Post on 08-Oct-2019
R.H. Dalitz, R.C. Herndon & Y.C. Tang,Nucl. Phys. B47 (1972) 109 Overbound
The overbinding problem
H3Λ H4Λ He4Λ He5
Λ
-0.13 MeV1+ -0.99 MeV
(Exp)-3.12 MeV
0+ -2.39 MeV
1+ -1.24 MeV
0+ -2.04 MeV
Pictures1-channel2-channel
Central YN interaction
Coupling A.R. Bodmer(1966)
D0
D2
ΛN ΣN
Phase-equivalent to Nijmegen D
0 20 40 (MeV)
20○
0
ΛN phase shift3S1
1S0
40○
Two pictures
N,NN,N ΛΣΣΛ VeQV
PaulisuppressionN
N
Λ
Λ
NΣ
D0Overbinding problem
H3Λ He4Λ He5
Λ
Overbinding
?
0+ -2.39
-0.13
Exp-3.12 MeV
ΛN int.
H3Λ He4Λ
Underbinding problem
He5Λ
Underbinding
-3.12
D2
?
-0.13
0+ -2.39 MeVExp
ΛN-ΣN int.
R.H. Dalitz et al. (1972)
1+ -1.03
0+ -1.04
30
20
10
0
-10
-20
(MeV)
0 1 2 3 4r (fm)
)( +Λ 0U
)( +Λ 1U
He4Λ
D2 interaction
1+ -1.24
0+ -2.39 MeV
Exp
)( +ΣΛ− 0U
)( +ΣΛ− 1U
-2.27
-1.04
Y. Akaishi, T. Harada, S. Shinmura and Khin Swe Myint, Phys. Rev. Lett. 84 (2000) 3539
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−===
Σ−Σ⇔Λ −
101
30
31
3
3
32 pnn
sss
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−===
Σ+Σ−⇔Λ +
101
30
31
3
3
32 npp
sss
H4Λ1+ 0+S=1 pairs
Contribution to UΣΛ
Λ-Σ coupling energy 1 : 9
1/2 3/2
+1/2
+1/2
+1/2
+1/2
+1/3
-1/3Cancel
Coherentlyadded
Y. Akaishi, T. Harada, S. Shinmura & Khin Swe Myint, Phys. Rev. Lett. 84 (2000) 3539
Th.A. Rijken
N N
N N
Λ
Λ
Σ
(MeV)
He4Λ
“The 0+-1+ difference is nota measure of ΛN spin-spin interaction.”
B. Gibson (Maui, 1993)
Exp D2 SC89(S)SC97f(S)SC97e(S)
PcohΣ=1.9 % PcohΣ=0.7 % PcohΣ=0.9 %PcohΣ=2.0 %
1+
-0.74
-2.180+
-2.100+-2.27
0+-2.390+ -2.51
0+
-0.06 -0.071+
1+
-1.211+
-1.041+
-1.24 -0.97
-0.68
-1.43-1.52
-1.20-1.04
-1.03
0.0
0+
1+ ( ) ( )EE 3N
1N ΛΛ + VV
25
21
( ) ( )EE NN31
23
23
ΛΛ + VV
“Is the 1S0 YN int. more attractive than the 3S1 YN int.?”
“Is there any evidence for coherently enhanced Λ-Σ coupling in 0+?”
No !
No !
A. Nogga, (2001)
Faddeev-Yakubovsky calculation of 4ΛHe
SC97e0+ 1+
PΣ
1E
3E
ΛVΣV
ΣΛΛΣ + VV
ΛVΣV
ΣΛΛΣ + VV
1.57% 1.08%
-1.49-0.43-0.17
1.161.18
-11.98-9.64
-5.90-5.30 -1.34
-0.12-0.03
1.552.00
-13.63-10.08
(MeV)
Real space
Model space
SC97e
0+ 1+
1E
3E
scΛV
sc,ΣΛΛΣV
scΛV
sc,ΣΛΛΣV
-1.37-0.09
1.18-6.09
-4.91
-5.47-5.38 -1.35-0.02
1.57-6.89 -5.32
(MeV)
Single-channel description of 4ΛHe
-4.13x3/5
Coherentlyenhanced
sc01S
sc13Sis more attractive than .
ΣΣΛΛΣΣΛΛΣ ++= VVVVsc,
{ } { }ΛΛΣ
ΣΣΣ +
−−Δ++ VTPPMPT1
ΛΣΣ−
= VP11
“Cooking”!
Model space
Stochastic variational calculation of 5ΛHe
H. Nemura, Y. Akaishi & Y. Suzuki,Phys. Rev. Lett. 89 (2002) 142504
The first successful ab initio 5-body calculationincluding Σ degrees of freedom
He5ΛH4ΛH3Λ
SC97e(S)
-2.75 [1.55%]-2.06 [1.49%]
-0.92 [0.98%]
-0.10 [0.15%]
-3.12 (MeV)
-2.04
-0.99
-0.13
pΣ
NN:G3RS
J.A. Carlson,AIP Conf. Proc. 224 (1991) 198
SC89: unbound
Rearrangement of 4He due to Λ sticking
α Λ-28 MeV -3 MeV
-8 MeV-23 MeV
H. Nemura et al., Phys. Rev. Lett. 89 (2002) 142504
Rearrangement in αΛΛM. Kohno et al.,
Phys. Rev. C68 (2003) 034302
VT
π
Σ N
NΛ
VT
πN N
N N
(S)
(D)
MeVMeV,)E(
MeV,)E()E(
T
CC
8544
333
31
=−≈
−≈≈
TV
VV
-44
PD(α)=10.2%
9.3%
Repulsion? Attraction?Y. Nogami et al.
Nucl. Phys. B19 (1970) 93Y. Akaishi et al.
Phys. Rev. Lett. 84 (2000) 3539NN Λ
Σ
H3Λ H3ΛHe4Λ He4
ΛHe5
Λ He5Λ
Overbinding
Underbinding
0+ -2.39
-0.13-0.13
Exp-3.12 MeV -3.12
0+ -2.39 MeVAn extraordinary
state
↑n ↑Λ ↑n ↑Λ
↑p −↑
Σ
↑n ↑Λ ↑n ↑Λ
↑n ↑Λ
0↑
Σ
↑n ↑Λ
↑n ↑p
He5Λ
↓p↑p↓n ↓p↑p↓n
Attractive
↓p
↑p
↓n
↑n ↑Λ
↓p
↑p
↓n
↑n ↑Λ
↑p
−↑
Σ
↑n↑Λ
RepulsiveNogami’s 3BF
Single channel
↓p↑p
↑n ↑Λ
↑n ↑Λ↓p↑p
↑n ↑Λ
↑p
0↑
Σ
↑n ↑Λ
↓p
↑p↑n ↑Λ
↓p↑p
↑n ↑Λ
0↑
Σ
↑n ↑Λ
He4Λ
↓p↑p
↑n ↑Λ
↑p −↑
Σ
↑n ↑Λ
Attractive
↓p
↑p↑n ↑Λ
↑p
−↑
Σ
↑n↑Λ
RepulsiveNogami’s 3BF
AttractiveAkaishi’s 3BF
Single channel
Effects of ΛNN three-body force
He5Λ
He4Λ
0.0(MeV)
−Σ
Λ
Origin ofoverbinding
Exp1+
0+
Exp
1+
0+-2.10
-1.74 -1.24
-2.39
-3.12
-5.39
−Σ
Λ
Restoration ofPauli principle
0Σ
Λ
CoherentΛ-Σ coupling
Essential dynamics
-2.30
-1.04
in T=0 nuclei
p p
ΛNN spin-spin
Three-body force due to coherent Λ-Σ coupling : [for D0]
( ) ⎥⎦⎤
⎢⎣⎡ σ+σσ+σσ+∑= ΛαααΛΛ
α
=αΛ )()(,
,,NN 2121213 2
1 rrrrr cbarrWUsststt
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−
−=⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
81
481
485
41
81
81
83
163
167
ssssss
tststs
tttttt
cbacbacba
)'(*
)()',( N,NN,N rVM
rVrrW ttttΛΣΣΛ Δ
=1
3
670.,N,NN,N =ββ−= ΛΣΛΣts VV
He5Λ
)H(1+Λ4
)H(0+Λ4
H3Λ
5323
21 ttW)( β+ 3 MeV
1.0 MeV
-0.44 MeV
-0.05 MeV
43229
81 ttW)( β+β+
432563
81 ttW)( β+β−−
332361
81 ttW)( β+β−−
Λ
ΣVt
Vt
0.56 + 0.92 (62%) MeV for SC97f
-3.03 MeV
-1.08 MeV
-2.28 MeV
Exp0+
1+
H4Λ He5Λ
Variational Monte CarloJ. Lomnitz-Adler, V.R. Pandharipande & R.A. Smith,
Nucl. Phys. A361 (1981) 399
Light hypernuclei
A.R. Bodmer & Q.N. Usmani, Nucl. Phys. A477 (1988) 621R. Sinha & Q.N. Usmani, Nucl. Phys. A684 （2001）586c
)()())(( NcoreN rTVPVrVV x2
411 πΛσΛ ⎥⎦
⎤⎢⎣⎡ σσ+ε+ε−−=
rr
Spin-spin
⎥⎦⎤
⎢⎣⎡ σ+σσ+= ΛΛπΛπΛ )()()(DS
NN jiji rTrTWV rrr
61122
0
Σ
Λ N1
N2π0+-1+ splitting
0.38 + 0.86 MeV(70%)
The major part is attributedto ΛNN and not to ΛN.
Spin-spin
ΣThe first observation of a bound Σ state
E167 : Phys. Lett. 231 (1989) 355
R.S. HayanoT. IshikawaM. Iwasaki
H. OutaE. TakadaH. Tamura
A. SakaguchiM. Aoki
T. Yamazaki
Σ – Nucleus, 4ΣHe
Σ−Σ ⋅+= tTVVUrr
nuclnucl τ0
(MeV)100
50
0
-50
2 R (fm) 4
0VU =Σ0h
+ΣtU
h
t Σ+
Σ0
Lane term
τVU 21
0 −=+ΣΣ t-h
T- t+
T. Harada, S. Shinmura, Y.Akaishi & H. Tanaka, Nucl. Phys. A507 (1990) 715
Observation of a 4ΣHe bound state
Σ4He
T. Nagae, R.E. Chrien et al.,Phys. Rev. Lett. 80 (1998) 1605
MeV.. 13044 ±±=+ΣB
MeV.. ..21007007 +
−±=Γ
4.6 MeV
7.9 MeV
T. Harada, Y.Akaishi et al.,Nucl. Phys. A507 (1990) 715
Neutron-excess hypernuclei
↑Λ ↑p
0↑Σ
↑Λ ↓p
0↑Σ
↑Λ↑n
0↑Σ
↑Λ ↓n
0↑Σ
tV31
−
tV31
)( st VV +−121
)( st VV +121
Protoninduced
Neutroninduced
Cancellationdue to isospin selection
Coherent Λ-Σ mixing
Relativistic mean field model
Baryons: n, p, Λ, Σ Mesons: σ, ρ, ω
“Normal state of infinite matter”
N.K. Glendenning, Astrophys. J. 293 (1985) 470.
Baryons in the medium carry the same quantum numbers in vacuum.
XX
X
0.0
A.A. Korsheninnikov et al,Phys. Rev. Lett. 87 (2001) 092501
Superheavy hydrogen
H)HeHe,(H 5261
1.7(MeV)
3H + 2n
-4.1
Khin Swe Myint & Y. Akaishi,Prog. Theor. Phys. Suppl. 146 (2002) 599
“Hyperheavy hydrogen”
-2.04
-4.4
MeV
-1.4
MeV
ΛN
Nfo
rce
2nH4 +Λ
H6Λ6Li ( π-, K+)
Λ++ nH3 2
H.I.7H 8HΛ Λ
Double-charge & strangeness exchange reaction
= 6H + α = 4H + 2n + αΛ Λ
StabilizerLi)K,(B 10-10
Λ+π
Li)K,(B 11-11Λ
+π
9Li
n
Λ
C. Kurokawa et al.
P.K. Saha, T. Fukuda
E521 @KEK
10B(π-,K+) spectrumP.K. Saha et al., KEK-PS-E521 collaboration
Preliminary!!
~40 counts
J-PARC
P.K. Saha, T. Fukuda et al., Phys. Rev. Lett. 94 (2005) 952502
BHF cal.Y. A. & K.S. Myint
γ0.21MeV
1-
2-2-1- -12.09
-12.11 -12.17
-12.28(PcohΣ=0.31%)
ΛNN
force
Li10Λ
D2 int.
SVM cal.
α + t + Λ + n + nbeyond 4-body model
Coherent Λ-Σ coupling
Y- [ NNN ]T=1/2: interactions
54321
from D2
-30
20
30
40
-20
-10
0
10
(MeV)
)( +ΛΣ− 0U
210 /)( =+
Σ TU
)( +Λ 0U
)( +Λ 1U
)( +ΛΣ− 1U
)( +Σ 1U
r (fm)
Coherent Λ-Σ coupling
4ΣH formation
San Dar Myint Oo
Λn
Σ0 p Σ-n
t
tt
α
Λn
Σ0 p Σ-n
Coupling scheme
nΛ-nΣ0-pΣ- coupling
SpectatorParticipant
h
Σ-nCoherent Λ-Σ coupling4
ΣH formation α formation
H4Λ
He5Λ
H3Λ
-2
-4
-6
-8
0
-BΛ
-2
-4
-6
-8
0
[MeV]
H5ΛΛ
He6ΛΛ
H4ΛΛ
Nagara-BΛΛ
[MeV]
Fully coupled channel (ΛΛ-NΞ-ΛΣ-ΣΣ) calculationsH. Nemura, S. Shinmura, Y. Akaishi & K.S. Myint, Phys. Rev. Lett. 94 (2005) 202502
6Li (K-,K+) 6ΛΛH
Missing-mass spectroscopy in S=-2 sectorvia one-step process !
6ΛΛH = [ t-Λ-Λ-n ] [ t-Σ-Λ-n ]
[ α-Ξ--n ]
Coherent Λ-Σ coupling
Nemur
a’smec
hanis
n
Alpha formation
Large Ξ- mixing
Coherent Λ-Σ coupling is essential dynamics.
)He(0-)He(0 44 +Σ
+Λ
Λcoh(Λ-Σ0 mixing) in dense neutron matter
Concluding remarks
The overbinding problem of has been virtually solved.
ΛNN forceRepulsive/attractive : “D0 picture”Attractive : “D2 picture”
He5Λ
A necessary conditionfor YN interaction
to study ΛΛA.
Neutron-rich hypernuclei can provideadditional evidences for coherent Λ-Σ coupling.
H)K,(Li 66Λ
+−π
EffectiveΛN interaction
consistency
H.I. 7ΛH, 8ΛH, …, 5ΛΛH, 7ΛΛH,… etc.
[ ]11 −⊗Σ −+ ZA
[ ]ZA 1−⊗Σ0
[ ]11 +⊗Σ − ZA-
[ ]ZA 1−⊗Λ
[ ]ZA 2−⊗ΛΛ
[ ]ZA 1−⊗Ξ0
[ ]11 +⊗Ξ − ZA-
[ ]1+⊗π ZA-
[ ]ZA [ ]1+ZA [ ]2+ZA
S=0 nucleiS=-1S=-2
500
400
300
200
100
0
Excitation energy(MeV)
)K,K( - +
)K,(),,K( -- ++ ππ)K,(),,K( - ++− ππ
Coherent Λ-Σ mixingin neutron-rich medium.
Issue @J-PARC