1. Content of the talk Exotic clustering in neutron-rich nuclei
Brief overview for the history of the cluster study
Cluster model v.s. Density functional theory for the study of the stability of the cluster states
Connection between cluster structure and shell structure

2. Excitation energy decaying threshold to subsystems
cluster structure with geometric shapes
mean-field, shell structure
(single-particle motion)

4. But the second 0+ state
has turned out to be gas like state
rather than the state
with geometrical configuration

5. P. Chevallier et al.
Phys. Rev 160, 827 (1967)

12. [ ] [ ] [ ] J = 0 Strong-coupling picture J = 0 Weak-coupling picture
The kinetic energy of 8Be subsystem increases
compared with that of the free 8Be [ ]
J = 0 [ ]
J = 0
Weak-coupling picture
There is no definite shape

13. The effect of Pauli principle[ ]
J = 0
The second and third alpha-clusters are excited to higher-nodal configurations.
If linear-chain is stable, there must exist some
very strong mechanism in the interaction side.

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

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

16. N. Itagaki, S. Okabe, K. Ikeda, and I. Tanihata
Phys. Rev. C (2001).

17. σ-orbit is important for the linear chain,
but not the lowest configuration around
3 alpha linear chain
N. Itagaki, S. Okabe, K. Ikeda, and I. Tanihata
Phys. Rev. C (2001).

18. Stabilization of “geometric shape” by adding valence neutrons
N. Itagaki, T. Otsuka, K. Ikeda, and S. Okabe,
Phys. Rev. Lett. 92, (2004).

19. N. Itagaki, T. Otsuka, K. Ikeda, and S. Okabe,
Phys. Rev. Lett. 92, (2004).

20. Mean field models
Quite general models designed for nuclei of all the mass regions (exotic cluster structure is not assumed a priori).
Appearance of cluster structure as results of studies using such general models give us more confidence for their existence.
Many people started analyzing cluster states
with mean field models including our chairman

22. A. S. Umar, J. A. Maruhn, N. Itagaki, and V. E. Oberacker Phys. Rev
A. S. Umar, J. A. Maruhn, N. Itagaki, and V. E. Oberacker Phys. Rev. Lett. 104, (2010).

23. Lifetime of linear chain
as a function of
impact parameter
A. S. Umar, J. A. Maruhn, N. Itagaki, and V. E. Oberacker Phys. Rev. Lett. 104, (2010).

24. 20C alpha chain states , Ex ~ 15 MeV region Skyrme Hartree-Fock calculation
SkI3
SkI4
Sly6
SkM*
J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura, Nucl. Phys. A 833 (2010).

25. J. A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura, Nucl. Phys
J.A. Maruhn, N. Loebl, N. Itagaki, and M. Kimura, Nucl. Phys. A 833 (2010).

26. Stability of 3 alpha linear chain with respect to the bending motion
Time Dependent Hartree-Fock calculation
Geometric shape is stabilized
by adding neutrons in (σ)2
16C (π)4
20C (π)4(δ)2(σ)2

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

28. 4 alpha linear chain in rotating frame
Pioneering work, but no spin-orbit, no path to bending motion

32. Linear chain configuration appears when angular momentum is given, however…..
Initial state is one-dimensional configuration
　 stability with respect to the bending motion 　　　
　　　was not discussed
Spin-orbit interaction was not included in the Hamiltonian

36. Cranked
Hartree-Fock
calculation

38. T. Ichikawa, J. A. Maruhn, N. Itagaki, and S. Ohkubo,
Phys. Rev. Lett. 107, (2011).

39. Coherent effect of adding neutrons and rotating the system
P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).
Exotic shape in extreme spin and isospin
Code – TAC
3D Cartesian harmonic oscillator basis
with N=12 major shells
Density functional DD-ME G. A. Lalazissis, T. Nikšić, D. Vretenar, and P. Ring Phys. Rev. C 71, (2005).

40. P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).

41. Rigid rotor J = I ω P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).

42. neutrons
P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett (2015).

43. valence neutrons P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).

44. protons
P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett (2015).

45. P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).

46. P. W. Zhao, N. Itagaki, and J. Meng,
Phys. Rev. Lett (2015).

48. Antisymmetrized Molecular Dynamics calculation
T. Baba, Y. Chiba, and M. Kimura, Phys. Rev. C 90, (2014)

49. Superposition of many Slater determinants – mean field model
Y. Fukuoka, S. Shinohara, Y. Funaki, T. Nakatsukasa, and K. Yabana,
Phys. Rev. C

50. Summary for this part
The stability of exotic cluster state can be studied with
mean field models as well as cluster models
Two mechanisms to stabilize the rod shape,
rotation (high spin) and adding neutrons (high Isospin)
coherently work in C isotopes
Coherent effects:
Rotation makes the valence neutron-orbit
in the deformation axis (σ-orbit) lower
Enhances the prolate deformation of protons (kinetic)
Pull down the proton orbits in one dimension (interaction)
In 15C-20C σ orbit(s) is occupied
as a lowest configuration of neutrons around 3 alpha linear chain
in the rotating frame