1. Hiroshi MASUI Kitami Institute of Technology Collaborators:K. KatoHokkaido Univ. K. IkedaRIKEN 22-26 Aug. 2011, APFB2011, Sungkyunkwan Univ., Seoul, Korea

2. Matter radius of nuclei near the drip-lines An “abrupt” change of the radius due to the weakly bound neutron or proton A. Ozawa 2001

3. Difference from typical halo nuclei: 6 He, 11 Be, 11 Li Core + Xn Core+n (+2n) Large S n values of 23 O and 24 O ( 2.7MeV and 3.7MeV ) 6 He : 0.98MeV 11 Li : 0.38MeV 11 Be: 0.50MeV 23 O : 2.7MeV 24 O : 3.7MeV Weakly-bound neutrons Strongly-bound neutrons 22 O SnSn SnSn

4. To reproduce the drip-line at 24 O  ab initio calc. + Realistic force  Effect of the thee-body interaction T. Otsuka et al, Phys. Rev. Lett. 105, 032501 (2010) G. Hagen et al., Phys. Rev. C 80, 021306(R) (2009)

5. Ab initio calc. + Realistic force G. Hagen et al., Phys. Rev. C 80, 021306(R) (2009) Coupled-cluster (2-body) + N3LO int.  -dependence: lack of many-body int.

6. Effect of the three-body interaction T. Otsuka et al, Phys. Rev. Lett. 105, 032501 (2010) 3-body int. Pauli-forbidden state Getting weakerfor more valence particle system

7. T. Otsuka et al, Phys. Rev. Lett. 105, 032501 (2010) Getting weakeras the number of valence particles increases

8. How about the radius? h  ~ 27 MeV b ~ 1.24 (fm) Very small radius G. Hagen et al., Phys. Rev. C 80, 021306(R) (2009) Coupled-cluster (2-body) + N3LO int.

9. Our approaches  Role of many valence neutrons 16 O+Xn model m-scheme COSM + Gaussian basis  Role of last one- or two-neutrons “Core” + n or “Core”+2n model A simplified model approach

10. M-Scheme COSM + Gaussian base H. Masui, K. Kato and K. Ikeda, Euro. Phys. Jour. A42 (2009) 535 Core ( 16 O) +Xn model space Gaussian radial function Stochastic approach for the basis set M-scheme approach

11. M-Scheme COSM approach Wave function for the valence nucleons: Radial part Product of Gaussian Spin-isospin part Total M and M T are fixed Coordinate system We check the expectation value of the total J as H. Masui, K. Kato and K. Ikeda, Euro. Phys. Jour. A42 (2009) 535

12. Expectation value of J 2 J=0 J=1/2 J=5/2 J=3/2

13. B=H=0.25 B=H=0.07 S n for O-isotopes NN-int.: Volkov No.2 (M=0.58)

14. Change the coresize with A 1/6 B=H=0.07 B=H=0.25 b: 1.723 (fm) b~A 1/6

15. Comparison with other approaches [3] G. Hagen et al., PRC 80 (2009) [2] B. Ab-Ibrahim et al., JPSJ 78 (2009) [1] H. Nakada, NPA764 (2006) □: [2] ■: [1] △: [3]+0.5(fm) ▲: [3] ○: fixed-b ●: m-COSM with b〜A 1/6

16. Result of M-scheme COSM ( 16 O+Xn model space) From 18 O to 22 O For 23 O and 24 O 16 O-core with a fixed size + valence neutrons 16 O-core with A 1/6 (Mean-field-like) +valence neutrons How large? (is the amount of the change of the radius)

17. Core+2n model We adjust the core radius and energy of the core+nsystem ⇒ calculate the core+2n system Core Core+n Core+2n Fit R rms E E (Core-n int.) (n-n int) R rms Calc. 16 O 17 O ( 16 O+n) 18 O ( 16 O+2n) 18 O 19 O ( 18 O+n) 20 O ( 18 O+2n) 20 O 21 O ( 20 O+n) 22 O ( 20 O+2n) 22 O 23 O ( 22 O+n) 24 O ( 22 O+2n)

18. Results for the core+2n model We define the difference between the calculated and experimental radii as

19. 20 O 21 O 22 O Difference of the radius between Calc. and Exp. 16 O- 17 O- 18 O, 18 O- 19 O- 20 O, 20 O- 21 O- 22 O

20. 22 O 23 O 24 O Difference of the radius between Calc. and Exp. 22 O- 23 O- 24 O

21. 22 O 23 O 24 O 0.238 (fm) A schematic figure to illustrate the change of the radius of 22 O R rms [1] 2.88±0.063.20±0.043.19±0.13 [1] A. Ozawa et al, NPA693 (2001)

22. Expansion of the core Matter radius

23. Summary We studied the energy and radius of oxygen isotopes with M-Scheme COSM and Core+2n model 1. Mean-field-like configuration with b~A 1/6 2. Shrunk core size configuration until 22 O H.O. : 0p-0h configuration Shrunk b⇒ High mom. ⇒ TOSM It is suggested that a coupled-channel model is necessary to be introduced The size of 22 O is drastically changed when a neutron is added ( 23 O)

24. Inclusion of the core excitation TOSM in 9 Li T. Myo, K. Kato, H. Toki and K. Ikeda, PRC76(2007) 2. Some config. are suppressed due to the Pauli-blocking 1. Different size for each orbit