Ξハイパー核の殻模型の研究

Shell model study
of p-shell X hypernuclei (12XBe)
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
for X hyper nuclei as compared to L hyper nuclei.
Theoretically, a pioneer work was done by Dover and
Gal (Ann. Phys. 146 (1983)) using the existent data
at that time.


The experiments of (K-,K+) reaction were performed
at KEK (Fukuda et al. PRC 58 (1998)) and AGS
(Khaustov et al. PRC 61 (2000))


VX~-21~24MeV
UX~-14MeV (Assuming a simple WS potential)
At JPARC, the experiment of (K-,K+) reaction is
planned to explore X hypernuclei.
Purpose of our study


To study the structure of X hypernuclei using
the 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 successful
in the study of L hypernuclei!
Experiment
Hotchi et al., PRC 64 (2001)
12C(p+,K+)12 C
L
Experiment
Chrien et al., NPA 478 (1988)
Shell model
+DWIA
Itonaga et al.,
PRC 49 (1994)
Woods-Saxon (K-P)+DWIA
From Hashimoto et al., PPNP 57
Motoba et al., PRC 38 (1988)
Shell model calculation
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
(11B+X-) (12C(K+,K-)12XBe)
Active space for nucleons: p-shell
X is fixed to the 0s1/2 orbit.
Effective interaction for nucleons: Cohen-Kurath
Effective interaction for N-X: YNG interaction by
Yamamoto (G matrix, kF dependence)
12

XBe
YN interaction model (VN-Xが引力的)



ESC04d (Rijken and Yamamto PRC 73 044008 (2006))
NHC-D (Nagels et al. PRD 15 2547 (1977))
Non-central part is not included.
H NY  H N + tY + vNY
CK
YNG
Single particle energy
12 Be
X
ESC04d (X)
Jp T kF
1-1 1 1.08
tY
UY tY+UY
E BE (Y)
11.8 -16.1
-4.4 -57.4
4.5
NHC-D(X)
NS97f(L)
1-1 1 1.05
1-1 1/2 1.24
11.8 -15.3
10.5 -22.5


-3.5 -57.4
-11.9 -65.1
4.5
12.2
kF in YNG is determined by the condition
BE(X,1-1)~4.5 MeV.
UX is comparable to the experimental data.
UX ~ 14MeV (Fukuda et al., Khaustov et al)
p-shell matrix element of YNG
N-X ESC04d
N-X NHC-D
N-L NSC
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

T
0
1
h
Vb D(ss) (D/Vb)
4.98 -15.81 -3.18
0.30 -2.96 -9.88
0
1
1/2
2.14
1.55
1.05
4.75
0.79
0.04
VNY ~ -V + Ds s
2.23
0.51
0.04
D for N-X is larger than that for N-L.
ESC04d gives quite large D.
D for ESC04d and NHC-D have opposite signs.
12 Be(11B+X)
X
3/25/21/23/2-
E (MeV)
-50
2-55
30-60
121-65
12
B
X
B
3/2-
12
Be
X




12
23-
02-
T=1/2
0-
T=1
T=0
11
-45
31-
12-
ESC04d
-50
E (MeV)
11
-45
B
X
10-
12-
12
5/2-
X
1/2-
Be
2-
3/201-
T=1/2
-55
-60
B
T=0
T=1
11B+X
21-
-65
NHC-D
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)
DWIA計算

12C(K-,K+)12 Be
X
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。
 ds ( ) 
ds ( )
SM
 
Z
eff (i  f ; )

d L
 d  L  K - p X- K +

(K-,K+)反応
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
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
-1
[0 p X0s]J p 1- ,T 1
T=1, 1- state in
Cohen-Kurath
11B or 11C
12 Be
X 2nd 3/2-
5.2MeV
T=1/2
12
X Be
1.5MeV
11B+X
(13%,34%,49%)
4.5MeV (59%,39%,1%)
12 Be
X
1.5MeV
4.5MeV
1st 1/211B+X
1st 3/2-
GS
11C+L
(13%,86%,1%)
(86%,12%,2%)
NHC-D
ESC04d
(P(3/2-1Xs1/2),P(1/2-1Xs1/2), P(3/2-2Xs1/2))
 12C(K-,K+)12XBe反応で強く励起される

1.8MeV
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）
4.4MeV
8.3MeV
(0%,0%,98%)
(5%,95%,0%)
10.7MeV
(94%,5%,0%)
12
LC
NS97f
Exicitation Function NHC-D
12 Be
X
1.5MeV
11B+X
(13%,86%,1%)
Smearing factor: 2MeV
4.5MeV
(86%,12%,2%)
NHC-D
Excitation Function ESC04d
12
XBe
1.5MeV
11B+X
(13%,34%,49%)
4.5MeV (59%,39%,1%)
ESC04d
Smearing factor: 2MeV
Excitation Functionの比較
ESC04d
X0p1/2
X0s1/2
NHC-D
• 波動関数（NY
Woods-Saxon potential
相互作用）の違
(Khaustov et al, PRC 61)
いが励起関数
に反映される。
Summary

ESC04dとNHC-Dに基
づいたものを用いて殻模型計算を行った。
12
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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+)12XBe反応に対する
励起関数を求めた。
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XBeに対してN-X相互作用として
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-X相互作用の情報を得られる可能性？
今後の課題
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Xp→LLに対する幅
連続状態の影響（p状態)
他のN-X相互作用を用いた計算

fss2 etc.

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