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Systematical calculation on alpha decay of superheavy nuclei

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Title: Systematical calculation on alpha decay of superheavy nuclei


1
Systematical calculation on alpha decay of
superheavy nuclei
  • Zhongzhou Ren1,2 (???), Chang Xu1 (??)
  • 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
  • Becquerel discovered a kind of unknown radiation
    from Uranium in 1896.
  • M. Curie and P. Curie identified two chemical
    elements (polonium and radium) by their strong
    radioactivity.
  • In 1908 Rutherford found that this unknown
    radiation consists of 4He nuclei and named it as
    the alpha decay for convenience.

4
Gamow Quantum 1928
  • In 1910s alpha scattering from natural
    radioactivity on target nuclei provided first
    information on the size of a nucleus and on the
    range of nuclear force.
  • In 1928 Gamow tried 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 (Zgt104).
  • GSI Z110-112 Dubna Z114-116,118
  • Berkeley Z110-111 RIKEN Z113.
  • 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 M3Y
    potential with the density distributions of the
    alpha particle and daughter nucleus.

8
2. The density-dependent cluster model
  • In Density-dependent cluster model, the
    cluster-core potential is the sum of the nuclear,
    Coulomb and centrifugal potentials.
  • R is the separation between cluster and core.
  • L is the angular momentum of the cluster.

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

10
Double-folded nuclear potential
11
2.2 Details of standard parameters
  • Where ci 1.07Ai1/3 fm a0.54 fm Rrms?1.2A1/3
    (fm).
  • The M3Y nucleon-nucleon interaction
  • two direct terms with different ranges, and an
    exchange term with a delta interaction.
  • 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
  • RC1.2Ad1/3 (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
  • In quasiclassical approximation the decay width ?
    is
  • P? is the preformation probability of the cluster
    in a parent nucleus.
  • The normalization factor F is

14
2.5 decay half-life
  • The wave number K(R) is given by
  • The decay half-life is then related to the width
    by

15
2.6 Preformation probability
  • For the preformation probability of ?-decay we
    use
  • P? 1.0 for even-even nuclei
  • P? 0.6 for odd-A nuclei
  • P?0.35 for odd-odd nuclei
  • These values agree approximately with the
    experimental data of open-shell nuclei.
  • They are also supported by a microscopic model.

16
2.7 Density-dependent cluster model
The Reid nucleon-nucleon potential
Nuclear Matter G-Matrix M3Y
Bertsch et al.
Satchler et al.
Hofstadter et al.
1/3?0
Alpha Scattering RM3Y
DDCM
Electron Scattering
Brink et al.
Tonozuka et al.
Nuclear Matter Alpha Clustering (1/3?0)
Alpha Clustering
1987 PRL Decay Model
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 Z70,
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 100-105 isotopes.
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)21.08c1(Z-90)/Ac2(Z-90)2/A
  • c3(Z-90)3/Ac4(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-lives of 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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