1. Cluster Phenomena in Stable and Unstable Nuclei Cluster Phenomena in Stable and Unstable Nuclei Y. Kanada-En’yo (Kyoto Univ.) Collaborators: Y. Hidaka(RIKEN), T. Ichikawa(YITP), Y. Hidaka(RIKEN), T. Ichikawa(YITP), M. Kimura(Hokkaido), F. Kobayashi(Kyoto), M. Kimura(Hokkaido), F. Kobayashi(Kyoto), T. Suhara (Matsue),Y. Taniguchi(NIMS), Y. Yoshida (Kyoto) T. Suhara (Matsue),Y. Taniguchi(NIMS), Y. Yoshida (Kyoto)

2. 1.Introduction

3. Cluster structures in stable and unstable nuclei Typical cluster structures known in stable nuclei 8 Be 12 C 20 Ne  +  33 16 O +  16 O* 12 C +  7 Li  + t  -cluster 40 Ca*, 28 Si*, 32 S* 36 Ar- , 24 Mg- , 28 Si-  Si-Si, Si-C, O-C, O-O Molecular orbital Be, C, O, Ne, F  -cluster excitation 14 C* 3  linear chain Unstable nuclei Heavier nuclei 

4. Cluster & Mean field Mean field, shell structure Independent single-particle v.s. Cluster: Many-body correlation Independent particle in MF Developed cluster Cluster excitation Shell structure ・ MF Cluster Cluster formation many-body correlation g.s. correlation excited states no correlation

5. Cluster structures 12 C Nucleon liquid 0 MeV 100 MeV Nucleon gas Energy 10 MeV 00 Shell & cluster corr. low density cluster excitation +  0 /3~  0 /5 Cluster gas, crystal high density Nuclear structure Cluster enhancement

6. Cluster phenomena in low density Heavy Ion collision Liquid-gas phase Multi fragmentation AMD cal.: 129 Xe+Sn E/A 50 MeV by A. Ono PRC66 (2002) QMD cal. by Watanabe PRL109 (2009) Supernova, Neutron star crust Nuclear pasta

7. Cluster structures in n-rich nuclei Molecular orbital n-rich Be, F, Ne  -cluster excitation n-rich C linear chain gs cluster correlation cluster weakening/ melting Clustering in deformed Neutron density in C* n-skin suppression large deformation breaking of magic number N=8, N=20 stable nuclei n-rich nuclei cluster gas

8. 16 O Roles of excess neutrons in cluster structures of n-rich nuclei Ne, F, O isotopes  Seya, Von Oerzten, Descouvemont et al., Itagaki et al., Dote et al., K-E et al. Arai et al., M. Ito et al. Be isotopes    Molecular Orbital: bonded clusters Atomic: Cluster resonance 10 Be shell model-like  16 O  6 He+He 18 O+  Strong coupling Weak coupling Normal states Scholz et al., Rogachev et al., Goldberg et al., Ashwood et al., Yildiz et al., Descouvemont, Kimura, Soic et al., Freer et al., Saito et al., Curtis et al., Milin et al., Bohlen et al.,

9. MO bond and Cluster res. in 22 Ne 16 O   MO-bond Cluster res. 22 Ne 18 O+  AMD study by Kimura, PRC75 (2007) Exp Scholz et al., Rogachev et al., Goldberg et al.,Ashwood et al., Yildiz et al., Theor: Descouvemont, Kimura, EXP AMD

10. MO structures in F isotopes  MO bond with 15 N +  core AMD study by Kimura et al., PRC83 (2011) 0h0h 2h2h 3h3h 1h1h play an important role in lowering intruder states in N~20 region also in Ne isotopes 19-29 F 21 F 23 F 25 F 27 F 29 F 19 F 3h3h 2h2h

11.  -cluster states in n-rich nuclei  Cluster resonances 6,8 He+  in Be 10 Be+  in 14 C 14 C+  in 18 O 18 O+  in 22 Ne Ex = several ~ 20 MeV New states discovered and suggested at -> information of nucleus-nucleus potential and valence neutron effects there. Theor: Seya, von Oerzten, Descouvemont et al.,Itagaki et al., K-E et al. Arai et al., M. Ito et al. Exp: Soic et al., Freer et al., Saito et al., Curtis et al., Milin et al., Bohlen et al., in  -decay,  -transfer,  -scattering Exp Scholz ‘72, Rogachev ‘01, Goldberg ‘04, Ashwood ‘06, Yildiz et al., Theor: Descouvemont ’88, Kimura ‘07 Exp Scholz et al., Rogachev et al., Goldberg et al.,Ashwood et al., Yildiz et al., Theor: Descouvemont, Kimura, Exp Soic 04, von Oertzen ‘04, Price 07, Haigh 08, Theor: Suhara ‘10

12. Rich cluster phenomena in nuclear systems Cluster formation/breaking in low-lying states Cluster excitation and resonances Molecular Bond in neutron-rich nuclei Many clusters : cluster gas, chain New types of cluster as functions of proton&neutron numbers and excitation energy 6,8 He+He in Be, 10 Be+  in 14 C, 14 C+  in 18 O, 18 O+  in 22 Ne A theoretical method: AMD (antisymmetrized molecular dynamics)

13. An approach for nuclear structure to study cluster and mean-field aspects cluster and mean-field aspects Stable and unstable nuclei Stable and unstable nuclei Ground and excited states Ground and excited states 2. A theoretical model: AMD

14. Effective nuclear force phenomenological) Energy Variation AMD wave fn. spatial isospin Intrinsic spins Slater det. Gaussian det Gaussian wave packet AMD method for structure study Similar to FMD wave fn. A variety of cluster st. Shell-model like st.

15. 3. Some topics of cluster phenomena

16. 3-1. MO bond in n-rich Be & vanishing of magic number & vanishing of magic number 3-2. Cluster resonances 3-3. Linear chain in n-rich C

17. 3-1. MO bond in n-rich Be & vanishing of magic number & vanishing of magic number 3-2. Cluster resonances 3-3. Linear chain in n-rich C

18. Cluster structures in neutron-rich Be 0 1 + Exp: Milin et al. ’05, Freer et al. ’06 10 Be: energy levels J(J+1) 0+ 2+ 4+ 2+ 4+ 10 Be 6 He+ 4 He Ito et al. Kobayashi et al. Kuchera et al. MeV AMD exp cluster res. MO bond Normal 0 2 + 0 3 + AMD calc. Y. K-E, et al. PRC (98)

19. + - + - +  -orbital αα αα ±  -orbital Molecular orbital(MO) structure in Be MO state Normal state 2  -core formation MO formation Level inversion in 11,12,13 Be Gain kinetic energy in developed 2α system vanishing of magic number in 11 Be, 12 Be, 13 Be MO formation Seya PTP65(81), von Oertzen ZPA354(96) N. Itagaki PRC61(00), Y. K-E.. Ito PLB588(04)

20. n-rich Energy 0 1 + 0 2 + 10 Be 12 Be, 11,13 Be Vanishing of N=8 magic number in neutron-rich Be 0 1 + 0 2 + Normal state Normal 0h  MO bond  deformation in 12 Be(gs) Intruder 2h  Y.K-E.PRC (03),(12), Ito PRL(08) Dufour NPA(10) 12 Be g.s. 0+ 13 Be g.s. 1/2-     Inelastic scat. life time: Iwasaki PLB481(00), Imai PLB673(09) Inversion Kondo et al. PLB690 (10)  abnormal parity of 13 Be(gs) B(GT) with charge ex.: Meharchand PRL108 (12)  intruder config. in 12 Be(gs)  12 Be(0 2 + ) with p-shell config. 1n-knockout reac.: Navin PRL85(00), Pain PRL96(06) Fortune PRC(06), Blanchon PRC(10) Shimoura PLB654 (07)

21. Breaking of magic number in 13 Be 12 Be+n Er (MeV) 0 1 2 2.0 (5/2+) (1/2-) 3.04 Simon07 1/2+ virtual st. Kondo10 (1/2-) 0.51 2.39 (5/2+) 1/2- ? 13 Be: unbound 13 Be spectra measured by 1n knock-out reactions at GSI(Simon et al. 2007) and RIKEN(Kondo et al.,2010) 13 Be p 1/2 s 1/2 p 3/2 d 5/2 s 1/2 1/2- is lowest in 13 Be intruder EXP. AMD calc. Y. K-E. PRC(12) Kondo10 Simon07 AMD 12 Be+n

22. 3-1. MO bond in n-rich Be & vanishing of magic number & vanishing of magic number 3-2. Cluster resonances 3-3. Linear chain in n-rich C

23.  0+20+2 K=0 + 1  0 + 3,4? 6 He+ 4 He Kuchera et al. Ito et al. Kobayashi et al.  Normal MO bond Exotic cluster res. also suggested    0 3 + 6,8 He+ 6,4 He 0+20+2 0+10+1 Freer PRL.82(99)(06) Saito NPA738 (04) Yang PRL112 (14 ）    t t 6 He+ 3 H MO bond ? Cluster res. ? 9 Li 10 Be 12 Be Cluster resonances 8 He+ 6 He in 14 Be 9 Li+ 6 He in 15 B  Ito et al. Y. K-E et al.

24.  t  t 6 He+ 3 H resonance 9 Li(3/2 3 - ) 9 Li(gs) 6 He+ 3 H cluster resonances in 9 Li 9 Li: energy levels(calculation) 1/2- 3/2- 5/2- 7/2- 6 He+ 3 H threshold 3/2- g.s. J(J+1) 9 Li MeV K=1/2- band Y. K-E. et al PRC.85(12)

25.   MO bond  t  t 6 He NO MO bond   10 Be 9 Li t decoupling K=0 + 2   K=0 + 1  t 3/2 - 1 K=0 + 3,4? g.s(3/2 - 1 ) K=1/2 - (3/2 - 3 )   t Cluster resonances 6 He Cluster structures in 10 Be and 9 Li

26. 3-1. MO bond in n-rich Be & vanishing of magic number & vanishing of magic number 3-2. Cluster resonances 3-3. Linear chain in n-rich C

27. Linear chain state in 14 C* 14 C AMD by T.Suhara and Y.K-E, Phys.Rev.C82:044301,2010. 3  linear chain protonneutron Neutron-rich 14 C Energy (Mev) 14,16 C Linear chain? von Oertzen ZPA354(96) EPJA21(04),PR 432(06) Itagaki PRC64(01) Suhara PRC82(10) Maruhn NPA833(10) 12 C g.s. 14 C g.s. + 12 C* not linear 12 C 14 C*, 16 C* 0202 + 0303 + Y.K-E.et al., T. Neff et al. Tohsaki et al., Funaki et al.

28. Linear chain in n-rich C Stretching effect in rotation 15 C*(19/2-)  =0.78 suggested to be a yrast state 11 Be+  Largely deformed 11 Be with MO-bond AMD by Y.K-E, PR432(2006) Meta stable for bending motion MO model for 14,16 C Itagaki et al. PRC64(01) HF calc. for 16,20 C by Maruhn et al. NPA833(10)

29. 4. Summary

30. Summary Rich cluster phenomena in n-rich nuclei  MO bond & breaking of N=8 shell  Cluster resonances  Linear chain Cluster formation, development, and valence neutrons play important roles in nuclear structure. Ikeda et al.PTP464-S (1968) Extended Ikeda diagram? by von Oertzen et al Taken from Phys. Report 432 (2006)

31. Many-body correlations at low density  -cond. in low density 12 C(0 2 ) + 16 O* Dilute  - cluster gas BEC-BCS BCS Unbound α α α Neutron matter Nuclear matter Dineutron at surface of neutron-rich nuclei Itagaki et al., Von Oertzen et al. α α α 14-20 C* α α α Price et al. Geometric （ crystal ？） Matsuo et al. PRC73 044309 (‘06) Cluster gas, chain ? Dineutron correlation ? Information of many-body correlations in low density, in isospin asymmetric systems.

32. Excitation energy multidimension * proton number * neutron number * excitation energy * density Neutron number proton number Low density Systematic study in a wide region