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ハイパー核の生成・崩壊スペクトル - J-PARC分室
KEK(東海)研究会「原子核媒質中のハドロン研究=魅力と課題」
2013年8月5-6日
KEK東海キャンパス・東海1号館116号室
ハイパー核の生成・崩壊
スペクトル
媒質中のハイペロンの性質を探る
原田 融
Toru Harada
Osaka Electro-Communication University/
J-PARC Branch, KEK Theory Center
1
Contents
1. Introduction
2. Hyperon mixing in hypernuclei
− DCX: (π−,Κ+), (Κ−,Κ+)
3. CDCC (連続離散化チャネル結合法)
− YΝΝ systems, (Κ−,π−/+)
4. Summary
Keywords
Hyperon mixing + TBF + DCX
2
Introduction
3
ストレンジネス核物理
 ストレンジネスは原子核深部を探るプローブ
–ハイペロンはパウリ排他律を受けない
 Impurity Physics
Keywords
Hyperon mixing
+ TBF
 Baryon-Baryon Interaction
– YN, YY Interaction based on SUf (3)
– 核力の統一的理解・斥力芯の起源
– “糊”としての役割
– 原子核構造の変化
 “Exotic” Nuclear Physics
– ストレンジネスが拓く新しい原子核の面白さ
 Neutron Starの構造と進化
– 高密度核物質, EOS, 最大質量, 冷却, …
Serious Problems from hyperon-mixing (Takatsuka)
4
Neutron star core
= “An interesting neutron-rich hypernuclear system”
xiY g=
=
Coupling constant ratio;
iY g iN (i σ , ω , ρ )
UΣ < 0
UΞ < 0
Λ,Σ,Ξ,..
UΣ > 0
UΞ < 0
Κ−, ..
UΣ > 0
UΞ > 0
[R. Knorren, M. Prakash, P.J.Ellis, PRC52(1995)3470]
[F. Weber, PPNP 54(2005)193]
Cassiopeia A nebula
NASA/CXC/SAO.
Hyperon-mixing
5
P. B. Demorest et al., Nature467(2010)1081
PSR J1614-2230
1.4M 
Maximum Mass/Radius
Hyperons and massive neutron stars
Z.H.Li, H.-J.Schulze,
PRC 78 (2008) 028801
BHF
without hyperons
with hyperons
BHF+TBF(UIX)
1.97M 
PSR J1614-2230
1.44M 
P. B. Demorest et al.,
Nature467(2010)1081
Maximum Mass/Radius
Softening on the EOS
YN,YY: extra repulsion TNIu
S. Nishizaki, T. Takatsuka, Y. Yamamoto,
PTP105(2001)607; NPA691(2001)432
短距離斥力をハイペ
ロン混合により回避
Hadron-Quark crossover
nC (Y ) ≈ (2 − 3)n0
K. Masuda, et al.,
arXiv:1205.3621v2 [nucl-th]
7
Thermal evolution of neutron stars
Rapid neutrino emission
via weak processes
(Direct/Modified Uruca)
Λ → p + e− +ν e
Σ − → Λ + e− +ν e
Cooper pair
1S [iner crust]
0
3P -3F (n),1S (p) [core]
2
2
0
 Standard cooling
YY pairing
 Hyperon cooling
[S. Tsuruta et al., Astrophys. J 691(2009)621]
Standard cooling with heating
TNI6u-EOS
1.47
Hyperon cooling
1.52
1.53
1.60 Msun
Cooling of Neutron star
Cooling relaxation?
Hyperon superfluidity v.s.YY intarctions
Nagara event ∆BΛΛ~0.67 MeV  no ΛΛ superfluidity ?
very sensitive to properties of YN, YY interactions
8
Dynamics in Strangeness Nuclear Systems
ΣΣ
Ξ
Fujita-Miyazawa
3BF
∆
ΛΣ
ΝΞ
ΛΛ
Ν∆
Λ Λ N
~28 MeV
ΞΝ-ΛΛ coupling
ΝΣ
N N N
very large ?
~72 MeV
ΝΛ
~300 MeV
Nuclei
S=0
ΛΝ-ΣΝ
coupling
S = −1
ΝΝ
~1-2 %
S = −2
Σ
N Λ N
Strong ΛNN 3BF ?
Hypernuclei
 Various effects on the hyperon mixing
 Related to the 3BF in nuclei
9
DWIA calculation for production cross sections
Inclusive differential cross section
J. Hufner et al, NPA234 (1974) 429;
E.H. Auerbach et al., Ann. Phys. 148 (1983) 381;
C.B. Dover et al.,PRC22 (1980) 2073.
Transition-amplitude for K−NπY.
,Σ
,Σ
Production Amplitude
M
M
F (R ) = Fˆ | Ψ A = CY ;τ f KN −π Y χ p( π− )* ( C R ) χ p( +K ) ( C R )Ψ A (R )
MB
MA
Distorted-waves for outgoing and incoming mesons
χ p( π− )*=
(r ) χ p( + ) (r )
K
∑
L
+)
4π (2 L + 1)i L j (LM
(r )YLM (rˆ )
Green’s function
The relation
10
Λ
Σ
0
Σ
+
Σ−
Hyperon mixing
in hypernuclei
12
G-matrix calculation in symmetric nuclear matter
Λ single-particle potential depth
∑
U Λ (k F , ε Λ=
)
N’
= ε Λ +ε N ) | k Λ , k N
k Λ , k N | g ΛN (ω
kN
) vYN + vYN
gYN (ω=
QN
gYN (ω )
ω − QTQ
Effects of the ΛN-ΣN coupling in nuclear matter
0
ΛN single channel
N
−20
N
Λ
−40
−50
ΛN-ΣN coupled channel
Λ
=
N
Λ N
Spin-isospin saturated
Exp.
Y.Nogami, E.Satoh, NPB19(1970)93
as= -1.8fm, at= -1.6fm
N
Λ
+
N
Λ
Ν‘
N
Σ
Λ
Σ
+
N
Λ N
Spin-isospin saturated
~−28
−30
N
+
=
−10
kF
Pauli-operator
G-matrix
(unit in MeV)
k F = 1.35fm −1
−34.2
ΛNN
three-body
force
repulsive
vΛN ,ΣN
−50.6
Overbinding!
−52.9
QN
vΛN ,ΣN
eΣN
suppressed
13
Λ single-particle energies in symmetric nuclear matter
U Λ (k F , ε Λ )
OBEP: Nijmegen YN potential Models
k F = 1.35fm −1
G-matrix calc. QTQ
Scattering length
as
at
0
-1.90fm
-1.96fm
(unit in MeV)
odd
-2.29fm
-1.88fm
-2.78fm
-1.41fm
-2.10fm
-1.86fm
-2.51fm
-1.75fm
+0.4
+4.5
+6.9
-12.8
-14.4
-0.9
-8.0
-9.2
+0.9
-0.2
-3.2
-12.7
-13.7
-10.0
-10
1S
0
-7.4
-12.3
-14.6
-22.9
-20.7
3S - 3D
1
1
-20
-28
-25.1
-30
-23.3
-31.6
NSC89
NHC-F
-30.8
Exp.
-40.5
-40
-26.0
Y. Yamamoto, H. Bando, PTP.Suppl.81(1985)9
Y. Yamamoto, et al.,PTP.Suppl.117(1994)361.
Th.A.Rijken, V.G.J.Stoks, Y.Yamamoto, PRC59(1999)21.
Th.A.Rijken, Y.Yamamoto, PRC73(2006) 044008.
-21.4
-31.1
-34.3
NSC97e
NSC97f
-38.5
NSC04a
NHC-D
Bando-Yamamoto
1985
-23.8
-21.5
Yamamoto et al.
1999
RijkenYamamoto
2006
-35.6
NSC08a
-34.0
NSC08b
RijkenYamamoto
2009
Overbinding Problem on s-Shell Hypernuclei
The Underbinding Problem
The Overbinding Problem
3
Λ
4
Λ
H
He
5
Λ
He
0.0
-0.31 MeV
3
Λ
H
4
Λ
5
Λ
He
He
0.0
1+
-1.24 MeV
-0.31 MeV
spin-spin
 
(σ N ⋅ σ Λ )
Underbound
0+ -2.39 MeV
[Exp.]
-3.12 MeV
Overbound
1+ -1.24 MeV
1+
0+
0+ -2.39 MeV
[Exp.]
-3.12 MeV
VΛN,ΣN
Q
VΣN,ΛN
e
suppressed
ΛN single-channel calc.
g-matrix calc. with ΛN-ΣN(D2)
Dalitz et al., NP B47 (1972) 109.
Akaishi et al., PRL 84 (2000) 3539.
15
“The 0+-1+ difference is not a measure of ΛN spin-spin interaction.”
by B.F. Gibson
Hyperon-mixing
ΛΝΝ three-body force
(unit in MeV)
4
Λ
4
Λ
( H)
Σ↑
He
n ↓ Λ ↑ p↓ p↑
0.0
1+
-1.24
1+
-1.08
spin-spin
ΛNN force
-2.39
0+
0.38
0.86
-2.28
0+
phenomenological
Exp.
VΛN + VΛNN
V = 6.20
VMC
R. Sinha, Q.N.Usmani,
NPA684(2001)586c
1+
1+
-1.03
-1.04
-1.04
0+
Coherent coupling
-2.27
0+
Pcoh.Σ = 1.9%
D2
1+
-1.20
1+
-1.21
-1.52
0+
1+
-0.68
-1.43
0+
Coherent coupling
-2.10
0+
+
Σ↑
+
n ↓ Λ ↑ p↓ p↑
1+
-0.70
Σ↑
n ↓ Λ ↑ p↓ p↑
-0.68
1+
-0.70
1+
-0.97
0+
Coherent coupling
-2.18
0+
Coherent coupling
-2.51
0+
Pcoh.Σ = 0.7%
Pcoh.Σ = 0.9%
Pcoh.Σ = 2.0%
SC97e(S)
SC97f(S)
SC89(S)
Breuckner-Hartree-Fock
Y. Akaishi, T.Harada, S.Shinmura, Khun Swe Myint,
PRL84(2000)3539
16
The Λ-Σ coupling effects in neutron matter
S.Shinmura, Khin Swe Myint, T.H., Y.Akaishi, J.Phys.G28(2002)L1
Excited (1p1h) states
usually included in g-matrix
Single particle potential for Λcoh.
Ground states
0
5.8%
1.4%
3.3%
NSC97e
MeV
-20
-40
8.2%
NSC89
16.3%
-60
Λcoh mixing
probability
coherent Λ-Σ coupling
22.6%
-80
0
0.5
1
1.5
2
2.5
nucleon density/normal density
3
The Λcoh mixing is enhanced in the neutron-excess
environment.
17
Production of neutron-rich Λ-hypernuclei with the DCX reaction
[email protected]
9
Λ
He
Li(π , K ) H
9
Be(π − , K ) He
6
−
+
6
Λ
+ 9
Λ
6
Λ
H
“Hyperheavy hydrogen”
Y.Akaishi, NPA738(2004)80c
Khin Swe Myint et al.,
FBS. Suppl. 12(2000)383
5H
Larger neutron-excess
Λ
Attraction
Λ binding energies
 Coherent Λ-Σ coupling in neutron-excess environment
Coherent Λ-Σ
coupling
Extremely
enhanced
18
First production of neutron-rich Λ hypernuclei
10
B(π − , K + ) 10Λ Li Λ spectrum by DCX (π−,Κ+) reaction at 1.2GeV/c
KEK-PS-E521
P. K. Saha, et al., PRL94(2005)052502
2.5 MeV FWHM
11.3±1.9 nb/sr
g.s.
Cross sections
- pπ=1.20 GeV/c
dσ
≈
d ΩL
11.3±1.9 nb/sr
- pπ=1.05 GeV/c
9Li+Λ
dσ
≈
d ΩL
5.8±2.2 nb/sr
~1/1000
g.s.
9Li+Λ
12
C(π + , K + ) 12Λ C
(1.2 GeV/c)
17.5±0.6 µb/sr
19
First observation of the superheavy hydrogen Λ6H
M. Agnello et al., NPA881(2012)269.
M. Agnello, et al., PRL108 (2012) 042501.
 observation of 3 candidate events of 6ΛH bound state
BΛ = 4.0 ± 1.1 MeV
 BR(DCX) / BR(NCX,12LC) ~ 3x10-3
R = (5.9 ± 4.0) · 10−6/K−stop
6
Λ
H
3 events
4
Λ
H(1+ ) + 2n
4
Λ
H(0+ ) + 2n
−
K Stop
+ 6 Li → Λ6 H + π + (252MeV/c)
6
Λ
H → 6 He + π − (130MeV/c)
[email protected]
 Produce neutron-rich hypernuclei: 6ΛH and 9ΛHe
 precise measurement of B.E. of 6ΛH is possible
20
(π-, K+) -Double Charge Exchange (DCX) Reaction
Two-step process:
π-
K+
π − p → K 0Λ
K 0 p → K +n
p
π p →π n
π 0 p → K +Λ
−
0
One-step process:
p
p
p
π-
n
n
Σ p ↔ Λn
p
p
p
K+
Hyperon-mixing
π − p → K +Σ−
−
via
doorways caused
by ΛN-ΣN coupling
K0
Λ
K 0 p → K +n
π − p → K +Σ−
Σ−
π − p →ΛK 0 Λ
Doorway
Σ−
p
Λ
n
Λ
n
21
Λ spectrum by DCX (π−,Κ+) reactions at 1.2GeV/c
Harada, Umeya,Hirabayashi, PRC79(2009)014603
Spreading potential dep.
WΣ
U X = 11 MeV is fixed. PΣ−=0.57%
10B
9Li+Λ
−WΣ =
2−
(sΛ)
3+
(pΛ)
UX =
Two-step mechanism
22
Σ− s.p. potentials (fitted to the Σ− atomic data)
VΣ ?
Density-dependent (DD) potential (Phenomenological )
C.J.Batty et al., Phys.Rep.287(1997)385,
E. Friedman and A. Gal, Phys. Rep. 452 (2007)89.
DD-A’
Relativistic mean-field (RMF) potential
RMF
J. Mares et al., NPA594(1995)311.
K.Tsubakihara et al., EPJA33(2007)295
LDA
Folding-model potential for LDA with G-matrix
D. Halderson, Phys. Rev. C40(1989)2173.
T.Yamada and Y.Yamamoto, PTP. Suppl. 117(1994)241
J. Dabrowski, Acta Phys. Pol. B31(2001)2179
T.Harada, Y.Hirabayashi, NPA759 (2005) 143; 767(2006)206
YNG-F
 Σ-1粒子ポテンシャルは強い斥力であることを示唆
23
28Si(π−,Κ+)
reaction
at 1.2GeV/c
28Si
Normalization
factor
RMF
DD-A’
Consistent with the
potentials
fitted to
−
Σ - atomic data !!
Σ
LDA-NF
LDA-S3
WS-sh
teff ρ
T.Harada, Y.Hirabayashi,
NPA759 (2005) 143
24
Σ s.p. energies in symmetric nuclear matter
−4.9
+10.3
May, 2010 update
U Σ (k F , ε Σ ) kF = 1.35 fm −1
G-matrix calc.
+40
−10.5
+30
1/2,1S
0
odd
+20
3/2,1S
0
−8.0
−17.1
−10
−30
+6.5
−1.5
+5.3
+6.7
−12.0
+6.7
−11.6
−2.5
Bando-Yamamoto
1985
+11.6
+2.4
−12.4
+13.8
−9.2
+41.2
−12.9
NSC89
NSC97f
Yamamoto et al.
1999
ESC08b
+13.4
−23.9
ESC08a
+7.5
fss2
Rijken-Yamamoto
2009
−8.8
−15.3
+20.3
−10.1
−4.2 −11.3
1/2, 3S - 3D
1
1
NHC-D
−14.3
+14.9
−14.9
−16.3
−20
+52.6
−24.6
NHC-F
0
+6.7
+44.6
+37.1
3/2, 3S - 3D
1
1
−6.6
−27.0
+4.1
+22.0
+11.3
−11.7
−8.4
−17.1
−10.6
+7.7
−18.9
+10
−5.6
−21.9
−26.9
−26.0
Fujiwara et al.
2006
including
Quark exchange
terms
ESC04d
−36.5
(unit in MeV)
ESC04a
Rijken-Yamamoto
2006
25
Studies of Ξ- s.p. potentials
28Si
VΞ ?
Ξ-hypernuclei via (K-,K+) reactions
[C.B. Dover, A.Gal, Ann. Phys. 146 (1989) 309.]
knowledge is limited
VΞ0 =
−24 ± 4 MeV for r0 =
1.1 fm (WΞ0  −1 MeV)
BNL-E885
DWIA analysis of 12C(K-,K+) data at 1.8GeV/c
T.Iijima et al.,NPA546(1992)588.
Tadokoro et al.,PRC51(1995)2656
12C
VΞ0  −16 MeV
P.Khaustov et al., PRC61(2000)054603
VΞ0  −14 MeV
12C
Semi-Classical Distorted Wave Model Analysis
M. Kohno et al.,PTP123(2010)157;NPA835(2010)358.
VΞ0 =
−20, −10, 0, +10, +20MeV
fss2
26
Ξ- spectrum in DCX (K-,K+) reactions at 1.8GeV/c
T. Harada, Y. Hirabayashi, A. Umeya, PLB690(2010)363.
16O
15N+Ξ-
WΞ0 ( E )  −3 MeV
Woods-Saxon
=
r0 1.1
=
fm, a 0.6 fm
VΞ0 = −24 MeV
1.5MeV FWHM
−14 MeV
 Spin-stretched Ξ– states can be populated due to the high momentum transfer.
ds/dΩ[15N(1/2-)⊗sΞ ](1-) = 6 nb/sr, ds/dΩ [15N(1/2-)⊗pΞ](2+) = 9 nb/sr for VΞ=-14 MeV.
27
Ξ-ΛΛ spectrum in DCX (K-,K+) reactions at 1.8GeV/c
16O
15N+Ξ-
Two-step mechanism
K − p → π 0Λ
π 0 p → K +Λ
Ξ−
w/o ΞN-ΛΛ coupling
One-step mechanism
K − p → K +Ξ−
Ξ − p ↔ ΛΛ
ΞN-ΛΛ coupling
Doorway
ΛΛ
Hyperon-mixing
[T. Harada, Y. Hirabayashi, A. Umeya, PLB690(2010)363]
[email protected]
−14MeV
with ΞN-ΛΛ coupling
28
Remark
Studies of the DCX reactions (π−,K+),(K−,K+)
for hypernuclear productions
are
very important and promising .
Keywords
Hyperon mixing
+
DCX
29
CDCC
(連続離散化チャネル結合法)
30
Observation of a Σ4He Bound State
BNL-AGS (1995-)
4
Σ
T. Nagae, T. Miyachi, T. Fukuda, H. Outa,
T. Tamagawa, J. Nakano,R.S.Hayano,
H. Tamura, Y. Shimizu, K. Kubota,
R. E. Chrien, R. Sutter, A. Rusek,
W. J. Briscoe, R. Sawafta,
E.V. Hungerford,A. Empl, W. Naing,
C. Neerman, K. Johnston, M. Planinic,
Phys.Rev.Lett. 80(1998)1605.
He
B=
4.4 ± 0.3
Σ+
Τ=1/2, 3/2
Τ=3/2
Γ = 7 ± 0.7
T  1/ 2
J π = 0+
MeV
MeV
4.6 MeV
7.9 MeV
Theoretical Prediction
T.Harada, S.Shinmura,
Y.Akaishi, H.Tanaka,
NPA507(1990)715.
31
Production by 𝐾 − beam from 3He targets
3He
𝚺
 72MeV
3H
𝚺
 75MeV
3He∗
Λ
 77MeV
p+p+Λ
(𝐊 − , 𝛑− )
𝟑
3n
𝚺
p+n+Λ
(𝐊 − , 𝛑𝟎 )
SCX
He
n+n+Λ
d+Λ
3H
Λ
(𝐊 − , 𝛑+ )
DCX
Model wave functions
ϕY
Φ (NN)
wfs calculated by realistic Tamagaki-C3G pot.
“NN” core
.........
Ψ ( He) = Φ ({ pp})ϕΛ + Φ ([ pn])ϕΣ+ ,t
3
Y
+Φ ({ pn})ϕΣ+ , s + Φ ({ pp})ϕΣ 0
[ N=
N1 N 2 − N 2 N1 3S1,T =0
1N2 ]
{N1=
N 2 } N1 N 2 + N 2 N1 1S0,T =1
Ψ ( n) = Φ ({nn})ϕ Λ + Φ ([ pn ])ϕ Σ− ,t
“NN” core
.........
.........
.......
.........
For (K-,π+)
3
Y
.........
.......
.......
For (K-,π-)
+Φ ({ pn})ϕΣ−, s + Φ ({nn})ϕΣ 0
33
Effective “2N”-Y potentials for 3ΣHe (Jπ=1/2+)
[pn]Σ+ −{pn}Σ+
{pn}Σ+−{pp}Σ0
{pp}Λ−[pn]Σ+
U 00 =
Φ 0 V ex Fˆ ex Φ 0
{pp}Σ0
{pp}Λ
[pn]Σ+
[pn]Σ+−{pp}Σ0
Real
YN potential NF made by Shinmura
Imag.
+spreading
(2N breakup)
Inclusive spectrum by 3He(K−,π-) reactions at 600MeV/c
Λ
3
Σ
{pp}Λ
Λ-Σ conv.
He
Σ
[pn]Σ+
{pp}Σ0
{pn}Σ+
微視的チャネル結合(MCC)法
ハイパー核物理
YN, YY int.
3BF
相互作用
-KMT, (KAT)
-g-matrix, effective int.
Folding model
OMP(SF,DF,DF,..)
核反応
-Elastic/Inelastic Scatt.
-Coupled-channels
-Faddeev, SHM, CDCC
核構造
-Shell-model, Cluster-model,
-FB-model, MF-model
-OCM, RGM, AMD, HF, MF
-Ab initio
生成・崩壊
+DWIA,CC,GFM,..
Inclusive/Exclusive
spectra
36
Model wave functions
ϕY
Φ (NN)
wfs calculated by realistic Tamagaki-C3G pot.
“NN” core
.........
Ψ ( He) = Φ ({ pp})ϕΛ + Φ ([ pn])ϕΣ+ ,t
3
Y
+Φ ({ pn})ϕΣ+ , s + Φ ({ pp})ϕΣ 0
[ N=
N1 N 2 − N 2 N1 3S1,T =0
1N2 ]
{N1=
N 2 } N1 N 2 + N 2 N1 1S0,T =1
Ψ ( n) = Φ ({nn})ϕ Λ + Φ ([ pn ])ϕ Σ− ,t
“NN” core
.........
.........
.......
.........
For (K-,π+)
3
Y
.........
.......
.......
For (K-,π-)
+Φ ({ pn})ϕΣ−, s + Φ ({nn})ϕΣ 0
37
Continuum-Discretized Coupled-Channel Method
(CDCC)
M. Kamimura et al.,
Prog. Theor. Phys. Suppl. 89, 1 (1986)
projectile
r
continuum
core+n
R
target
by Takashina
 We can describe the spectra taking into account the continuum couplings
together with the nuclear breakup processes.
38
CDCC method for continuum ppΛ states
Coupled-Channel Equation (pp-Λ)
Microscopic Folding Potential for “pp”-Λ
Effective ΛN potential  SG-type (Phenomenological) a, reff
Method of momentum bins (discretization)
Realistic ΝN potential by G3RS
kf (fm-1)
0+(L=0)
1.0
ρ
0.8
r
0.4
⊗Λ
0.6
0.2
0.0
{pp}1S0
Elementary cross section of K-nπΛ reaction
Λ
870 MeV/c
Coupled-channels DWIA calculation for Λ production
Coupled-channel Green’s function
T.Harada, NPA672(2000)181
 (E ) = G
 ( 0) ( E ) + G
 ( 0) ( E )UG
  (E )
G
f
f
f
f
GΛ(0)0



(0)
G
(0)


Λ
1
Gˆ ( E f ) =





(0)
G

ΛN 

Im Gˆ =
Uˆ
 U 0,0 U 0,1  U 0,N 
U U
 
1,0
1,1

=

 



U N ,N 
U N ,0 
†
( − )†
(0) ˆ ( − )
ˆ
ˆ
ˆ
Ω
G
Ω
+
G
{Im
}
∑
∑ {WΛi }Gˆ
Λi
i
i
Λ escape
Strength function
Spreading (2N breakup)
Green’s function method
Morimatsu, Yazaki, NPA483(1988)493
Green’s function
41
Inclusive spectrum in 3He(K−,π−)ppΛ at 870MeV/c
Test of convergence
nbin=10
0 ≤ 𝑙 ≤ 𝑙max = 0
nbin=5
0 ≤ 𝑘f ≤ 𝑘max = 1.0 fm−1
nbin=5
kf (fm-1)
nbin=10
0+(L=0)
1.0
0.8
0.8
⊗Λ
𝟑
He
0.6
0.4
0.4
0.2
0.2
0.0
(𝐊 − , 𝛑− )
kf (fm-1)
1.0
0.6
nbin=5
nbin=10
p+p
0.0
0+(L=0)
Inclusive spectrum in 3He(K−,π−)ppΛ at 870MeV/c
𝑞Λ ~80 MeV/c
Total, S =1/2
L= 0+
1−
2+
Inclusive spectrum in 3He(K−,π−)ppΛ at 870MeV/c
𝑞Λ ~300 MeV/c
Total, S =1/2
1−
L= 0+
2+
3−
Remark
 The coupled-channel framework is very important for
calculating the spectra of the 3He(K−,π∓) reactions.
taking into account K-N-πY amplitudes and threshold-differences .
 The effective “2N”-Y potential is constructed from the
MS theory with correlation functions.
More detailed investigations are needed.  Full 3B calculations
 The calculated spectra of the 3He(K−,π+) reaction may be
consistent with the E774 data due to the admixture of the
NN core states.
depending the ΣNN structure determined from the “2N”-Y potential.
 Both the π− and π+ spectra provide valuable information
to understand the nature of the ΣNN states and also the
YN (ΣN) interactions. To determine a quasibound state [+ −] or cusp state [− +].
45
Conclusion
Studies of
the production and spectroscopy of
strangeness nuclei are
very interesting and exciting
at J-PARC.
ストレンジネスが拓く新しい状態の発見、”エキゾチック”な原子核
バリオン-バリオン間相互作用の理解、短距離斥力の起源
ハイぺロン混合と中性子星の2大問題
中性子星物質の状態方程式の解明
46
Thank you very much.
47
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