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

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

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

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

[ ] [ ] [ ] 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

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.

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

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

N. Itagaki, S. Okabe, K. Ikeda, and I. Tanihata Phys. Rev. C 64 014301 (2001).

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 64 014301 (2001).

Stabilization of “geometric shape” by adding valence neutrons N. Itagaki, T. Otsuka, K. Ikeda, and S. Okabe, Phys. Rev. Lett. 92, 142501 (2004).

N. Itagaki, T. Otsuka, K. Ikeda, and S. Okabe, Phys. Rev. Lett. 92, 142501 (2004).

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

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, 212503 (2010).

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, 212503 (2010).

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).

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).

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

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

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

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

Cranked Hartree-Fock calculation

T. Ichikawa, J. A. Maruhn, N. Itagaki, and S. Ohkubo, Phys. Rev. Lett. 107, 112501 (2011).

Coherent effect of adding neutrons and rotating the system P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015). Exotic shape in extreme spin and isospin Code – TAC 3D Cartesian harmonic oscillator basis with N=12 major shells Density functional DD-ME2 G. A. Lalazissis, T. Nikšić, D. Vretenar, and P. Ring Phys. Rev. C 71, 024312 (2005).

P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

Rigid rotor J = I ω P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

neutrons P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

valence neutrons P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

protons P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

P. W. Zhao, N. Itagaki, and J. Meng, Phys. Rev. Lett. 115 022501 (2015).

Antisymmetrized Molecular Dynamics calculation T. Baba, Y. Chiba, and M. Kimura, Phys. Rev. C 90, 064319 (2014)

Superposition of many Slater determinants – mean field model Y. Fukuoka, S. Shinohara, Y. Funaki, T. Nakatsukasa, and K. Yabana, Phys. Rev. C 88 014321

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