Effect of tensor interaction on shell structure of heavy and superheavy nuclei

1. Effect of tensor interaction on shell structure of heavy and superheavy nuclei Xian-Rong Zhou Department of physics, Xiamen University, Xiamen, China Collaborator: H. Sagawa, University of Aizu, Japan KITPC, Jun 21th, 2012

2. Magic numbers Z N

3. Magic number beyond 208Pb Macroscopic-microscopic model Z=114, N=184 Skyrme Hartree-Fock approximation Z=124 or 126, N=184 Relativistic mean field Z=120, N=172, or 184 Z=126, N=184 Z=114, N=184

4. Why there is divergence? Mean-field Single-particles energies Shell structure Spin-orbit strength A.V. Afanasjev, et al., PRC 67, 024309 (2003) M. Bender, et al., NPA 723, 354 (2001)

5. Role of spin-orbit splitting Nature 422, 05069 (2006)

6. Role of tensor force in spherical SHF E. B. Suckling, et al., Eur. Phys. Lett. 90, 12001 (2010)

7. Motivation: to consider deformation Single-particles energies Shell structure Deformation Spin-orbit partners partially occupied Spin-orbit strength Tensor

8. Spherical SHF + BCS

9. Present work: heavy and superheavy nuclei Deformed SHF + Tensor + Time-odd BCS

10. SHF equation SHF Eq. Total energy:

11. Tensor interaction Triplet-even and triplet-odd zero-range tensor force, T, U: free parameters.

12. Modification due to tensor force The vector part of spin-orbit density in SHF is The associated part of SHF energy density is given by With the modification of tensor correlations, the spin-orbit potential

13. Where α and β have the contributions of central exchange and tensor term

14. Time-odd components of SHF Contribution: Time-odd component for HF eq. Extra term for Ueven from spin density

15. Tensor paprameters for different Skyrme interaction

16. V=1000 V=1250 Density dependent surface Pairing with Lipkin-Nogami number projection For medium heavy nuclei For heavy nuclei PRC 79, 034306, 2009

17. Pairing strength in superheavy nuclei X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

18. Deformation of Kr isotopes X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

19. Deformation of 80Zr X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

20. Single-particle energies of 249Bk X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

21. Single-particle energies of 251Cf X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

22. Single-particle energies of neutrons and protons for 254No X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

23. Binding energies vs deformation for298114184 X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

24. Single-particle energies of protons for298114184 X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

25. Single-particle energies of neutrons for298114184 X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

26. Gaps ofprotons for298114184 X. R. Zhou, H. Sagawa, J. P. G 39 (2012) 085104

27. Summary • Our calculations indicate that the SLy5+T interaction gives a proper descriptions of shape changes and the deformation of the ground state of 80Zr. • 2.It is shown that the single-particle spectra of 249Bk and 251Cf are sensitive to the modification of the spin-orbit splitting due to the tensor correlations. The orderings of the proton and neutron single particle states are reasonably described by SLy5+T interaction in comparison with the experimental data. Z 3. For superheavy nuclei, we find the pronounced energy gaps at Z=114 and Z=120 at the spherical minimum irrespective of the tensor interaction. However, the tensor correlations of SLy5+T interaction make a larger shell gap at Z=114 than that at Z=120. Near the deformed local minimum at β 2~0.6, we find again the Z=120 shell gap for all the four interactions.

28. Thank you! Furong Lake Xiamen Univ.