Systematical calculation on alpha decay of superheavy nuclei

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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

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Outline

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Double-folded nuclear potential
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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.

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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.

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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

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2.5 decay half-life

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

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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.

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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
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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.

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The variation of the nuclear alpha-core potential
withdistance R(fm) in the density-dependent
cluster model and in Buck's model for 232Th.
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The variation of the sum of nuclear
alpha-coreand Coulomb potential with distance R
(fm) in DDCM and in Buck's model for 232Th.
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The variation of the hindrance factor for Z70,
80, 90, 100, and 110 isotopes.
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The variation of the hindrance factor with mass
number for Z 90-94 isotopes.
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The variation of the hindrance factor with mass
number for Z 95-99 isotopes.
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The variation of the hindrance factor with mass
number for Z 100-105 isotopes.
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• Table 1 Half-lives of superheavy nuclei

AZ AZ Q?(MeV) T?(exp.) T?(cal.)
294118 290116 11.8100.150 1.8(8.4/-0.8)ms 0.8ms
292116 288114 10.7570.150 33(155/-15)ms 64ms
290116 286114 10.8600.150 29(140/-33)ms 38ms
289114 285112 9.8950.020 30.4(X)s 5.5s
288114 284112 10.0280.050 1.9(3.3/-0.8)s 1.4s
287114 283112 10.4840.020 5.5(10/-2)s 0.1s
285112 281110 8.8410.020 15.4(X)min 37.6min
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• Table 2 Half-lives of superheavy nuclei

AZ AZ Q?(MeV) T?(exp.) T?(cal.)
284112 280110 9.3490.050 9.8(18/-3.8)s 30.1ms
277112 273110 11.6660.020 280(X)?s 53?s
272111 268109 11.0290.020 1.5(2.0/-0.5)ms 1.4ms
281110 277108 9.0040.020 1.6(X)min 2.0min
273110 269108 11.2910.020 110(X)?s 93?s
271110 267108 10.9580.020 0.62(X)ms 0.58ms
270110 266108 11.2420.050 100(140/-40)?s 78?s
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• Table 3 Half-lives of superheavy nuclei

AZ AZ Q?(MeV) T?(exp.) T?(cal.)
269110 265108 11.3450.020 270(1300/-120)?s 79?s
268Mt 264Bh 10.2990.020 70(100/-30)ms 22ms
269Hs 265Sg 9.3540.020 7.1(X)s 2.3s
267Hs 263Sg 10.0760.020 74(X)ms 22ms
266Hs 262Sg 10.3810.020 2.3(1.3/-0.6)ms 2.2ms
265Hs 261Sg 10.7770.020 583(X)?s 401?s
264Hs 260Sg 10.5900.050 0.54(0.30)ms 0.71ms
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• Table 4 Half-lives of superheavy nuclei

AZ AZ Q?(MeV) T?(exp.) T?(cal.)
267Bh 263Db 9.0090.030 17(14/-6)s 12s
266Bh 262Db 9.4770.020 1s 1s
264Bh 260Db 9.6710.020 440(600/-160)ms 237ms
266Sg 262Rf 8.8360.020 25.7(X)s 10.6s
265Sg 261Rf 8.9490.020 24.1(X)s 8.0s
263Sg 259Rf 9.4470.020 117(X)ms 266ms
261Sg 257Rf 9.7730.020 72 (X)ms 34ms
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Cluster radioactivity Nature 307 (1984) 245.
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Nature 307 (1984) 245.
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Phys. Rev. Lett. 1984
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Phys. Rev. Lett.
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Dubna experiment for cluster decay
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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.

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Half-lives of cluster radioactivity (1)

Decay Q/MeV Log10 Texpt Log10 TFormula Log10RM3Y
221Fr207Tl14C 31.29 14.52 14.43 14.86 221Ra207Pb14C 32.40 13.37 13.43 13.79 222Ra208Pb14C 33.05 11.10 10.73 11.19 223Ra209Pb14C 31.83 15.05 14.60 14.88 224Ra210Pb14C 30.54 15.90 15.97 16.02 226Ra212Pb14C 28.20 21.29 21.46 21.16 228Th208Pb20O 44.72 20.73 20.98 21.09 230Th206Hg24Ne 57.76 24.63 24.17 24.38
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Half-lives of cluster radioactivity (2)
Decay Q/MeV Log10 Texpt Log10 TFormula Log10RM3Y(2)
231Pa207Tl24Ne 60.41 22.89 23.44 23.91 232U208Pb24Ne 62.31 20.39 21.00 20.34 233U209Pb24Ne 60.49 24.84 24.76 24.24 234U206Hg28Mg 74.11 25.74 25.12 25.39 236Pu208Pb28Mg 79.67 21.65 21.90 21.20 238Pu206Hg32Si 91.19 25.30 25.33 26.04 242Cm208Pb34Si 96.51 23.11 23.19 23.04
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The small figure in the box is the Geiger-Nuttall
law for the radioactivity of 14C in even-even Ra
isotopic chain.

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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

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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

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DDCM for alpha decay
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Further development of DDCM
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DDCM of cluster radioactivity
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New formula of half-life of fission
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Spontaneous fission half-lives in g.s. and i.s.
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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

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Thanks

• Thanks for the organizer of this conference