1. Structures of Exotic 131,133 Sn Isotopes for r-process nucleosynthesis Shisheng Zhang 1,2 ( 张时声 ) 1. School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China 2. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 29th, June 2012 KITPC Joint Workshop on Nuclear Physics, Beijing, China 11th June – 30th June, 2012

2. Outline  Background and Motivation  nuclear structure  nuclear astrophysics  Goals  Theoretical Methods  Results and discussions  Summary and outlook

3. Background : nuclear structure Theoretical understanding ? Not yet! Experiments: Four strong single particle bound levels with striking similarity  level spacings  strengths recently measured in 131 Sn and 133 Sn K. L. Jones et al., Nature, 465, 454 (2010). R. L. Kozub et al., (submitted to PRL 2012).

4. Background : nuclear astrophysics bound levels resonant levels (above neutron capture thresholds) neutron capture (NC) cross section synthesis of heavy elements in the r- process in supernovae NC reaction rate R. Surman, J. Beun, G. C. McLaughlin and W. R. Hix, PRC 79, 045809 (2009). ?? Significantly impact ! Global impact of 130 Sn(n,  ) on r-process abundances

5.  3 contributions to neutron capture cross section Background : nuclear astrophysics S(n) Direct Capture Resonant Capture H F Averaging over many closely-spaced levels strong dependence on level density model For Fermi gas model, when is HF applicable? Levels above S(n) are unknown contribution to  total unknown Strong bound single particle levels below S(n) contribute ratios to  RC and  HF are unknown g.s. ExEx

6. Outline  Background and Motivation  nuclear structure  nuclear astrophysics  Goals  Theoretical Methods  Results and discussions  Summary and outlook

7. Goals Understand the structure of the bound and resonant levels in 133 Sn and 131 Sn from the theoretical point of view and check if similarity appears in theoretical calculations Determine if the density of unbound resonant levels is sufficiently high to enable valid statistical model calculations for NC cross section calculations on 130,132 Sn

8. Outline  Background and Motivation  nuclear structure  nuclear astrophysics  Goals  Theoretical Methods  Results and discussions  Summary and outlook

9.  Shell model  large scale shell model (LSS)  Phenomenological models  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Theoretical Methods

10.  Large scale shell model (LSS)  extended paring-plus-quadrupole models with monopole corrections (EPQQM) model  Pairing terms, quadrupole-quadrupole term, octupole- octupole term, hexadecupole-hexadecupole term, monopole corrections are included in Hamiltonian.  Model space from the experimental data:  upper neutron orbits 2f 7/2, 3p 3/2, 1h 9/2, 3p 1/2, 2f 5/2 (without 1i 13/2 since this orbit have not been seen experimentally so far ). Unfortunately, the calculations with it require prohibitively large amounts of computer memory when NUSHELLX code used. Shell models H. Jin, M. Hasegawa, S. Tazaki, K. Kaneko and Y. Sun, PRC 84, 044324 (2011).

11.  Shell model  large scale shell model (LSS)  Phenomenological models  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Theoretical Methods

12.  Nilsson s.p. potential with new parameter set Phenomenological model J. Y. Zhang, Y. Sun, M. Guidry, L. L. Riedinger and G. A. Lalazissis, Phys. Rev. C 58, R2663 (1998). 133 Sn 131 Sn

13. Nucleus Methods 133 Sn 131 Sn Bound orbitals Resonant orbitals Bound orbitals Resonant orbitals RMF+ACCC+BCS (present work) YYYY RMF Y1i 13/2, Y above, N YN LSS YNNN KYSPP YNNN Nilsson Y1i 13/2, Y above, N NN FRDM YNNN HFB YNNN Previous Work:

14.  bound orbitals: RMF (NL3 eff. interaction)  resonant orbitals: RMF-ACCC  pairing correlations: BCS approx. A fully self-consistent microscopic method! Successfully describe the properties for 120 Sn, 58-98 Ni, 122-138 Zr, 17 Ne, 26-31 Ne, 131,133 Sn RMF+ACCC+BCS Method S. S. Zhang, S. G. Zhou, J. Meng and G. C. Hillhouse, PRC 82, 2031 (2004). S. S. Zhang, IJMPE 82, 2031 (2009). MPLA (2004) IJMPE (2009) EPJA (2012) Present work submitted to PRC(2012) arXiv (2011) 1. Narrow and not narrow 2. l =0 and l > 0 3. bound-type method

15. Outline  Background and Motivation  nuclear structure  nuclear astrophysics  Goals  Theoretical Method  Results and discussions  Summary and outlook

16. Results Relative Excitation Energy [MeV]

17. Similarity Such similarity does not happen at all shell closures…

18. similar

19. Such similarities are not the norm: the case for 47,49 Ca ( 39,41 Ca) across N=28 (20) shell closure display significant changes in level spacings. Discussion I B. A. Brown et al, PRC 58, 2099 (1998).

20.  Levels above the neutron capture threshold are limited. At most one s. p. resonant level 1i 13/2 appears in the effective energy window.  Need 5 ( s wave) -10 (high l ) levels per MeV  We predict level spacing far too sparse for HF model use Discussion II T. Rauscher et. al. Atom. Data. and Nucl. Data. Tab. 75, 1 (2000). T. Rauscher et. al. Phys. Rev. C 56, 1613 (1997).

21. Outline  Background and Motivation  nuclear structure  nuclear astrophysics  Goals  Theoretical Method  Results and discussions  Summary and outlook

22.  Reproduce four observed strong s.p. bound levels in 131,133 Sn, and similarity of level spacing and strength with our approach.  Such similarity does not always occur across shell closures (e.g. N = 20, 28).  Predict no single-particle levels at energies above and near the neutron threshold S(n), and only one level up to 2.5 MeV above the S(n)  The density of resonant levels is too low to enable statistical models with Fermi gas level densities to calculate neutron capture cross sections. Summary

23.  Our analysis suggests that alternative methods of calculating the neutron captures on 130,132 Sn must be utilized for r- process nucleosynthesis studies.  This result also suggests the necessity for experimental measurements of s.p. bound and resonant level structure of heavy neutron-rich nuclei that are in and near the r-process.  Systematical study on odd-A Sn isotopes will be made in near future. Outlook

24. Collaborators  M. S. Smith, G. Arbanas and R. L. Kozub, ORNL, USA (this work)  U. Lombardo, INFN, Italy  S. G. Zhou and E. G. Zhao, ITP, Beijing Thank you ！

25. Fermi gas model Total Fermi gas state density : : the level density parameter : spacing of the proton (neutron) s.p. states near Fermi energy. the energy shift : is an empirical parameter equal to pairing energy; : excitation energy

26.  Shell model  large scale shell model (LSS)  Phenomenological models  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Methods

27.  Large scale shell model (LSS)  realistic effective interactions :  derived from charge-dependent (CD) Bonn NN potential  Model space from the experimental data :  2f 7/2, 3p 3/2, 1h 9/2, 3p 1/2, 2f 5/2 and 1i 13/2 (included but not confirmed from experimentally; can be estimated to be 2.694  0.2 MeV; above the 132 Sn + n threshold 2.45(5) MeV )  134-142 Sn (even and odd Sn isotopes) Shell models I M. P. Kartamyshev, T. Engeland, M. Hjorth-Jensen and E. Osnes, Phys. Rev. C 76, 024313 (2007). EXP.

28.  Shell model  large scale shell model (LSS)  Phenomenological models  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Methods

29.  Koura-Yamada's s.p. potential (KYSPP)  Central component is an extension of the Woods-Saxon potential Phenomenological approaches H. Koura, M. Yamada, NPA 671, 96 (2000). S. Chiba, H. Koura etc. PRC 77, 015809 (2008). × √

30.  Shell model  large scale shell model (LSS)  Phenomenological model  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Methods

31.  finite-range droplet model (FRDM)  with a folded-Yukawa s.p. potential  Lipkin-Nogami paring Macroscopic-microscopic T. Rauscher, etc. PRC 57, 2031 (1998). NLSH × √

32.  Shell model  large scale shell model (LSS)  Phenomenological model  Koura-Yamada's s.p. potential (KYSPP)  Nilsson s.p. potential with new parameter set  Macroscopic-microscopic model  finite-range droplet model (FRDM)  Microscopic mean field model  HFB  RMF  RMF+ACCC+BCS Methods

33.  Skyrme-HFB  RMF model Microscopic mean field model T. Rauscher, etc. PRC 57, 2031 (1998). NLSH × √