Harada, Toru Osaka - - PowerPoint PPT Presentation

SLIDE 1

特定領域研究「ストレンジネスで探るクォーク多体系」理論班主催 「ストレンジクォークを含むクォーク多体系分野の理論的将来を考える」研究会 2009年2月27-28日, 熱海市

ハイパー核反応の今後

原田 融

Harada, Toru 大阪電気通信大学

Osaka Electro-Communication University Neyagawa 572-8530, Osaka, Japan harada@isc.osakac.ac.jp

SLIDE 2

• これまでにどういう新しい物理を明らか

にしてきたか？

・生成のメカニズムとDWIA計算の改良 ・nucleus potentialの性質

原子 v.s.(反応 ・中性子過剰ハイパー核生成 シグマ混合率

• 今後、どういう新しい展開が期待できる

のか？

・２重荷電交換反応によるハイパー核生成！

• J-PAＲCに対して、どういう実験を提

案していくのか？

SLIDE 3

Momentum transfer to -hyperons

pF

～270 MeV/c

q MeV/c

1.20 GeV/c

N→

0.6 GeV/c

n→ n→ n→

Stopped

q  MeV/c q MeV/c

spin-stretched states substitutional states

SLIDE 4

Hypernuclear Production Reactions

・反応の特徴を生かす ・状態を選択的に励起

(K,)

720 MeV/c

(,K)

1040 MeV/c

q～300MeV/c q～350MeV/c q～60MeV/c

1 max

[ ]

N J J

j j

    1

[( ) ( ) ]

N J

n j n j

 

 

 

“Spin-Stretched’’ “Substitutional” H.Bando, T.Motoba, J.Zofka, Int.J.Mod.Phys. A5(1990)4021

neutron Lambda

1s 1p 1d 2s 1f d f7/2

3/2 n



+ +

(,K) reactions

by R.Hausmann and W.Weise

(K,)

Stooped K-

SLIDE 5

Distorted wave impulse approximation （DWIA)

Elementary cross sections (Fermi-averaging)

Double-Differential Cross Sections

( )* ( ) 2

( , ) | | | | ( )

K K f

S f U i E E

 

    

    

    



q

Meson distorted-wave functions (Eikonal approximation )

Strength function

2

( , )

n K

d d S dE d d

 

   

 

 

         q

( )* ( ) ( )

ˆ ( ) ( ) 4 (2 1) ( ) ( )

L K LM LM L

L i j r Y



  

    

 



r r r 

' ( ) ( ) ( ) 2 ' '

2 1 ( ) ( ) 4 (2 ' 1) ( ; ) ( ; ) 2 1

l l L LM l l K ll

l j r l j k r j k r L





    

    



  

* '

ˆ ( 0 ' | )( 0 '0| 0) (k )

l M K

l l M LM l l L Y

観測/測定

素過程 π+ + “n” → K+ + 







n

Y

p 

K

p 

p





入射粒子 標的核 核内核子 （陽子・中性子）

（+, K+)

放出粒子

SLIDE 6

Optimal Fermi-averaging for the ++n → K++ t-matrix in -hypernuclear production from (+, K+) reactions

T.H and Y.Hirabayashi, NPA744(2004)323

SLIDE 7

=206 MeV

(K,)

720 MeV/c

q～60MeV/c 14 MeV =245 MeV

C.B. Dover et al., PRC22 (1980) 2073.

(,K)

1225 MeV/c

q～300MeV/c 73 MeV

Quasi-free production spectrum

R.H.Dalitz, A.Gal, PL64B(1976)154

2 2

( )(1 ) ( ) 4 2

F N N N

k q M M U U M M M 

   

     

F F

k q k q M M   

 

   

Fermi gas model

peak position

elem

( , )

L L

d d R d dE d              

width

270 MeV /c －58 MeV －28 MeV 174 MeV 30 MeV (K-,): 2 MeV (,K+,): 56 MeV (K-,): 14 MeV (,K+,): 73 MeV

SLIDE 8

(+,K+)反応による-QF生成

 spectrum by reaction at 1.20, 1.05GeV/c

12C

P.K.Saha et al., KEK-E438, E521

1.20GeV/c 1.05GeV/c

q～380 MeV/c q～400 MeV/c

peak width (MeV) (MeV) ～～

1.20GeV/c 1.20GeV/c

～～

1.05GeV/c 1.05GeV/c

 

SLIDE 9

Elementary cross sections of →‐ reactions

T.O.Binford, et al. PR183(1969)1134

(b/sr)

1000 1200 1400 1600 1800 200 400 600 800

 momentum (MeV/c)

LAB

d d        



1050 1200

p→

1200

p→

N(1650)S11 N(1675)D15 N(1710)P11 N(1720)P13

K+ K+ K+ K+

SLIDE 10

Optimal Fermi-averaging for an elementary t-matrix

• pt

2

• pt

2

ˆ ( ; , ) (2 )

K K p K

k E d t p d v

  

  

 

 

        q

+ +



N

p 

K

p 

p





• T. Harada and Y.Hirabayashi, NPA744 (2004) 323.

“Optimal” cross section Optimal Fermi-averaged t-Matrix

*

2

• pt

2

ˆ sin ( ; , ) ( ) ˆ ( ; , ) sin ( )

Lab N N

N N N N N N N N

d p dp t E p p p t p d p dp p

    

      

  

 

  

p p

q

On-shell T-matrix

* 2 * 2 f i

( )

N N N

E E m m 



       p q p

* N K  

   p p p p

“On-energy-shell’’ equation

given given

S,A.Gurvitz, PRC33(1986)422: Optimal factorization

SLIDE 11

1.20GeV/c 1.05GeV/c

Optimal cross section of the ++n→K++ reaction in nuclei

• pt

2

• pt

2

ˆ ( , ) (2 )

K K p K

k E d t E d v

 

  

 

 

       

1.05 1.20 ++n→K++Cross Section



M(+n)

SLIDE 12

 spectrum by reaction at 1.2GeV/c

28Si

KEK-E438

  / d d   

1s(1/2)h 1p(3/2)h 1d(5/2)h 1p(1/2)h

S p d

The contribution of deep hole-states is important !

SLIDE 13

• The calculated spectra in QF region can

explain the experimental data at 1.20 and 1.05GeV/c.

• The  energy-dependence originates from

the nature of the “optimal Fermi-averaging” t-matrix.

1.20GeV/c 1.05GeV/c

Need careful consideration for energy-dependent

• f the elementary cross section.
• pt

2

( , )

n K

d d S dE d d

 

  

 

 

         q

-nucleus potential

well-known well-known

Strength function “Optimal Fermi-averaging” t-matrix

• pt

ˆ ( ; , ) t p

  q

make the width look narrow

CReactions

SLIDE 14

Is the -nucleus potential for  atoms consistent with the (, K+) data?

T.H and Y.Hirabayashi, NPA759(2005)143 T.H and Y.Hirabayashi, NPA767(2006)206

28Si 209Bi

Isospin dependence of -nucleus potentials for N > Z

SLIDE 15

• G. Backenstoss, et al., Z. Phys. A273(1975)137

C.J. Batty, et al.,Phys.Lett.B 74 (1978) 27 R.J. Powers, et al.,PRC47(1993)1263

RMF

Observation of  atomic X-ray

n=3 n=4 n=5 n=6 n=9 n=10 n=3 n=4 n=5 n=6 n=9 n=10

Shifts Widths

Only 23 measurements !!

C →u  →u Mg →u Al → u Si → u S → u Ca →u Ti →u Ba →u W → u Pb → u

SLIDE 16

DD RMF LDA-S3 WS-sh teff LDA-NF

Imag.

DD-A’ LDA-S3 WS-sh RMF LDA-NF teff ρ

DD RMF LDA-S3 WS-sh teff LDA-NF

Real

DD-A’ LDA-S3 WS-sh RMF LDA-NF teff ρ

‐-nucleus optical potentials in 27Al+‐

Real part Imag. part Real part

• Imag. part

(weak) attractive weak (< 10MeV)

Type I

repulsive strong (30-40MeV)

Type II

SLIDE 17

‐-nucleus potentials fitted to the ‐-atomic data

• J. Mares et al., NPA594(1995)311

C.J.Batty et al., Phys.Rep.287(1997)385

RMF

• J. Dabrowski, Acta Phys. Pol. B31(2001)2179

LDA-NF DD-A’ LDA-S3 WS-sh teff ρ

T.Yamada and Y.Yamamoto, PTP. Suppl. 117(1994)241 T.Harada, in: Proceedings of the 23nd INS Symp. 1995, p.211 C.J.Batty, E.Friedman, A.Gal, PTP. Suppl. 117(1994)227 R.S.Hayano, NPA478(1988)113c

1 1

( ) ( ) 2 4 1 ( ) ( ) (0) (0) r r U b B r b B r m

 

        



                                                 

Density-dependent (DD) potential Relativistic mean-field (RMF) potential Local density approximation (LDA) with YNG-NF

• D. Halderson, Phys. Rev. C40(1989)2173

Local density approximation (LDA) with SAP3 (simulates ND) Shallow Woods-Saxon potential:

teff ρ–type potential (B0=B1=0): Repulsive Attractive

p n

( ) ( ) ( ) r r r     

n p

( ) ( ) ( ) r r r     

   

(V0,W0)=(－10,－9) MeV a0=0.36+i0.20 fm

SLIDE 18

Strong-shifts and widths on ‐ atoms ‐28Si

28Si

SLIDE 19

‐原子のX線データは核のどの領域をみているのか？

DD-A’ teff ρ

核半径

C.J. Batty et al., Phys.Rep.287(1997)385

32S

• Cf. （stopped K-,+）

SLIDE 20

H.Noumi, et al. PRL89(2002)072301

(-,K+)反応による生成

標的： 28Si, 58Ni, 115In, 209Bi 原子核内部から粒子を生成

 spectrum by reaction at 1.2GeV/c

28Si

Woods-Saxon form

1 exp[( ) / ] V iW U r R a

  

   

1/3 0(

1) fm R r A  

0.67 fm a  1.1fm r  150 MeV V

 

15 MeV W  

+90 MeV

－40 MeV

(NEW) P.K.Saha, et al., PRC70(2004)044613

SLIDE 21

n 

“Optimal” elementary cross sections

Double-Differential Cross Sections

( )* ( ) 2

( , ) | | | | ( )

K K f

S f U i E E

 

    

    

    



q

Meson distorted-wave functions (Eikonal or Full optical model approximation ) Strength function

Strength function

f i

E E   

K 

  q p p

• pt

2

( , )

n K

d d S dE d d

 

  

 

 

        q

Distorted-wave Impulse Approximation (DWIA)

Calculations for Hypernuclear Production

' ( ) ( ) ( ) 2 ' '

2 1 ( ) ( ) 4 (2 ' 1) ( ; ) ( ; ) 2 1

l l L LM l l K ll

l j r l j k r j k r L





    

    



  

( )* ( ) ( )

ˆ ( ) ( ) 4 (2 1) ( ) ( )

L K LM LM L

L i j r Y



  

    

 



r r r 

* '

ˆ ( 0 ' | )( 0 '0| 0) (k )

l M K

l l M LM l l L Y 

SLIDE 22

“Optimal” cross section of ‐p→K+ reactions in nuclei

Ours

• pt

2

• pt

2

ˆ ( ; , ) (2 )

K K p K

k E d t p d v

  

  

  

 

        q

Standard

SLIDE 23

 spectrum by reaction at 1.2GeV/c

DD-A’ LDA-S3 WS-sh RMF LDA-NF teff ρ

T.Harada, Y.Hirabayashi, NPA759 (2005) 143

SLIDE 24

DD-A’ LDA-NF teff ρ LDA-S3 WS-sh RMF

28Si

reaction at 1.2GeV/c

T.Harada, Y.Hirabayashi, NPA759 (2005) 143



SLIDE 25

Comparison with resent studies

• J. Dabrowski, J. Rozynek, Acta. Phys.
• Pol. B35 (2004) 2303.
• J. Dabrowski, PRC60 (1999) 025205.

PWIA Analysis with the Square-Well potential

+20 +10

• 10
• 20

+40 +20

• 20

“The  s.p. potential is repulsive inside nucleus. Only NHC-F is acceptable.”

28Si 9Be

Chiral dynamics in the nuclear medium

UMeV repulsive W~ 21MeV

• M. Kohno, Y. Fujiwara, et al., nucl-th/0611080 (2006)

Semi-Classical Distorted Wave Model Analysis

“The repulsive  potential is not so strong as ~100MeV.”

Local Optimal Fermi-averaged t-matrix DWIA

• H. Maekawa, A.Ohnishi, et al., Eur.Phys.J.A33(2007)269.
• N. Kaiser, PRC71 (2005) 068201

SLIDE 26

T.H, A.Umeya, Y. Hirabayashi, PRC79(200)014603

Feasibility of extracting a  admixture probability in the neutron-rich hypernucleus

10 10Li



SLIDE 27

KEK-PS-E521

• P. K. Saha, et al., PRL94(2005)052502

Li Li

2.5 MeV FWHM

g.s. g.s.

Cross sections

L

d d   

11.3±1.9 nb/sr

• p=1.20 GeV/c

～1/1000 17.5±0.6 b/sr at 1.20 GeV/c

12 12

C( , ) C K  

 

• p=1.05 GeV/c

L

d d   

5.8±2.2 nb/sr

neutron-rich  hypernucleus

 spectrum by DCX reaction at 1.2GeV/c

10 10

B( , ) Li K  

 

First successful measurements

SLIDE 28

(－, K+) －Double Charge Exchange (DCX) Reaction ・One-step process: ・Two-step process:

p K    

0 p

K 



  p n  



 K p K n



 p K  

 

  p n



  

- coupling K+

p p p  n

-

p n 

K0

K p K n





p K    K+

p p p p   n

-

n 

Doorway

p K 

 

 

SLIDE 29

ˆ

X X

U U U U

 

      

U

(0) (0) (0)

ˆ ( ) G G 



 

        G

(0) (0)

ˆ ˆ ˆ ˆ ˆ ( ) ( ) ( ) ( )       G G G UG

Strength function

Green’s function method

Morimatsu, Yazaki, NPA483(1988)493

Coupled-channel Green’s function

( ) (0) ( ) ( ) (0) ( ) ,

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Im {Im } {Im } { }

Y T

G G G G W G



     

    

† † †

 escape  escape Spreading (nuclear-core breakup） = Complicated excited states

2

1 ˆ ( ) | | | | ( ) Im d d ( )G( ; , ) ( )

K f

S f O i E E F i F



               

  r r

r r r r

†

Green’s function

K+

p p p p   n

-

n 

T.Harada, NPA672(2000)181

Coupled-channel DWIA calculations

(0)† † (0) (0) p K p K p K p K

t G t t G U G U G t

   

               

                 

 

SLIDE 30

Model for calculations

10 9 9

Li Li Be  

 

    

2 2

1    

9Li+ 9Be+ 



68 MeV

3 2 T 

Single-particle shell model wf. Distorted waves for mesons

Eikonal distortion: ( ) / 2 20 mb,

K 

     

K 

   

Elementary cross section : d/d] Optimal Fermi-averaging ～10-20 b/sr (p=1.2GeV/c) Hyperon-nucleus potentials

,

( ) /(1 exp[( ) / ])

Y Y Y

U V iW r R a

   

  

Woods-Saxon form

0.6 fm a 

2/3

1.128 0.439 fm r A  

1/3 0(

1) fm R r A  

9 9

1 Li- Be- /(1 exp[( ) / ]) 3

X j X j

U v V r R a  

 

      



 

-coupling pot. spreading potential : energy-dependent = excited states 30 MeV for 

p K  

 

 

SLIDE 31

 spectrum by DCX reaction at 1.2GeV/c

W = 20-30 MeV は生成の解析と矛盾しない。

Spreading potential dep.

10B 11 MeV

X

U 

is fixed. P=0.57%

W=

p s

Li

SLIDE 32

P～0.4-0.6% (U ～10 MeV ) でスペクトルの一致が良い。

 spectrum by DCX reaction at 1.2GeV/c

Coherent - coupling dep.

20 MeV W



 

is fixed.

10B

0.075 %

s p

0.57% 0.68% 0.47% 0.30%

SLIDE 33

 spectrum by DCX stopped reaction

 Beでも混合が

と仮定した場合

10Be





data

SLIDE 34

Summary

ＤＣＸ (,K+)反応による中性子過剰ハイパー核の生成 スペクトルのＤＷＩＡ計算を行い、理論的考察を行った。

これまでの解析との矛盾しない。

・10B(,K+)10Liにおいて、One-step 過程: －p→ K+, p→n 反応による中性子過剰ハイパー核の生成メカニズムとその効果 を調べた。 W -MeV, Ux ～MeV, P ～1 % 未満 d/d] ～10-20 b/sr ・10B(,K+)10Liの実験データとの比較から、 One-step 過程によっ て実験スペクトルを説明できる可能性があることが分かった。

10 9 9

Li Li Be a b

 

    

・(,K+)反応は admixtureの割合などハイパー核の波動関数 の詳細な情報を得る可能性がある。

生成スペクトルは波動関数の性質に強く影響を受ける。

SLIDE 35

A.Umeya, T.H, PRC79(200)014603

- coupling effect in the neutron-rich hypernucleus in a microscopic shell-model calculation

10 10Li



SLIDE 36

“The 0+-1+ difference is not a measure of N spin-spin interaction.” by B.F. Gibson



 p p n 







 p p n 







 p p n 





+ +

 three-body force

4He 

• Y. Akaishi, T.Harada, S.Shinmura, Khin Swe Myint,

PRL84(2000)3539

Coherent coupling

1+

• 1.03

1+

• 1.04
• 1.04

0+

• 2.27

0+

D2

coh.Σ

9% 1. P 

1+

• 1.20

1+

• 1.21
• 1.52

0+

• 2.10

0+

SC97e(S)

coh.Σ

7% 0. P 

1+

• 0.68

1+

• 0.70
• 1.43

0+

• 2.18

0+

SC97f(S)

coh.Σ

9% 0. P 

• 0.68

1+

• 0.70

1+

• 0.97

0+

• 2.51

0+

SC89(S)

coh.Σ

0% 2. P 

Coherent coupling Coherent coupling Coherent coupling

Breuckner-Hartree-Fock

• R. Sinha, Q.N.Usmani,

NPA684(2001)586c (unit in MeV)

0.0

1+

• 1.24
• 2.39

0+

Exp.

1+

• 1.08
• 2.28

0+

VMC

4

( H)



6.20 V  0.38 0.86 spin-spin

NN force

ΛN ΛNN

V +V

phenomenological

SLIDE 37

- coupling effects on the ‐ spectrum

4He  4He 

without without ・couplingの効果はスペクトル の再現に重要 ・を経由したハイパー核生成

 production via production via 

17% per 

SLIDE 38

Calculated energy levels of the  hypernucleus

by the shell-model calculation with -coupling

NSC97e,f

10 Li 

[%] 0[%]

0.071 0.162 0.098 0.086 0.070 0.159 0.104 0.187 0.128 0.098 0.096 0.183 -mixing Prob.

P= 0.350% P= 0.345% E M P



     数100keV

Umeya, Harada, PRC79(200)014603

SLIDE 39

- coupling strengths

Fermi-type coupling Gamow-Teller-type coupling - mixing probability P(10

Li) = 0.345%,

Energy-shift E=280 keV

Fermi型 Gamow-Telleri型 Total

Coherently enhanced reduced

(1) コヒーレントな Fermi型とGT型結合 (2) 中性子過剰核ではT(T+1)に比例

Umeya, Harada, PRC79(200)014603

10 Li 

SLIDE 40

T.H and Y. Hirabayashi, (2009) in preparation.

Coulomb-assisted  -nucleus bound state in the (K, +) production reaction

SLIDE 41

‐-nucleus optical potentials in 57Co+‐

Real

+ DD-A’ + LDA-NF

Coulomb

+ teff ρ

repulsive Imag.

LDA-NF teff ρ DD-A’

1,3/2 0,3/2

1 1 2 6

D

U g g  

1,1/2 0,1/2

1 1 4 12 g g  

strongly repulsive repulsive attractive attractive

Quark Pauli- forbidden

SLIDE 42

--57Co

Nuclear density distributions

58Ni Coulomb

LDA-NF DD

Coulomb Coulomb

Narrow  bound state !! Attraction: Coulomb-assisted + Repulsion: push out the -wave functions.

• Cf. deeply pionic atoms

SLIDE 43

Momentum transfer in (K－,+) reactions

pF

～270 MeV/c

p→

180MeV/c

0.6 GeV/c

110MeV/c

SLIDE 44

-nucleus bound states in the reaction

DD

58Ni



q ~ 110 MeV/c

1.5MeV FWHM

SLIDE 45

DD LDA-NF teff ρ LDA-S3 WS-sh RMF

58Ni

reaction at 00 MeV/c

T.Harada, Y.Hirabayashi, (2009), in preparation.



1.5MeV FWHM

SLIDE 46

208Pb



1 11/ 2

1h

DD LDA-NF teff ρ DD LDA-NF teff ρ

1 11/ 2

1h

1 5/ 2

2d 

1 7/ 2

1g 

T.Harada, Y.Hirabayashi, (2009), in preparation.

1.5MeV FWHM

reaction at 00 MeV/c

SLIDE 47

-hypernuclear production from the nuclear (K, K+) reaction

16O(K, K+)16C at pK=1.65GeV/c

-

SLIDE 48

 hypernuclear spectrum in the (K-,K+) reactions

• Green’s関数法によるスペクトル
• Wood-Saxon型ポテンシャル
• U= 24MeV

W=  1MeV

• 12C(K,K)スペクトルから検討

U=  16MeV

• Shinmura’s model-D folding pot.

rc= 0.454 DWIA

Coulomb-assisted hybrid bound state

Tadokoro et al.,PRC51(1995)2656

2MeV FWHM U=24MeV

208Pb(K-,K+) at 1.65GeV/c

Folding pot. T.Koike, Y.Akaishi

SLIDE 49

ポテンシャルを探る

BNL-E885

• 束縛領域のスペクトルを再現する

4MeV FWHM

• Wood-Saxon型ポテンシャルの深さパ

ラメータを決める

DWIA

12 + 12

C(K ,K ) Be

 ‐

at 1.8GeV/c

P.Khaustov et al.,PRC61(2000)054603-1 核ポテンシャル Well depth～12-14MeV

素過程 ～35b/sr

YNG Folding potentialによる解析(rc=0.47)

SLIDE 50

T.H, A.Umeya, Y. Hirabayashi, (2009), in preparation

Double -hypernuclear production via a p→coupling in the (K, K+) reaction

16 16C



SLIDE 51

Observation of a Observation of a Double Hypernucleus Double Hypernucleus

H.Takahashi et al.,PRL87(2001)212502

6He 

静止-によるハイブリッド・エマルジョン法 KEK-E37 KEK-E373

NAGARA event

6He 

12 6 4

C He He t

 

   

5He

p  



 

H

2M B M

 

 

:{ 1 } 1/8 4/8 3/8 H N      

H-dibaryon

R.L. Jaffe, PRL38(1977)195

6

( He) 4.7 MeV B

 

 

D.J. Prowse, PRL17(1966)783

• M. Danysz et al., NP49(1963)121

10

( Be) 4.5 MeV B

 

 

1.3 MeV 

10 9 *

( Be Be (3.1MeV)+ + ) p  

 



13

( Be) 4.8 MeV B

 

 

• S. Aoki et al., PTP85(1991)1287

6He 

0.18 0.11

1.01 0.20 MeV B

  

  

0.18 0.11

7.25 0.19 MeV B

  

 

6 6 5

( He) ( He) 2 ( He) B B B

     

  

• 3.12±0.02

SLIDE 52

(－, K+) －Double Charge Exchange (DCX) Reaction ・One-step process: ・Two-step process:

K p 



 

0 p

K 



  K p K

  

  p



  

- coupling

K+

p p p p   

(b)

K-

 

K+

p p p  p 

0

(a)

K-

 

0 p

K 



 

K p 

 



Doorway

K p K

  

 

SLIDE 53

Elementary Cross sections for (K-,K+) reactions

Bando et al., Int.J.Mod.Phys. A5(1990)4021

K p K

  

   

p K  

 

   K n 

 

  

, K p p K  

 

     

Dover and Gal, Ann. Phys, 146 (1983) 309.

1.65 MeV/c 1.65 MeV/c

SLIDE 54

Spinflip and non-spinflip productions

• f the -hypernucleus

in (K, ) reactions

4He



SLIDE 55

Elementary cross section of Kn→ reactions

Spin-nonflip Spin-nonflip Spin-fl Spin-flip ip

SLIDE 56

Short-range Short-range correlation correlation

q q ef

eff ～３５０MeV/c

MeV/c

Cross section of the 4He(4He reaction

 with the recoil effects

at 1.0 GeV/c 0+ 1+

OFA

4He



SLIDE 57

Production of the -hypernuclear bound  states in the (K, ) reactions

SLIDE 58

Two-body N potentials in free space

T=1/2 T=3/2

attractive attractive repulsive repulsive N→N conv. Strong absorption

Sigma-nucleon absorptive potential (SAP) Strong spin-isospin dependence

SAP-D(F): S-matrix equivalent to Nijmegen model-D (model-F)

SLIDE 59

 s.p. energies in symmetric nuclear matter

Bando-Yamamoto 1985 Yamamoto et al. 1999

( , )

F

U k 

 

1

1.35 fm

F

k





G-matrix calc.

NSC89 

    

fss2 

    

  

(unit in MeV)

     

   

NHC-F



NHC-D

1/2,1S0

• dd



    

1/2, 3S1- 3D1 3/2,1S0 3/2, 3S1- 3D1



   

NSC97f



ESC04a 

    

ESC04d 

    

Rijken-Yamamoto 2006 Fujiwara et al. 2006

SLIDE 60

Possible existence of three-body NN states

0,3/2 1,1/2

1 1 2 2

N N

g g

 

 

1,1/2 0,1/2

3 1 4 4

N N

g g

 



1,3/2 1,1/2

2 1 3 3

N N

g g

 

 SAP-F SAP-D

Bound

Y.H.Koike, T.Harada, NPA611(1996)461

• I. R. Afnan and B. F. Gibson, PRC 47 (1993) 1000. Separable-pot + Faddeev calc. → =8MeV
• H. Garcilazo, et al., PRC75(2007) 034002; PRC76(2007) 034001.

Chiral constituent quark model pot.+ Faddeev calc. → =2.1MeV UBS ND NF

T=1,S=1/2

SLIDE 61

Lab cross sections for the elementary process

K N→ 

G.P.Gopal, et P.Gopal, et al., NPB119(1977)362 al., NPB119(1977)362

Non-spin-flip Spin-flip

Non-spin-flip Non-spin-flip +Spin-flip

SLIDE 62

3He(K-,+) spectrum at 600 MeV/c

Theoretical calculations

d+ T=1,S=1/2

-conv. E= 1.46 MeV (+0.55 MeV) = 9.05 MeV

SLIDE 63

• これまでにどういう新しい物理を明らか

にしてきたか？

・生成のメカニズムとDWIA計算の改良 ・nucleus potentialの性質

原子 v.s.(反応 ・中性子過剰ハイパー核生成 シグマ混合率

• 今後、どういう新しい展開が期待できる

のか？

・２重荷電交換反応によるハイパー核生成！

• J-PAＲCに対して、どういう実験を提

案していくのか？