Shell model studyof p-shell hypernuclei 　 (12

Be)

杉本聡京都大学元場俊雄

大阪電通大山本安夫

都留文科大

Introduction Up to now, the experimental information are limited fo

r hyper nuclei as compared to hyper nuclei. Theoretically, a pioneer work was done by Dover and

Gal (Ann. Phys. 146 (1983)) using the existent data at that time.

V~-21~24MeV The experiments of (K-,K+) reaction were performed at

KEK (Fukuda et al. PRC 58 (1998)) and AGS (Khaustov et al. PRC 61 (2000))

U~-14MeV (Assuming a simple WS potential) At JPARC, the experiment of (K-,K+) reaction is planne

d to explore hypernuclei.

Purpose of our study To study the structure of hypernuclei using t

he shell model with effective interactions deduced from realistic NY interaction model.

To perform a reaction calculation with the wave function from the shell model to explore what can be obtained from the experimental data. DWIA for (K-,K+)

This method has been quite successfulin the study of hypernuclei!

ExperimentChrien et al., NPA 478 (1988)

From Hashimoto et al., PPNP 57

Shell model+DWIAItonaga et al.,PRC 49 (1994)

Woods-Saxon (K-P)+DWIAMotoba et al., PRC 38 (1988)

ExperimentHotchi et al., PRC 64 (2001)

12C(,K+)12C

Shell model calculation 12

Be (11B+-) (12C(K+,K-)12Be)

Active space for nucleons: p-shell is fixed to the 0s1/2 orbit. Effective interaction for nucleons: Cohen-Kurath Effective interaction for N-: YNG interaction by Yama

moto (G matrix, kF dependence) YN interaction model (VN- がががが )

ESC04d (Rijken and Yamamto PRC 73 044008 (2006)) NHC-D (Nagels et al. PRD 15 2547 (1977))

Non-central part is not included.

がCK YNG

NY N Y NYH H t v がが が がが

Single particle energy 12

Be

kF in YNG is determined by the condition BE(

)~4.5 MeV. Uis comparable to the experimental data.

U ~ 14MeV (Fukuda et al., Khaustov et al)

J T kF tY UY tY+UY E BE (Y)

ESC04d () 1-1 1 1.08 11.8 -16.1 -4.4 -57.4 4.5

NHC-D() 1-1 1 1.05 11.8 -15.3 -3.5 -57.4 4.5

NS97f() 1-1 1/2 1.24 10.5 -22.5 -11.9 -65.1 12.2

p-shell matrix element of YNG

forN-is larger than that for N- ESC04d gives quite large for ESC04d and NHC-D have opposite signs.

T Vb

Vb

N-ESC04d0 4.98 -15.81 -3.18

1 0.30 -2.96 -9.88

N-NHC-D0 2.14 4.75 2.23

1 1.55 0.79 0.51

N-NSC 1/2 1.05 0.04 0.04

~NYV V が

12Be(11B+)

The spectra for ESC04d and NHC-D show different behavior. The orders of the lowest two levels are different because of the

sign changes of spin-spin part between ESC04d and NHC-D. ESC04d: intermediate (strong) coupling NHC-D: weak coupling (at least in the T=0 channel)

-65

-60

-55

-50

-45

0-

3-2-

1-

2-

0-

1-

2-1-

3/2-1/2-

5/2-

12

B

T=1

T=1/2

11B

E (

MeV

)

12

Be

T=0 ESC04d

3/2-

0-

1-

2-

3-

-65

-60

-55

-50

-45

3-

2-

1-0-

1-

2-

2-

0-1-

2-3/2-

3/2-

1/2-

12

B

E (

MeV

)

12

Be

11B

T=1/2

T=1T=0

NHC-D

5/2-

1-

11B+

DWIA 計算 12C(K-,K+)12

Be 　 殻模型計算で得られた波動関数を用いて

DWIA 計算を行った。

(K-,K+) 反応 運動量移行が大きい（ ~500MeV/c@pK-

=1.6GeV/c) ので J-stretched の状態が強く励起される。

アイソスピン移行は 1

SMeff

( ) ( )( ; )

L L K p K

d dZ i f

d d

1

1 , 1[0 0 ]

J Tp s

T=1, 1- state in 12Be

12C(K-,K+)12Be 反応で強く励起されるの

は T=1,1- の状態。 ESC04d と NHC-D では波動関数の中身が

大きく違う。（相互作用の違いを反映）

11B+1.5MeV

4.5MeV

(13%,34%,49%)

(59%,39%,1%)

12Be

ESC04d

11B+1.5MeV

4.5MeV

(13%,86%,1%)

(86%,12%,2%)

12Be

NHC-D

(P(3/2-1s1/2),P(1/2-

1s1/2), P(3/2-2s1/2))

T=1/2

11C+

8.3MeV

10.7MeV(5%,95%,0%)

(94%,5%,0%)

4.4MeV(0%,0%,98%)

12C

NS97f

1.8MeV

GS

5.2MeV

11B or 11C

1st 3/2-

1st 1/2-

2nd 3/2-

Cohen-Kurath

Exicitation Function NHC-D

Smearing factor: 2MeV

11B+1.5MeV

4.5MeV

(13%,86%,1%)

(86%,12%,2%)

12Be

NHC-D

Excitation Function ESC04d11B+

1.5MeV

4.5MeV

(13%,34%,49%)

(59%,39%,1%)

12Be

ESC04d

Smearing factor: 2MeV

Excitation Function の比較

• 波動関数（ NY相互作用）の違いが励起関数に反映される。

ESC04d NHC-D

Woods-Saxon potential(Khaustov et al, PRC 61)

0s1/2

0p1/2

Summary 12

Be に対して N- ががががががが ESC04d と NHC-D に基づいたものを用いて殻模型計算を行った。

ESC04d と NHC-D とでは波動関数の中身が大きく違う。 殻模型波動関数を用いて 12C(K-,K+)12

Be 反応に対する励起関数を求めた。

励起関数は波動関数の違いを反映し ESC04d と NHC-D とで大きく異なる。→ N- 相互作用の情報を得られる可能性？

今後の課題 p→ ががががが がががががががが p がが がががががががががががが

fss2 etc.