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

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

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

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, (2010) G. Hagen et al., Phys. Rev. C 80, (R) (2009)

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

Expansion of the core Matter radius

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)

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