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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

Outline

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

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.

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.

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.

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.

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.

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.

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.

Double-folded nuclear potential

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.

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.

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

2.5 decay half-life

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

by

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.

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

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.

The variation of the nuclear alpha-core potential

withdistance R(fm) in the density-dependent

cluster model and in Buck's model for 232Th.

The variation of the sum of nuclear

alpha-coreand Coulomb potential with distance R

(fm) in DDCM and in Buck's model for 232Th.

The variation of the hindrance factor for Z70,

80, 90, 100, and 110 isotopes.

The variation of the hindrance factor with mass

number for Z 90-94 isotopes.

The variation of the hindrance factor with mass

number for Z 95-99 isotopes.

The variation of the hindrance factor with mass

number for Z 100-105 isotopes.

- Table 1 Half-lives of superheavy nuclei

- Table 2 Half-lives of superheavy nuclei

- Table 3 Half-lives of superheavy nuclei

- Table 4 Half-lives of superheavy nuclei

Cluster radioactivity Nature 307 (1984) 245.

Nature 307 (1984) 245.

Phys. Rev. Lett. 1984

Phys. Rev. Lett.

Dubna experiment for cluster decay

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.

Half-lives of cluster radioactivity (1)

Half-lives of cluster radioactivity (2)

The small figure in the box is the Geiger-Nuttall

law for the radioactivity of 14C in even-even Ra

isotopic chain.

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

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

DDCM for alpha decay

Further development of DDCM

DDCM of cluster radioactivity

New formula of half-life of fission

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

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

Thanks

- Thanks for the organizer of this conference