. Pol. B 34, 2153 (2003)ADSGoogle Scholar
  17. 17.
    A. Parkhomenko, A. Sobiczewski, Acta. Phys. Pol. B 36, 3095 (2005)ADSGoogle Scholar
  18. 18.
    I. Ahmad, Phys. Scr. T 125, 78 (2006)ADSGoogle Scholar
  19. 19.
    I. Ahmad, R.R. Chasman, Phys. Rev. C 80, 064315 (2009)ADSGoogle Scholar
  20. 20.
    N. Schwierz, I. Wiedenhöver, A. Volya, arXiv:nucl-th/07093525 (2007)Google Scholar
  21. 21.
    N. Wang, M. Liu, X. Wu, J. Meng, Phys. Lett. B 734, 215 (2014)ADSGoogle Scholar
  22. 22.
    V.V. Pashkevich, A.Ya. Rusanov, Nucl. Phys. A 810, 77 (2008)ADSGoogle Scholar
  23. 23.
    Z.-Y. Wu, C. Qi, R. Wyss, H.-L. Liu, Phys. Rev. C 92, 024306 (2015)ADSGoogle Scholar
  24. 24.
    F.R. Xu, P.M. Walker, R. Wyss, Phys. Rev. C 59, 731 (1999)ADSGoogle Scholar
  25. 25.
    G.G. Adamian, L.A. Malov, N.V. Antonenko, R.V. Jolos, Phys. Rev. C 97, 034308 (2018)ADSGoogle Scholar
  26. 26.
    A. Sobiczewski, K. Pomorski, Prog. Part. Nucl. Phys. 58, 292 (2007)ADSGoogle Scholar
  27. 27.
    M. Asai, F.P. Heßberger, A. Lopez-Martens, Nucl. Phys. A 944, 308 (2015)ADSGoogle Scholar
  28. 28.
    Ch. Theisen, P.T. Greenlees, T.-L. Khoo, P. Chowdhury, T. Ishii, Nucl. Phys. A 944, 333 (2015)ADSGoogle Scholar
  29. 29.
    D. Ackermann, Ch. Theisen, Phys. Scr. 92, 083002 (2017)ADSGoogle Scholar
  30. 30.
    D. Vautherin, D.M. Brink, Phys. Rev. C 5, 626 (1972)ADSGoogle Scholar
  31. 31.
    J. Boguta, A.R. Bodmer, Nucl. Phys. 292, 413 (1977)Google Scholar
  32. 32.
    P. Ring, Prog. Part. Nucl. Phys. 37, 193 (1996)ADSGoogle Scholar
  33. 33.
    M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)ADSGoogle Scholar
  34. 34.
    F. Hofmann, H. Lenske, Phys. Rev. C 57, 2281 (1998)ADSGoogle Scholar
  35. 35.
    H. Lenske, C. Fuchs, Phys. Lett. B 345, 355 (1995)ADSGoogle Scholar
  36. 36.
    S.A. Fayans, S.V. Tolokonnikov, E.L. Trykov, D. Zawischa, Nucl. Phys. A 676, 49 (2000)ADSGoogle Scholar
  37. 37.
    S.V. Tolokonnikov, E.E. Saperstein, Phys. At. Nucl. 73, 1684 (2010)Google Scholar
  38. 38.
    M. Baldo, P. Schuck, X. Viňas, Phys. Lett. B 663, 390 (2008)ADSGoogle Scholar
  39. 39.
    M. Baldo, L.M. Robledo, P. Schuck, X. Viňas, Phys. Rev. C 87, 064305 (2013)ADSGoogle Scholar
  40. 40.
    G.A. Lalazissis, D. Vretenar, P. Ring, Phys. Rev. C 57, 2294 (1998)ADSGoogle Scholar
  41. 41.
    S.-G. Zhou, J. Meng, P. Ring, Phys. Rev. C 68, 034323 (2003)ADSGoogle Scholar
  42. 42.
    J. Meng, H. Toki, S.-G. Zhou, S.-Q. Zhang, W.-H. Long, L.-S. Geng, Prog. Part. Nucl. Phys. 57, 470 (2006)ADSGoogle Scholar
  43. 43.
    J.J. Li, W.H. Long, J. Margueron, N. Van Giai, Phys. Lett. B 732, 169 (2014)ADSGoogle Scholar
  44. 44.
    D. Vretenar, A.V. Afanasjev, G.A. Lalazissis, P. Ring, Phys. Rep. 409, 101 (2005)ADSGoogle Scholar
  45. 45.
    H. Liang, J. Meng, S.-G. Zhou, Phys. Rep. 570, 1 (2015)ADSMathSciNetGoogle Scholar
  46. 46.
    J. Meng, S.-G. Zhou, J. Phys. G 42, 093101 (2015)ADSGoogle Scholar
  47. 47.
    S.-G. Zhou, Phys. Scr. 91, 063008 (2016)ADSGoogle Scholar
  48. 48.
    G.G. Adamian, N.V. Antonenko, W. Scheid, Phys. Rev. C 81, 024320 (2010)ADSGoogle Scholar
  49. 49.
    G.G. Adamian, N.V. Antonenko, S.N. Kuklin, W. Scheid, Phys. Rev. C 82, 054304 (2010)ADSGoogle Scholar
  50. 50.
    G.G. Adamian, N.V. Antonenko, S.N. Kuklin, B.N. Lu, L.A. Malov, S.G. Zhou, Phys. Rev. C 84, 024324 (2011)ADSGoogle Scholar
  51. 51.
    A.N. Kuzmina, G.G. Adamian, N.V. Antonenko, W. Scheid, Phys. Rev. C 85, 014319 (2012)ADSGoogle Scholar
  52. 52.
    J. Dechargé, D. Gogny, Phys. Rev. C 21, 1568 (1980)ADSGoogle Scholar
  53. 53.
    J.W. Negele, D. Vautherin, Phys. Rev. C 5, 1472 (1972)ADSGoogle Scholar
  54. 54.
    J.W. Negele, D. Vautherin, Phys. Rev. C 11, 1031 (1975)ADSGoogle Scholar
  55. 55.
    N. Tsoneva, H. Lenske, Phys. Rev. C 77, 024321 (2008)ADSGoogle Scholar
  56. 56.
    G.A. Lalazissis, J. Konig, P. Ring, Phys. Rev. C 55, 540 (1997)ADSGoogle Scholar
  57. 57.
    J. Meng, K. Sugawara-Tanabe, S. Yamaji, A. Arima, Phys. Rev. C 59, 154 (1999)ADSGoogle Scholar
  58. 58.
    S.-G. Zhou, J. Meng, P. Ring, Phys. Rev. Lett. 91, 262501 (2003)ADSGoogle Scholar
  59. 59.
    W. Koepf, P. Ring, Z. Phys. A 339, 81 (1991)ADSGoogle Scholar
  60. 60.
    A. Baran, Phys. Rev. C 61, 024316 (2000)ADSGoogle Scholar
  61. 61.
    M. Jaminon, C. Mahaux, Phys. Rev. C 40, 354 (1989)ADSGoogle Scholar
  62. 62.
    Z.-Y. Ma, J. Rong, B.-Q. Chen, Z.-Y. Zhu, H.-Q. Song, Phys. Lett. B 604, 170 (2004)ADSGoogle Scholar
  63. 63.
    W.-H. Long, N. Van Giai, J. Meng, Phys. Lett. B 640, 150 (2006)ADSGoogle Scholar
  64. 64.
    V. Derya, N. Tsoneva, T. Aumann, M. Bhike, J. Endres, M. Gooden, A. Hennig, J. Isaak, H. Lenske, B. Loher, N. Pietralla, D. Savran, W. Tornow, V. Werner, A. Zilges, Phys. Rev. C 93, 034311 (2016)ADSGoogle Scholar
  65. 65.
    A.P. Tonchev, S.L. Hammond, J.H. Kelley, E. Kwan, H. Lenske, G. Rusev, W. Tornow, N. Tsoneva, Phys. Rev. Lett. 104, 072501 (2010)ADSGoogle Scholar
  66. 66.
    G.G. Adamian, N.V. Antonenko, H. Lenske, S.V. Tolokonnikov, E.E. Saperstein, Phys. Rev. C 94, 054309 (2016)ADSGoogle Scholar
  67. 67.
    J. Dechargé, J.-F. Berger, M. Girod, K. Dietrich, Nucl. Phys. A 716, 55 (2003)ADSGoogle Scholar
  68. 68.
    M. Bender, K. Rutz, P.-G. Reinhard, J.A. Maruhn, W. Greiner, Phys. Rev. C 60, 034304 (1999)ADSGoogle Scholar
  69. 69.
    A.V. Afanasjev, S. Frauendorf, Phys. Rev. C 71, 024308 (2005)ADSGoogle Scholar
  70. 70.
    M.J. Martin, Nucl. Data Sheets 63, 723 (1991)ADSGoogle Scholar
  71. 71.
    M.J. Martin, Nucl. Data Sheets 70, 315 (1993)ADSGoogle Scholar
  72. 72.
    E. Litvinova, P. Ring, Phys. Rev. C 73, 044328 (2006)ADSGoogle Scholar
  73. 73.
    E. Vigezzi, J. Phys. Conf. Ser. 981, 012007 (2018)Google Scholar
  74. 74.
    E. Litvinova, P. Ring, V. Tselyaev, Phys. Rev. C 75, 064308 (2007)ADSGoogle Scholar
  75. 75.
    E. Litvinova, A.V. Afanasjev, Phys. Rev. C 84, 014305 (2011)ADSGoogle Scholar
  76. 76.
    E. Litvinova, Phys. Rev. C 85, 021303 (2012)ADSGoogle Scholar
  77. 77.
    D. Tarpanov, J. Dobaczewski, J. Toivanen, B.G. Carlsson, Phys. Rev. Lett. 113, 252501 (2014)ADSGoogle Scholar
  78. 78.
    A.V. Afanasjev, E. Litvinova, Phys. Rev. C 92, 044317 (2015)ADSGoogle Scholar
  79. 79.
    L.-G. Cuo, H. Sagawa, P.F. Bortignon, Phys. Rev. C 89, 044314 (2014)ADSGoogle Scholar
  80. 80.
    A. Idini, F. Barranco, E. Vigezzi, Phys. Rev. C 85, 014331 (2012)ADSGoogle Scholar
  81. 81.
    A. Idini, G. Potel, F. Barranco, E. Vigezzi, R.A. Broglia, Phys. Rev. C 92, 031304 (2015)ADSGoogle Scholar
  82. 82.
    T. Lisinski, T. Duguet, K. Bennaceur, J. Meuer, Eur. Phys. J. A 40, 121 (2009)ADSGoogle Scholar
  83. 83.
    G. Gori, F. Ramponi, F. Barranco, P.F. Bortignon, R.A. Broglia, G. Colò, E. Vigezzi, Phys. Rev. C 72, 011302 (2005)ADSGoogle Scholar
  84. 84.
    T. Duguet, T. Lesinski, K. Hebeler, A. Schwenk, Mod. Phys. Lett. 25, 1989 (2010)ADSGoogle Scholar
  85. 85.
    N.V. Antonenko, L.A. Malov, Izv. RAN Ser. Phys. 78, 1402 (2014)Google Scholar
  86. 86.
    R.V. Jolos, L.A. Malov, N.Yu. Shirikova, A.V. Sushkov, J. Phys. G 38, 115103 (2011)ADSGoogle Scholar
  87. 87.
    M. Bender, W. Nazarewicz, P.-G. Reinhard, Phys. Lett. B 515, 42 (2001)ADSGoogle Scholar

Copyright information

© SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • G. G. Adamian
    • 1
  • L. A. Malov
    • 1
  • N. V. Antonenko
    • 1
    • 2
  • H. Lenske
    • 3
  • Kun Wang
    • 4
  • Shan-Gui Zhou
    • 4
    • 5
    • 6
    • 7
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia
  2. 2.Tomsk Polytechnic UniversityTomskRussia
  3. 3.Institut für Theoretische Physik der Justus-Liebig-UniversitätGießenGermany
  4. 4.CAS Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  5. 5.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  6. 6.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy Ion AcceleratorLanzhouChina
  7. 7.Synergetic Innovation Center for Quantum Effects and ApplicationHunan Normal UniversityChangshaChina

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