1. N. Itagaki Yukawa Institute for Theoretical Physics, Kyoto University

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

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

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

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

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

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

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

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

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 states in 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 16 C and 20 C J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura Nucl. Phys. A 833 1-17 (2010).

14. Convergence Behavior 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. K  =0 + K  =2 + K  =1 + K  =1 - 16 C

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

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

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

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

24. THSR wave function

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

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

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

29. 28 Si = 16 O+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 function N.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. r.m.s. radius of 12 C (fm) 3α3α Solid, dotted, dashed, dash-dotted  σ = 2,3,4,5 fm