1. Probe into the nuclear charge radii of superheavy and exotic nuclei via the experimental decay data
Yibin Qian
Department of Applied Physics, Nanjing University of Science and Technology
Collaborators:
Zhongzhou Ren (Nanjing University)
Dongdong Ni (Macao University of Sci. & Tech.)
Tiekuang Dong (Purple Mountain Observatory)
Good afternoon, everyone, I am glad to have the opportunity to give this talk. I have actually just graduated from Nanjing University in this summer, and my supervisor is Prof. Zhongzhou Ren. My other collaborators: Dongdong Ni, and Tiekuang Dong.

2. Outline Motivation of this work
Charge radii of heavy and superheavy nuclei from a decay data
Charge radii of exotic nuclei from the data of proton emission and cluster emission
Half-lives of a decay from natural nuclides based on the experimental charge radii
Summary

3. Research background
1911 Rutherford atomic model (alpha scattering experiment)
At the early stage of nuclear physics, information on nuclear size were obtained from scattering cross sections for alpha particles on light nuclei.
The first indications concerning nuclear radii of heavy nuclei were supplied by alpha-decay lifetimes.
Until the 1950s, electron scattering on nuclei has been used to probe nuclear density distributions [other particles (p, π±, μ…) scattering on nuclei were also used].
During1960s-1970s (peak period for electron scattering experiments), many charge density distributions for stable nuclei were obtained.

4. Available methods to measure nuclear charge radii
(1) Transition energies in muonic nuclei
(2) Elastic electron scattering experiments
providing information on charge radii R
(3) Kαx-ray isotope shifts (KIS)
(4) Optical isotope shifts (OIS)
providing information on isotopic changes δR
The (1-3) methods have been performed only on stable nuclei (several tens of milligrams of a target material are required)
The (4) method can be performed for radioactive atoms with lifetimes down to 1 ms.

5. Motivation of this work
Lifetimes T½ & BR ??
量子理论
S, L, P, T
Energy B, Sp, Sn, Qα…
Radius R, Rn, Rc

6. The first result on charge radii of superheavy nuclei（based on a decay data）

8. MTPADN for a decay
Assuming the spherical a particle interacts with the axially symmetric deformed daughter nucleus.
The nuclear and Coulomb potentials between cluster and daughter are constructed in the double folding model:

9. The density distribution of the spherical alpha-particle is
The density distribution of the core nucleus is depicted in a deformed Fermi form
is fixed by integrating the density distribution equivalent to mass or atomic number of nuclei.

10. The total potential of the a-core system is composed of the attractive nuclear part and the repulsive Coulomb part:
For one certain angle b, one can obtain the decay width G(b) with the modified two-potential approach, the l factor is adjusted to reproduce the experimental Q value. The final decay width can then be obtained by integrating the partial width along the directions.

11. Correlation between radii and decay data
Alpha-decay half-life
Density distribution of daughter nuclei
radius r0 and diffuseness a
RMS charge radius

12. Dependence of the theoretical results on the radius parameter of charge density distribution: (a) alpha-decay half-life of 212Po, (b) rms charge radius of 208Pb
D. Ni, Z. Ren, T. Dong and Y. Qian, PRC, 87 (024310), 2013.

13. Dependence of the theoretical results on the diffuseness parameter of charge density distribution: (a) alpha-decay half-life of 212Po, (b) rms charge radius of 208Pb
D. Ni, Z. Ren, T. Dong and Y. Qian, PRC, 87 (024310), 2013.

14. Key points of our calculations
The diffuseness a is fixed at its standard value of 0.54 fm because the results show weak sensitivity to it. The parameter r0 can be considered as the connection between decay half-lives and radii.
The r0 value is exactly determined to reproduce the available experimental data of alpha-decay half-lives. Next, the rms charge radius of the daughter nucleus is evaluated from the Fermi density distribution with the resulting r0 value.

15. Simple formula for nuclear charge radiiRt RC
V(r) V0 Q r
X1, X2, X3 are the parameters to be determined
D. Ni, Z. Ren, T. Dong and Y. Qian, PRC, 87 (024310), 2013.

16. The formula is not only simple in form but also easy to see the physical meanings.
Through a least-square fit to the available charge radii for odd-A nuclei with 65≤Z≤87 , the three parameters are determined as follows:
The standard deviation of the calculations is

17. Comparison of the extracted rms charge radii with the experimental data versus the mass number A for odd-A nuclei with Z= 65-87

18. Extracted charge radii of superheavy odd-A nuclei with Z = 102-115 versus the mass number A
I. Angeli and K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
The uncertainty of the results occurs along with the large error bars of the experimental data.
Y. Qian, Z. Ren and D. Ni, Phys. Rev. C, 89, (2014)

19. List of the extracted charge radii along with the error bars for superheavy odd-odd nuclei with Z=
I. Angeli and K.P. Marinova, At Data Nucl. Data Tables 99, 69 (2013)

21. Report of the Referee on this manuscript
“… In the present paper, a completely new method to determine the nuclear radius is presented …”
“… Since other methods … cannot be applied if the nucleus is very unstable, the present method can be a powerful tool to determine the nuclear radius in nuclei … ”

22. Proton emission from drip-line nuclei
The residual daughter nuclei are very proton-rich with short lifetimes. So the known methods to measure their radii are not available at present. ＋
The interaction potentials between proton and daughter are numerically constructed in the single-folding model.

23. Charge radii from proton emission
Proton emssion half-life
The decay width Γp is calculated using the modified two-potential approach with the single-folding potential.
The spectroscopic factor Sp is calculated using the relativistic mean-field theory.
The r0 value is exactly determined to reproduce the available experimental half-lives of proton emission. Next, the rms charge radius of the daughter nucleus is evaluated from the density distribution with the resulting r0 value.
RMS charge radius

24. Comparison of the extracted rms charge radii from the proton-emission data with the results of the formula for the proton-rich nuclei with Z= Note that there are generally unavailable measured radii for these nuclei.
I. Angeli, At Data Nucl. Data Tables 87, 185 (2004)

25. Extracted rms charge radii of proton-rich nuclei with Z=68-82
Extracted rms charge radii of proton-rich nuclei with Z= The available data for 184Pb are also shown.

26. Cluster emission in the trans-lead region＋
The residual daughter nuclei are near 208Pb with long lifetimes. Their radii are already known. We pay attention to the emitted clusters that are neutron-rich.
The interaction potentials between cluster and daughter are numerically constructed in the double-folding model.

27. Charge radii from cluster emission
Cluster emssion half-life
The decay width Γ is obtained by using the modified two-potential approach with the double-folding potential.
The cluster preformation factor is given by
D. Ni, Z. Ren, T. Dong, and C. Xu, PRC 78 (2008)
The density distribution of daughter nuclei are specified by their experimental charge radii.
The r0 parameter of the cluster density distribution is exactly determined to reproduce the experimental half-lives of cluster emission.
RMS charge radius

28. Extracted rms charge radii of light neutron-rich nuclei
I. Angeli, At Data Nucl. Data Tables 87, 185 (2004)

30. a decay half-lives of natural nuclides
As mentioned before, the diffuseness parameter a is fixed at it standard value (different for heavy and medium nuclei) due to its weak sensitivity to results.
The parameter r0, representing the density distribution of daughter nuclei, is specified by their experimental charge radii.
Next, the calculation procedure is proceeded within the specified r0 value from the measured charge radii, leading to the final results of a decay half-lives.

31. Detailed comparison of calculated results with experimental data and other theoretical values (in years).
Density distribution of daughter nuclei is deduced from the experiment charge radii.

32. Summary An alternative way to investigate nuclear size:
Heavy and superheavy nuclei with Z=98-116,
proton-rich nuclei with Z=68-82,
light neutron-rich nuclei
Other common methods such as electron scattering are not available for these nuclei.
This is the first result on nuclear charge radii of heavy and superheavy nuclei and exotic nuclei based on nuclear decay data.
Improve the description of a decay based on the specific density distribution of daughter nuclei from the experimental charge radii.

33. 谢谢！ Thanks for your attention！

36. Modified two-potential approach (MTPA)
The cluster (particle)-daughter potential is divided into two regions by the separation radius R, one introduces two auxiliary potentials:
S. A. Gurvitz, P. B. Semmes, W. Nazarewicz and T.Vertse, PRA 69 (2004)

37. Once the bound state wave function is solved in the potential U(r), the decay width is obtained as
The value of is chosen well in such a way that the potential V(r) can be well approximated by the repulsive part (i.e. the attractive part disregards) for
S. A. Gurwitz, P.B. Semmes, W. Nazarewicz and T.Vertse, PRA 69 (2004)

39. Current researches about electron scattering
With the development of radioactive ion beam facilities, it is possible to produce short-lived exotic nuclei and investigate their properties in laboratories
Facilities under
construction:
RIKEN in Japan (133Cs)
GSI in Germany

40. Electron scattering on unstable nuclei
Configuration of the SCRIT-based radioisotope-electron scattering system in RIKEN
Facilities for short-lived unstable nuclei in Tohoku University