Hiroshi MASUI

Kitami Institute of Technology

Collaborators: K. Kato Hokkaido Univ.K. Ikeda RIKEN

22-26 Aug. 2011, APFB2011, Sungkyunkwan Univ., Seoul, Korea

Matter radius of nuclei near the drip-linesAn “abrupt” change of the radius due to the

weakly bound neutron or proton

A. Ozawa 2001

Difference from typical halo nuclei: 6He, 11Be, 11Li

Core + XnCore+n (+2n)

Large Sn values of 23O and 24O ( 2.7MeV and 3.7MeV )

6He : 0.98MeV11Li : 0.38MeV11Be: 0.50MeV

23O : 2.7MeV24O : 3.7MeV

Weakly-bound neutrons Strongly-bound neutrons

22O

Sn Sn

To reproduce the drip-line at 24O

ab initio calc. + Realistic force

Effect of the thee-body interactionT. Otsuka et al, Phys. Rev. Lett. 105, 032501 (2010)

G. Hagen et al., Phys. Rev. C 80, 021306(R) (2009)

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.

Effect of the three-body interactionT. Otsuka et al, Phys. Rev. Lett. 105, 032501 (2010)

3-body int.

Pauli-forbidden state

Getting weakerfor more valence particle system

T. Otsuka et al, Phys. Rev. Lett. 105, 032501 (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, 021306(R) (2009)

Coupled-cluster (2-body) + N3LO int.

Our approaches

Role of many valence neutrons16O+Xn model m-scheme COSM + Gaussian basis

Role of last one- or two-neutrons “Core” + n or “Core”+2n modelA simplified model approach

M-Scheme COSM + Gaussian base H. Masui, K. Kato and K. Ikeda, Euro. Phys. Jour. A42 (2009) 535

•Core (16O) +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 MT are fixed

Coordinate system

We check the expectation value of the total J as <J2>

H. Masui, K. Kato and K. Ikeda, Euro. Phys. Jour. A42 (2009) 535

Expectation value of J2

J=0J=1/2

J=5/2

J=3/2

B=H=0.25

B=H=0.07

B=H=0.07

Sn for O-isotopes

NN-int.: Volkov No.2 (M=0.58)

Change the coresize with A1/6

B=H=0.07

B=H=0.25

b: 1.723 (fm)

b~A1/6

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 〜 A1/6

Result of M-scheme COSM (16O+Xn model space)

•From 18O to 22O

•For23O and24O

16O-core with a fixed size + valence neutrons

16O-core with A1/6 (Mean-field-like) +valence neutrons

How large?(is the amount of the change of the radius)

Core+2n modelWe adjust the core radius and energy of the core+nsystem⇒ calculate the core+2n system

Core

Core+n

Core+2n

Fit

Rrms

E

E

(Core-n int.)

(n-n int)

Rrms

Rrms

Calc.

16O

17O (16O+n)

18O (16O+2n)

18O

19O (18O+n)

20O (18O+2n)

20O

21O (20O+n)

22O (20O+2n)

22O

23O (22O+n)

24O (22O+2n)

Results for the core+2n model

We define the difference between the calculated and experimental radii as

20O 21O

22O

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

22O 23O 24O

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

22O 23O 24O

0.238 (fm)

A schematic figure to illustrate the change of the radius of 22O

Rrms[1] 2.88±0.06 3.20±0.04 3.19±0.13

[1] A. Ozawa et al, NPA693 (2001)

Expansion of the core

Matter radius

SummaryWe studied the energy and radius of oxygen isotopeswith M-Scheme COSM and Core+2n model

1. Mean-field-like configuration with b~A1/6

2. Shrunk core size configuration until 22O

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 22O is drastically changed when a neutron is added (23O)

Inclusion of the core excitation

TOSM in 9Li 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