N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

1. Exotic cluster structure in light nuclei N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

2. D.M. Brink and J.J. Castro, Nucl. Phys. A216 (1973) Appearance of “alpha matter” in low nuclear density region

3. weakly interacting state of (strongly bound) clusters Excitation energy decay threshold to clusters single-particle motion of of protons and neutrons Nuclear structure

4. Synthesis of 12C from three alpha particles 0+2 Ex =7.65MeV Γα 3αthreshold Ex = 7.4 MeV Γγ 2+ Γγ 0+ The necessity of dilute 3alpha-cluster state has been pointed out from astrophysical side, and experimentally confirmed afterwards

6. Tip-to-Tip Collision 4He+8Be

7. b = 0.2 fm collision 4He+8Be

8. Lifetime of linear chain as a function of impact parameter

9. weakly interacting state ofclusters Excitation energy decay threshold to clusters cluster structure with geometric shapes single-particle motion of protons and neutrons

10. 10Be πσ （σ）2 （π）２ N. Itagaki and S. Okabe, Phys. Rev. C 61 044306 (2000)

11. N. Itagaki, S. Okabe, K. Ikeda, and I. Tanihata PRC64 (2001), 014301

12. N. Itagaki, S. Okabe, K. Ikeda, and I. Tanihata PRC64 (2001), 014301

13. Investigation of the linear chain statesin collaboration with Frankfurt Maruhn group • The model is not cluster but mean-field model • Interactions are quite general (Skyrme interactions designed for nuclei including heavier ones) Linear-chain structure of three clusters in 16C and 20C J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura Nucl. Phys. A 833 1-17 (2010).

14. ConvergenceBehavior An excited quasistable (?) state appears as an apparently converged configuartion for 1000‘s of iterations. Sometimes convergence indicators are as good as for the ground state. Subsequently, there is rapid conversion to the ground state via triaxial shapes.

15. 16C Kp=1- Kp=1+ Kp=0+ Kp=0+ Kp=2+

16. Stability of 3 alpha linear chain with respect to the bending motion Solid -- 20C Dotted -- 16C Geometric shape is stabilized by adding neutrons

17. How can we stabilize geometric shapes like linear chain configurations? • Adding valence neutrons • Rotating the system

22. weakly interacting state ofclusters Excitation energy decay threshold to clusters cluster structure with geometric shapes single-particle motion of protons and neutrons

23. weakly interacting state ofclusters Excitation energy decay threshold to clusters cluster structure with geometric shapes single-particle motion of protons and neutrons

24. THSR wave function

25. Discussion for the gas-like state of alpha’s moves on to the next step – to heavier regions Gas-like state of three alpha’s around 40Ca? Tz. Kokalova et al. Eur. Phys. J A23 (2005) 28Si+24Mg  52Fe Hoyle state around the 40Ca core?

27. 24Mg = 16O+2alpha’s 0+ Energy E0 7th state, candidate for the resonance state Large E0 transition strength

28. Squared overlap with 16O+2alpha’s (THSR)

29. 28Si = 16O+3alpha’s

30. Summary • Nuclear structure changes as a function of excitation energy • Cluster structure appears around the decay threshold, and geometric configurations are stabilized by adding neutrons or giving large angular momentum • Studies of gas-like structure of alpha-clusters are extended to heavier nuclei

31. Virtual THSR wave functionN.Itagaki., M. Kimura, M. Ito, C. Kurokawa, and W. von Oertzen, Phys. Rev. C 75 037303 (2007) To apply THSR wave function to heavier systems, we must simplify it Integral over {Ri} in the THSR wave function is performed by Monte Carlo integration

32. 3α Solid, dotted, dashed, dash-dotted  σ = 2,3,4,5 fm r.m.s. radius of 12C (fm)