Preformation Amplitude

  • Doru S. DelionEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 819)


In this Chapter, we present the α-like microscopic theory based on the concept of the preformation probability of the light partner. This approach can be applied to the emission of light clusters like α-particle, 8Be, or 12,14C and 16O. We extensively describe the Multi-step Shell Model (MSM) technique to built preformation amplitude, by applying this procedure to 208Pb + α and 40Ca + α systems. Then, we analyze superfluid emitters by using the BCS approach. We also present α-decay processes from superheavy nuclei and analyze the preformation factor for two-proton emission within the BCS approach.


Daughter Nucleus Spectroscopic Factor Superheavy Nucleus Quartet State Hindrance Factor 
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  1. 1.
    Mang, H.J.: Calculation of α-transition probabilities. Phys. Rev. 119, 1069–1075 (1960)ADSCrossRefGoogle Scholar
  2. 2.
    Săndulescu, A.: Reduced widths for favoured alpha transitions. Nucl. Phys. A 37, 332–343 (1962)zbMATHCrossRefGoogle Scholar
  3. 3.
    Mang, H.J.: Alpha decay. Ann. Rev. Nucl. Sci. 14, 1–28 (1964)ADSCrossRefGoogle Scholar
  4. 4.
    Liotta, R.J., Pomar, C.: Multi-step shell-model treatment of Sux-Particle system. Nucl. Phys. A 362, 137–162 (1981)ADSCrossRefGoogle Scholar
  5. 5.
    Liotta, R.J., Pomar, C.: A graphical procedure to evaluate the many-body shell-model equations. Nucl. Phys. A 382, 1–19 (1982)ADSCrossRefGoogle Scholar
  6. 6.
    Delion, D.S., Suhonen, J.: Microscopic Description of α-like Resonances. Phys. Rev. C 61, 024304/1–12 (2000)Google Scholar
  7. 7.
    Heenen, P.-H.: Microscopic R-Matrix theory in a generator coordinate basis: (II) Study of resonance widths and application to α-16O scattering. Nucl. Phys. A 272, 399–412 (1976)ADSCrossRefGoogle Scholar
  8. 8.
    Takigawa, N., Lee, S.Y.: Nuclear Gory effect and α-40Ca Scattering. Nucl. Phys. A 292, 173–189 (1977)ADSCrossRefGoogle Scholar
  9. 9.
    Manngård P., PhD Thesis, Åbo Akademi, Åbo (1996)Google Scholar
  10. 10.
    Cwiok, S., Dudek, J., Nazarewicz, W., Skalski, J., Werner, T.: Single-particle energies, wave functions, quadrupole moments and g-factors in an axially deformed Woods-Saxon potential with applications to the two-centre-type nuclear problem. Comput. Phys. Commun. 46, 379–399 (1987)ADSCrossRefGoogle Scholar
  11. 11.
    Vertse, T., Pál, K.F., Balogh, A.: GAMOW, a program for calculating the resonant state solution of the Radial Schrödinger Equation in an arbitrary optical potential. Comput. Phys. Commun. 27, 309–322 (1982)ADSCrossRefGoogle Scholar
  12. 12.
    Curuchet, P., Vertse, T., Liotta, R.J.: Resonant random phase approximation. Phys. Rev. C 39, 1020–1031 (1989)ADSCrossRefGoogle Scholar
  13. 13.
    Brussaard, P.J., Glaudemans, P.W.M.: Shell-Model Applications in Nuclear Spectroscopy. North-Holland, Amsterdam (1977)Google Scholar
  14. 14.
    Schuck, P., Wittman, R., Ring, P.: Lett. Nuovo Cim. 17, 107 (1976)CrossRefGoogle Scholar
  15. 15.
    Strottman, D.: Weak coupling calculation of 212Po using realistic matrix elements. Phys. Rev. C 20, 1150–1154 (1979)ADSCrossRefGoogle Scholar
  16. 16.
    Firestone, R.B., Shirley, V.S., Chu, S.Y.F., Baglin, C.M., Zipkin, J.: Table of Isotopes CD-ROM, 8th edn, Version 1.0. Wiley, New York (1996)Google Scholar
  17. 17.
    Dodig-Crnkovic, G., Janouch, F.A., Liotta, R.J., Sibanda, L.J.: Absolute α-decay rates in 212Po. Nucl. Phys. A 444, 419–435 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    Dodig-Crnkovic, G., Janouch, F.A., Liotta, R.J.: An exact shell-model treatment of α-clustering and absolute α-decay. Nucl. Phys. A 501, 533–545 (1989)ADSCrossRefGoogle Scholar
  19. 19.
    Blendowske, R., Fliessbach, T., Walliser, H.: Microscopic calculation of the 14C decay of Ra nuclei. Nucl. Phys. A 464, 75–89 (1987)ADSCrossRefGoogle Scholar
  20. 20.
    Blendowske, R., Fliessbach, T., Walliser, H.: Systematics of cluster-radioactivity-decay constants as suggested by microscopic calculations. Phys. Rev. Lett. 61, 1930–1933 (1988)ADSCrossRefGoogle Scholar
  21. 21.
    Barker, F.C.: 12O Ground-state decay by 2He emission. Phys. Rev. C 63, 047303/1–2 (2001)Google Scholar
  22. 22.
    Barmore, B., Kruppa, A.T., Nazarewicz, W., Vertse, T.: A new approach to deformed proton emitters: non-adiabadic coupled-channels. Nucl. Phys. A 682, 256c–263c (2001)ADSCrossRefGoogle Scholar
  23. 23.
    Ohkubo, S. (ed.): Alpha-clustering and molecular structure of medium-weight and heavy nuclei. Prog. Theor. Phys. Suppl. 132, 1–228 (1998)Google Scholar
  24. 24.
    Fioravanti, R., Viano, G.A.: Rotational bands and surface waves in α-40Ca elastic scattering. Phys. Rev. C 55, 2593–2603 (1997)ADSCrossRefGoogle Scholar
  25. 25.
    Ohkubo, S.: Alpha-cluster model theory of 44Ti and effective two-body interaction. Phys. Rev. C 38, 2377–2385 (1988)ADSCrossRefGoogle Scholar
  26. 26.
    Langanke, K.: Explanation of the backangle anomaly and isotope effect within a microscopic study of elastic α-scattering on even Ca isotopes. Nucl. Phys. A 377, 53–83 (1982)ADSCrossRefGoogle Scholar
  27. 27.
    Wada, T., Horiuchi, H.: Resonating-group-method study of α+40Ca elastic scattering and 44Ti structure. Phys. Rev. C 38, 2063–2077 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    Sakuda, T., Ohkubo, S.: Coexistence of α-clustering and shell structure in 40Ca. Z. Phys. A 349, 361–362 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    Sakuda, T., Ohkubo, S.: Structure study of 40Ca by α+36Ar cluster model. Phys. Rev. C 49, 149–155 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    Yamada, T., Ohkubo, S.: Core-excited α-cluster structure in 44Ti. Z. Phys. A 349, 363–365 (1994)ADSCrossRefGoogle Scholar
  31. 31.
    Ohkubo, S., Hirabayashi, Y., Sakuda, T.: α-Cluster structure of 44Ti in core-excited α+40Ca model. Phys. Rev. C 57, 2760–2762 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    Delion, D.S., Suhonen, J.: Microscopic description of α + Ca Quasimolecular resonances. Phys. Rev. C 63, 061306(R)/1–5 (2001)Google Scholar
  33. 33.
    Vertse T., Curuchet P., Civitarese O., Ferreira, L.S., Liotta, R.J.: Application of Gamow resonances to continuum nuclear spectra. Phys. Rev. C 37, 876–879 (1988)ADSCrossRefGoogle Scholar
  34. 34.
    Vertse, T., Liotta, R.J., Maglione, E.: Exact and approximate calculation of giant resonances. Nucl. Phys. A 584, 13–34 (1995)ADSCrossRefGoogle Scholar
  35. 35.
    Langanke, K.: Explanation of the backangle anomaly and isotope effect within a microscopic study of elastic α-scattering on even Ca isotopes. Nucl. Phys. A 377, 53–83 (1982)ADSCrossRefGoogle Scholar
  36. 36.
    Dudek, J., Szymanski, Z., Werner, T.: Woods-Saxon potential parameters optimized to the high spin spectra in the Lead region. Phys. Rev. C 23, 920–925 (1981)ADSCrossRefGoogle Scholar
  37. 37.
    Allatt, R.G., et. al.: Fine structure in 192Po α decay and shape coexistence in 188Pb. Phys. Lett. B 437, 29–34 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    Barker, F.C.: Width of the 12O ground state. Phys. Rev. C 59, 535–538 (1999)ADSCrossRefGoogle Scholar
  39. 39.
    Frekers, D., et al.: Resonances in low energy 40Ca(α, α)-scattering and quasimolecular band in 44Ti. Z. Phys. A 276, 317–324 (1976)ADSCrossRefGoogle Scholar
  40. 40.
    Frekers, D., Santo, R., Langanke, K.: Identification of quasimolecular resonances in low energy α-40Ca scattering and effects of compound nucleus excitation. Nucl. Phys. A 394, 189–220 (1983)ADSCrossRefGoogle Scholar
  41. 41.
    Yamada, T., et al.: Experimental examination of the lowest alpha cluster states in 44Ti. Phys. Rev. C 41, 2421–2424 (1990)ADSCrossRefGoogle Scholar
  42. 42.
    Richard B.F., Singh B.: Table of Superdeformed Nuclear Bands and Fission Isomers, LBL-35916 (1994)Google Scholar
  43. 43.
    Werner, T.R., Dudek, J.: Shape coexistence effects of super- and hyperdeformed configurations in rotating nuclei with 58 ≤ Z ≤ 74. Atomic Data and Nucl. Data Tabl. 50, 179–267 (1992)ADSCrossRefGoogle Scholar
  44. 44.
    de Voight, M.L.A., Dudek, J., Szymanski, Z.: High-spin phenomena in atomic nuclei. Rev. Mod. Phys. 55, 949–1046 (1983)ADSCrossRefGoogle Scholar
  45. 45.
    Ring, P., Schuck, P.: The Nuclear Many-Body Problem. Springer-Verlag, New York (1980)CrossRefGoogle Scholar
  46. 46.
    Varga, K., Lovas, R.G., Liotta, R.J.: Cluster-configuration shell model for alpha decay. Nucl. Phys. A 550, 421–452 (1992)ADSCrossRefGoogle Scholar
  47. 47.
    Delion, D.S., Liotta, R.J.: Microscopic description of α decay from superdeformed nuclei. Phys. Rev. C 58, 2073–2080 (1998)ADSCrossRefGoogle Scholar
  48. 48.
    Flerov, G.N.: Atom. Ener. 26, 138 (1969)Google Scholar
  49. 49.
    Sandulescu, A., Gupta, R.K., Scheid, W., Greiner, W.: Synthesis of new elements within the fragmentation theory: application to Z = 104 and 106 elements. Phys. Lett. B 60, 225–228 (1976)ADSCrossRefGoogle Scholar
  50. 50.
    Gupta, R.K., Parvulescu, C., Sandulescu, A., Greiner, W.: Further possibilities with Pb-targets for synthesizing super-heavy elements. Z. Phys. A 283, 217–218 (1977)ADSCrossRefGoogle Scholar
  51. 51.
    Gupta, R.K., Sandulescu, A., Greiner, W.: Interaction barriers, Nuclear shapes and the optimum choice of a compound nucleus reaction for producing super-heavy elements. Phys. Lett. 67B, 257–261 (1977)Google Scholar
  52. 52.
    Gupta, R.K., Sandulescu, A., Greiner, W.: Synthesis of Fermium and Transfermium elements using Calcium-48 beam. Z. Naturforsch 32a, 704 (1977)ADSGoogle Scholar
  53. 53.
    Săndulescu, A., Poenaru, D.N., Greiner, W.: Fiz. Elem. Chastits At Yadra 11, 1334 (1980)Google Scholar
  54. 54.
    Săndulescu, A., Poenaru, D.N., Greiner, W.: New type of decay of heavy nuclei intermediate between fission and α decay. Sov. J. Part. Nucl. 11, 528 (1980)Google Scholar
  55. 55.
    Oganessian, Yu.Ts.: The synthesis and decay properties of the heaviest elements. Nucl. Phys. A 685, 17c–36c (2001)ADSCrossRefGoogle Scholar
  56. 56.
    Oganessian, Yu.Ts., et. al.: Heavy element research at Dubna. Nucl. Phys. A 734, 109–123 (2004)CrossRefGoogle Scholar
  57. 57.
    Hofmann, S., Münzenberg, G.: The discovery of heaviest elements. Rev. Mod. Phys. 72, 733–767 (2000)ADSCrossRefGoogle Scholar
  58. 58.
    Hofmann, S., Münzenberg, G., Schädel, M.: On the discovery of superheavy elements. Nucl. Phys. News 14(4), 5–13 (2004)Google Scholar
  59. 59.
    Nazarewicz, W., et al.: Theoretical description of superheavy nuclei. Nucl. Phys. A 701, 165c–171c (2002)ADSCrossRefGoogle Scholar
  60. 60.
    Strutinsky, V.M.: Shell effects in nuclear masses and deformation energies. Nucl. Phys. A 95, 420–442 (1967)ADSCrossRefGoogle Scholar
  61. 61.
    Strutinsky, V.M.: “Shells” in deformed nuclei. Nucl. Phys. A 122, 1–33 (1968)ADSCrossRefGoogle Scholar
  62. 62.
    Smolanczuk, R.: Properties of the hypothetical spherical superheavy nuclei. Phys. Rev. C 56, 812–824 (1997)ADSCrossRefGoogle Scholar
  63. 63.
    Denisov, V.Yu., Hofmann, S.: Formation of superheavy elements in cold fusion reactions. Phys. Rev. C 61, 034606/1–15 (2000)Google Scholar
  64. 64.
    Smolanczuk, R.: Formation of superheavy elements in cold fusion reactions. Phys. Rev. C 63, 044607/1–8 (2001)Google Scholar
  65. 65.
    Zagrebaev, V.I., Arimoto, Y., Itkis, M.G., Oganessian, Yu.Ts.: Synthesis of superheavy nuclei: How accurately can we describe it and calculate the cross sections? Phys. Rev. C 65, 014607/1–13 (2001)Google Scholar
  66. 66.
    Adamian, G.G., Antonenko, N.V., Scheid, W.: Isotopic trends of the production of superheavy nuclei in cold fusion reactions. Phys. Rev. C 69, 044601(R)/1–5 (2004)Google Scholar
  67. 67.
    Itkis, M.G., Oganessioan, Yu.Ts., Zagrebaev, V.I.: Fission barriers of superheavy nuclei. Phys. Rev. C 65, 044602/1–7 (2002)Google Scholar
  68. 68.
    Gamow, G.: Zur Quantentheorie des Atomkernes. Z. Phys. 51, 204–212 (1928)ADSzbMATHCrossRefGoogle Scholar
  69. 69.
    Royer, G.: Alpha emission and spontaneous fission through quasimolecular shapes. J. Phys. G: Nucl. Part. Phys. 26, 1149–1170 (2000)ADSCrossRefGoogle Scholar
  70. 70.
    Royer, G., Gherghescu, R.: On the formation and alpha decay of superheavy elements. Nucl. Phys. A 699, 479–492 (2002)ADSCrossRefGoogle Scholar
  71. 71.
    Zhang, H., Zuo, W., Li, J., Royer, G.: α Decay half lives of new superheavy nuclei within a generalized liquid drop model. Phys. Rev. C 74, 017304/1–4 (2006)Google Scholar
  72. 72.
    Kumar, S., Balasubramaniam, M., Gupta, R.K., Münzenberg, G., Scheid, W.: The formation and decay of superheavy nuclei produced in 48Ca-induced reactions. J. Phys. G: Nucl. Part. Phys. 29, 625–639 (2003)ADSCrossRefGoogle Scholar
  73. 73.
    Typel, S., Brown, B.A.: Skyrme Hartree-Fock calculations for the α decay Q-values of superheavy nuclei. Phys. Rev. C 67, 034313/1–6 (2003)Google Scholar
  74. 74.
    Roy Chowdhury, P., Samanta, C., Basu, D.N.: α Decay half-lives of new superheavy elements. Phys. Rev. C 73, 014612/1–6 (2006)Google Scholar
  75. 75.
    Mohr, P.: α-Nucleus potentials, α-decay half-lives, and shell closures for superheavy nuclei. Phys. Rev. C 73, 031301(R)/1–5 (2006)Google Scholar
  76. 76.
    Buck, B., Merchand, A.C.: A consistent cluster model treatment of exotic decays and alpha decays from heavy nuclei. J. Phys. G 15, 615–635 (1989)ADSCrossRefGoogle Scholar
  77. 77.
    Poenaru, D.N., Plonski, I.-H., Greiner, W.: α-Decay half lives of superheavy nuclei. Phys. Rev. C 74, 014312/1–5 (2006)Google Scholar
  78. 78.
    Sobiczewski, A., Patyk, Z., Cwiok, S.: Deformed superheavy nuclei. Phys. Lett. B 224, 1–4 (1989)ADSCrossRefGoogle Scholar
  79. 79.
    Gambhir, Y.K., Bhagwat, A., Gupta, M.: Microscopic description of superheavy nuclei. Ann. Phys. (NY) 320, 429–452 (2005)ADSzbMATHCrossRefGoogle Scholar
  80. 80.
    Dupré, Z.A., Bürvenich, T.J.: Predictions of α-decay half lives based on potential from self-consistent mean-field models. Nucl. Phys. A 767, 81–91 (2006)ADSCrossRefGoogle Scholar
  81. 81.
    Xu, F.R., Zhao, E.G., Wyss, R., Walker, P.M.: Enhanced stability of superheavy nuclei due to high-spin isomerism. Phys. Rev. Lett. 92, 252501/1–4 (2004)Google Scholar
  82. 82.
    Delion, D.S., Liotta, R.J., Wyss, R.: α Decay of high-spin isomers in superheavy nuclei. Phys. Rev. C 76, 044301/1–8 (2007)Google Scholar
  83. 83.
    Hofmann, S., et al.: The new isotope 270110 and its decay products 266Hs and 262Sg. Eur. Phys. J. A 10, 5–10 (2001)ADSCrossRefGoogle Scholar
  84. 84.
    Itkis, M.G. et. al.: FUSION06: Reaction Mechanism and Nuclear Structure at the Coulomb Barrier, AIP Conference Proceedings, vol. 853, p. 231 (2006).Google Scholar
  85. 85.
    Grigorenko, L.V., Johnson, R.C., Mukha, I.G., Thomson, I.J., Zhukov, M.V.: Two-proton radioactivity and three-body decay: general problems and theoretical approach. Phys. Rev. C 64, 054002/1–12 (2001)Google Scholar
  86. 86.
    Dudek, J., Nazarewicz, W., Werner, T.: Discussion of the improved parametrisation of the Woods-Saxon potential for deformed nuclei. Nucl. Phys. A 341, 253–268 (1980)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Theoretical Physics DepartmentInstitute of Physics and Nuclear EngineeringBucharestRomania

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