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Systematical calculation on alpha decay of superheavy nuclei

Systematical calculation on alpha decay of superheavy nuclei. Zhongzhou Ren 1,2 ( 任中洲 ), Chang Xu 1 ( 许昌 ) 1 Department of Physics, Nanjing University, Nanjing, China 2 Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, China. Outline.

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Systematical calculation on alpha decay of superheavy nuclei

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  1. Systematical calculation on alpha decay of superheavy nuclei • Zhongzhou Ren1,2 (任中洲), Chang Xu1 (许昌) • 1Department of Physics, Nanjing University, Nanjing, China • 2Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, China

  2. Outline • 1. Introduction • 2. Density-dependent cluster model • 3. Numeral results and discussions • 4. Summary

  3. 1. Introduction • Becquereldiscovered a kind of unknown radiation from Uranium in 1896. • M. CurieandP. Curieidentified two chemical elements (polonium and radium) by their strong radioactivity. • In 1908Rutherfordfound thatthis unknown radiation consists of4He nuclei and named it asthe alpha decay for convenience.

  4. Gamow: Quantum 1928 • In 1910salpha scatteringfrom natural radioactivity on target nuclei provided first information on the size of a nucleus and on the range of nuclear force. • In 1928Gamowtried to apply quantum mechanics to alpha decay and explained it as a quantum tunnelling effect.

  5. Various models • Theoretical approaches :shell model, cluster model, fission-like model, a mixture of shell and cluster model configurations…. • Microscopic description of alpha decay is difficult due to: • 1. The complexity of the nuclear many- • body problem • 2. The uncertainty of nuclear potential.

  6. Important problem: New element • To date alpha decay is still a reliable way to identify new elements (Z>104). • GSI: Z=110-112;Dubna: Z=114-116,118 • Berkeley: Z=110-111; RIKEN: Z=113. • Therefore an accurate and microscopic model of alpha decay is very useful for current researches of superheavy nuclei.

  7. Density-dependent cluster model • To simplify the many-body problem into a few-body problem: new cluster model • The effective potential between alpha cluster and daughter-nucleus: double folded integral of the renormalized M3Ypotential with the density distributions of the alpha particle and daughter nucleus.

  8. 2. The density-dependent cluster model • InDensity-dependent cluster model, the cluster-core potential is the sum of thenuclear,Coulombandcentrifugalpotentials. • Ris the separation between cluster and core. • Lis the angular momentum of the cluster.

  9. 2.1 Details of the alpha-core potential •  is the renormalized factor. • 1 ,2are the density distributions of cluster particle and core (a standard Fermi-form). • Or 1 is a Gaussian distribution for alpha particle (electron scattering). • 0is fixed by integrating the density distribution equivalent to mass number of nucleus.

  10. Double-folded nuclear potential

  11. 2.2 Details of standard parameters • Whereci =1.07Ai1/3 fm; a=0.54 fm; Rrms1.2A1/3 (fm). • TheM3Ynucleon-nucleon interaction: • two direct terms with different ranges, and an exchange term with a deltainteraction. • The renormalized factor in the nuclear potential is determined separately for each decay by applying the Bohr-Sommerfeld quantization condition.

  12. 2.3 Details of Coulomb potential • For the Coulomb potential between daughter nucleus and cluster, a uniform charge distribution of nuclei is assumed • RC=1.2Ad1/3(fm) and Ad is mass number of daughter nucleus. • Z1 and Z2 are charge numbers of cluster and daughter nucleus, respectively.

  13. 2.4 Decay width • Inquasiclassical approximationthe decay widthis • Pis the preformation probability of thecluster in a parent nucleus. • The normalization factorFis

  14. 2.5 decay half-life • The wave numberK(R)is given by • Thedecay half-lifeis then related to thewidthby

  15. 2.6 Preformation probability • Forthe preformation probabilityof -decay we use • P= 1.0foreven-evennuclei; • P =0.6forodd-Anuclei; • P=0.35forodd-oddnuclei • These values agree approximately with the experimental data ofopen-shell nuclei. • They are also supported bya microscopic model.

  16. 2.7 Density-dependent cluster model The Reid nucleon-nucleon potential Bertsch et al. Nuclear Matter: G-Matrix M3Y Satchler et al. Hofstadter et al. 1/30 Electron Scattering DDCM Alpha Scattering RM3Y Brink et al. Tonozuka et al. Nuclear Matter Alpha Clustering (1/30) 1987 PRL Decay Model Alpha Clustering

  17. 3. Numeral results and discussions • 1. We discuss the details of realistic M3Y potential used in DDCM. • 2. We give the theoretical half-lives of alpha decay for heavy and superheavy nuclei.

  18. The variation of the nuclear alpha-core potential withdistance R(fm) in the density-dependent cluster model and in Buck's model for 232Th.

  19. The variation of the sum of nuclear alpha-coreand Coulomb potential with distance R (fm) in DDCM and in Buck's model for 232Th.

  20. The variation of the hindrance factor for Z=70, 80, 90, 100, and 110 isotopes.

  21. The variation of the hindrance factor with mass number for Z= 90-94 isotopes.

  22. The variation of the hindrance factor with mass number for Z= 95-99 isotopes.

  23. The variation of the hindrance factor with mass number for Z= 100-105isotopes.

  24. Table 1 : Half-lives of superheavy nuclei

  25. Table 2 : Half-lives of superheavy nuclei

  26. Table 3 : Half-lives of superheavy nuclei

  27. Table 4 : Half-lives of superheavy nuclei

  28. Cluster radioactivity: Nature 307 (1984) 245.

  29. Nature 307 (1984) 245.

  30. Phys. Rev. Lett. 1984

  31. Phys. Rev. Lett.

  32. Dubna experiment for cluster decay

  33. DDCM for cluster radioactivity • Although the data of cluster radioactivity from 14C to 34Si have been accumulated in past years, systematic analysis on the data has not been completed. • We systematically investigated the experimental data of cluster radioactivity with the microscopic density-dependent cluster model (DDCM) where the realistic M3Y nucleon-nucleon interaction is used.

  34. Half-lives of cluster radioactivity (1)

  35. Half-lives of cluster radioactivity (2)

  36. The small figure in the box is the Geiger-Nuttall law for the radioactivity of 14C in even-even Ra isotopic chain.

  37. New formula for cluster decay half-life • Let us focus the box of above figure where the half-lives of 14C radioactivity for even-even Ra isotopes is plotted for decay energies Q-1/2. • It is found that there is a linear relationship between the decay half-lives of 14C and decay energies. • It can be described by the following expression

  38. Cluster decay and spontaneous fission • Half-live of cluster radioactivity • New formula of half-lives of spontaneous fission • log10(T1/2)=21.08+c1(Z-90)/A+c2(Z-90)2/A • +c3(Z-90)3/A+c4(Z-90)/A(N-Z-52)2

  39. DDCM for alpha decay

  40. Further development of DDCM

  41. DDCM of cluster radioactivity

  42. New formula of half-life of fission

  43. Spontaneous fission half-lives in g.s. and i.s.

  44. 4. Summary • We calculate half-lives of alpha decay by density-dependent cluster model (new few-body model). • The model agrees with the data of heavy nuclei within a factor of 3 . • The model will have a good predicting ability for the half-livesof unknown mass range by combining it with any reliable structure model or nuclear mass model. • Cluster decay and spontaneous fission

  45. Thanks • Thanks for the organizer of this conference

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