KEK Aug. 4, 2015
KEK理論センター JPARC分室、JAEA先端基礎研究センター共催研究会「ストレンジネス核物理の発展方向」
Aug. 3–7, 2015
19Fを標的とする sd殻ハイパー核の生成断面積(Productions of sd-shell hypernuclei)
Atsushi UMEYA (Nippon Inst. of Tech.)
Toshio MOTOBA (Osaka E.C. Univ.)
KEK Aug. 4, 2015Introduction
S = −1 sector (Λ hypernuclei, ΛN interaction)(π+,K+) reaction (for wide-mass region)
O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57, 564 (2006).
γ spectroscopy (for p-shell hypernuclei)H. Tamura, Nucl. Phys. A827, 153c (2009).
Effective ΛN interaction (for s- and p-shell hypernuclei)VeffΛN = V0+Vσσ σN ·σΛ+VSLS ℓΛN ·(s
Λ+ sN)+VALS ℓΛN ·(s
Λ− sN)+VTensor S12
• p-shell model D.J. Millener, Nucl. Phys. A 804, 84 (2008).• Few-body E. Hiyama, Prog. Part. Nucl. Phys. 63, 339 (2009).
Next stage of hypernuclear studies• sd-shell region←− This study• S = −2 sector (Ξ hypernuclei)• ΛN-ΣN coupling interaction, ΞN-ΛΛ coupling interaction
1
KEK Aug. 4, 2015Λ hypernuclei in sd-shell region
• The level structures of sd-shell nuclei are richer and more complexthan those of p-shell nuclei.
For example• Parity doublet E(19Ne, 1/2−) − E(19Ne, 1/2+g.s.) = 0.275MeV• Rotational band
Effects of hyperon addition for these core nuclei?• Even the Λ single-particle energies are not well known experimentally.Production experiments• (K−, π−) reaction — J-PARC E13 (Production of 19
ΛF, γ spectroscopy)
• (e, e′K+) reaction — JLab, MAMI
This studyEnergy levels, production cross-sections and electro-magnetictransitions of 19
ΛF (balence 2N in sd-shell)
2
KEK Aug. 4, 2015Energy levels of 11C, 19F, 19Ne
0
1
2
3
4
5
6
7
0.000
2.124
6.791
1/2+1/2−5/2+
0.0000.110
5/2−0.1971.346
1/2+1/2−5/2+
0.0000.238
5/2−0.2751.508
Ene
rgy
(MeV
)
11C 19F 19Ne
3/2−
1/2−
4.4455/2−
5.0203/2−
6.7437/2−1/2+
3
KEK Aug. 4, 2015J-PARC E13 Experiment
1/2+
3/2+
5/2+
7/2+
1/2+ 1/2−
1+ (0.000)
3+ (0.937)
0− (1.081)0+ (1.042)
Exp. MeV
M1
E2
E2 E1M1 M1
ΛN spin-spin interaction
E13 : 19ΛF spectroscopy
18F19ΛF
The first study of sd-shell hypernuclei
19F (K−, π− ) J-PARC E13γ spectroscopy(E1, M1, E2 transitions)for low-lying states of 19
ΛF
⇓This studyCalculation of theproduction cross-sectionof 19Λ
F by the (K−, π−)reaction at incidentmomentum of 1.8 GeV/c
4
KEK Aug. 4, 2015Shell model calculation (1)
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n
0~ω basis statespositive parity
1~ω basis statesnegative parity
5
KEK Aug. 4, 2015Shell model calculation (2)
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n p n
two-bodyinteraction
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n
single-particle energy
core energy
6
KEK Aug. 4, 2015Shell-model wave functions (1)
Model space (for 19Λ
F)• 16 nucleons are inert in the 16O core.• 2 valence nucleons move in the sd-shell orbits.• 1p-1h 1~ω-excited states are considered for J− states.• Λ hyperon is assumed to be in the 0s, 0p, sd-shell orbits.
Core states (18F) + parity (J+core) (0s)4 (0p)12 (sd)2 (0p-0h)
− parity (J−core) (0s)4 (0p)11 (sd)3 (1p-1h)
Λ single-particle state + parity ( j+Λ
) 0sΛ1/2, 0dΛ5/2, 0dΛ3/2, 1sΛ1/2− parity ( j−
Λ) 0pΛ3/2, 0pΛ1/2
4 types of basis states (1) J+core ⊗ j+Λ
positive (2) J+core ⊗ j−Λ
negative
(3) J−core ⊗ j+Λ
negative (4) J−core ⊗ j−Λ
positive
7
KEK Aug. 4, 2015Shell-model wave functions (2)
4 types of basis states (For example, basis states of 19Λ
F)
J+core ⊗ j+Λ
positive J+core ⊗ j−Λ
negative
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n Λ
0p3/2
0s1/2
0d5/2 0d3/2
0p1/2
1s1/2
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n Λ
0p3/2
0s1/2
0d5/2 0d3/2
0p1/2
1s1/2
J−core ⊗ j+Λ
negative J−core ⊗ j−Λ
positive
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n Λ
0p3/2
0s1/2
0d5/2 0d3/2
0p1/2
1s1/2
0p3/2
0s1/2
0d5/2
0d3/2
0p1/2
1s1/2
p n Λ
0p3/2
0s1/2
0d5/2 0d3/2
0p1/2
1s1/2
8
KEK Aug. 4, 2015Shell-model HamiltonianTwo-body interactionNN effective interaction⟨(sd)2|V |(sd)2⟩
modified Kuo-Brown G-matrixNP85, 40 (1966).PTP52, 509 (1974).
⟨p−1 sd|V |p−1 sd⟩Warburton-Brown PSDT
PRC46, 923 (1992)
ΛN effective interaction⟨NΛ|V |NΛ⟩
NSC97fPRC59, 21 (1999)
Using 2.5VALS to adjust LS splitting
Single-particle energiesfor nucleon orbits
with respect to 16O core
−25
−20
−15
−10
−5
0
5
Sing
le-p
artic
le e
nerg
y
(MeV
)
−21.86
−15.70
−4.14−3.27
0.94
−14.78
−24.000p3/2
0p1/2
0d5/2
1s1/2
0d3/2
Adjusting s.p.e. of 0p3/2 and 0p1/2to reproduce the energy levelsof the 19F J− states
9
KEK Aug. 4, 2015Numerical Results : Energy levels for 19
ΛF and 18F
0
1
2
3
Ene
rgy
(M
eV)
1+
3+
0+
0− 5+
1+
2−
2+
2+1−
3+1+3− 2+
1/2+
3/2+ 5/2+ 9/2+ 1/2− 7/2+ 1/2+ 11/2+
3/2− 5/2−
3/2+ 5/2+
3/2− 1/2+ 1/2− 7/2− 5/2−
PSfrag replacements
∆E = 0.419 MeV
18F (exp.) 18F (cal.) 19Λ
F (cal.)(18O (exp.)) (18O (cal.)) (19
ΛO (cal.))
10
KEK Aug. 4, 2015Configuration of ground state of 19F
| 19F; 1/2+g.s. ⟩ = +√
0.11 | (16O)(0d5/2)3 ⟩
+√
0.31 | (16O)(0d5/2)2T=1,J=0(1s1/2) ⟩
−√
0.14 | (16O)(0d5/2)2T=0,J=1(1s1/2) ⟩
+√
0.11 | (16O)(0d5/2)(0d3/2)(1s1/2) ⟩
+√
0.17 | (16O)(1s1/2)3 ⟩
+ · · ·The ground state of 19F is not described by a simple configurationdue to the 1s
1/2orbit.
=⇒ In the production of 19Λ
F, transition strengths are fragmentedamong several states and have small values.
(Magnetic moment of 19F cal. 2.89µN
, exp. 2.62µN
)
11
KEK Aug. 4, 2015Spectroscopic factors of pickup reaction from 19F
0
1
2
3E
nerg
y (M
eV)
1+
3+ 0+0− 5+
1+
2−
2+
2+1− 3+1+3− 2+
0 1C2S (Exp.)
0.65
1.470.270.38
0.74
1.04
0.220.50
1+
3+ 0+0− 5+
2−
2+1−3−
1+2+
0 1C2S (Cal.)
0.52
0.680.180.23
0.250.63
0.21
12
KEK Aug. 4, 2015Cross sections of 19F(π+, K+) and 19F(K−, π−)
−20
−15
−10
−5
0
5
10
0 10 20
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
9/2+ 9/2+
7/2−
3/2−
3/2−(Τ=1)
7/2−
5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (π+,K+) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pπ = 1.05 GeV/c, θLab= 2
q = 316–346 MeV/c−20
−15
−10
−5
0
5
10
0 500 1000 1500 2000
0sΛ
0pΛ
sdΛ
1/2+
1/2+ 1/2+(Τ=1)1/2+
1/2+(Τ=1)
3/2−
3/2−
3/2−(Τ=1)
1/2+ 1/2+
1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 0.80 GeV/c, θLab= 2
q = 51–74 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
13
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different incident momemta (1)
−20
−15
−10
−5
0
5
10
0 100 200 300 400 500
0sΛ
0pΛ
sdΛ
5/2+
5/2+ 1/2+ 5/2+ 3/2+ 5/2+(Τ=1)
3/2− 3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
3/2− 1/2−
1/2+
1/2+(Τ=1)
1/2+
1/2−(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 0.80 GeV/c, θLab= 10
q = 142–151 MeV/c−20
−15
−10
−5
0
5
10
0 20 40 60 80 100 120
0sΛ
0pΛ
sdΛ
5/2+
5/2+ 5/2+ 7/2+ 5/2+(Τ=1)
5/2+
3/2− 3/2− 5/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
5/2+ 5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.10 GeV/c, θLab= 10
q = 200–208 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
14
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different incident momemta (2)
−20
−15
−10
−5
0
5
10
0 10 20 30 40
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
5/2+ 5/2+ 5/2+(Τ=1) 9/2+ 7/2+ 5/2+
9/2− 7/2−
3/2−
3/2−(Τ=1)
3/2+ 5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.50 GeV/c, θLab= 10
q = 272–279 MeV/c−20
−15
−10
−5
0
5
10
0 10 20 30
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
9/2+
7/2−
3/2−
3/2−(Τ=1)
7/2−
3/2+ 5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 10
q = 324–332 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
15
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different scattering angles (1)
−20
−15
−10
−5
0
5
10
0 50 100 150 200
0sΛ
0pΛ
sdΛ
5/2+
5/2+ 1/2+
3/2− 3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
3/2− 1/2−
1/2+ 1/2+
1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 2
q = 126–149 MeV/c−20
−15
−10
−5
0
5
10
0 50 100 150
0sΛ
0pΛ
sdΛ
5/2+
5/2+
3/2− 3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
3/2− 1/2−
1/2+ 5/2+(Τ=1)1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 4
q = 164–182 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
16
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different scattering angles (2)
−20
−15
−10
−5
0
5
10
0 50 100
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
5/2+
3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 6
q = 213–224 MeV/c−20
−15
−10
−5
0
5
10
0 10 20 30 40 50 60
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
5/2+
3/2− 7/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
3/2+ 5/2+ 5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 8
q = 267–276 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
17
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different scattering angles (3)
−20
−15
−10
−5
0
5
10
0 10 20 30
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
9/2+
7/2−
3/2−
3/2−(Τ=1)
7/2−
3/2+ 5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 10
q = 324–332 MeV/c−20
−15
−10
−5
0
5
10
0 5 10 15
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
9/2+
3/2− 7/2−
7/2−
5/2+
5/2+(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 12
q = 381–387 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
18
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) for low-lying states (1)
0
1
2
3
Exc
itatio
n E
nerg
y E
(MeV
)
1/2+(0) 0.000
3/2+(0) 0.419
5/2+(0) 0.727 9/2+(0) 1.156 7/2+(0) 1.289 1/2−(0) 1.311 1/2+(1) 1.317
11/2+(0) 1.564 3/2−(0) 1.965 5/2−(0) 2.169
3/2+(1) 3.082 5/2+(1) 3.151
3/2−(0) 3.223 1/2+(0) 3.203
1/2−(0) 3.331
0 10 20 30
0.26
0.00
8.15 0.00 0.03
16.85 0.09 0.00
0.07 0.00
1.81 1.33 0.03
34.18 1.89
0 10 20 30
1.92
0.04
12.38 0.00 0.18
17.73 0.68 0.00
0.08 0.00
2.72 2.02
35.61 0.00
1.97
0 10 20 30
6.13
0.29
14.24 0.00 0.49
13.51 2.15 0.00
0.06 0.00
3.11 2.40 0.00
26.96 1.49
0 10 20
7.97
0.72
11.18 0.00 0.76
6.50 2.87 0.00
0.03 0.00
2.45 1.99 0.00
12.93 0.71
PSfragreplacem
ents
19F (K−, π−) 19Λ
F pK = 1.80 GeV/c
Cross Section dσ/dΩ (µb/sr)
Energy Level θLab= 2 4 6 8
10
12
19
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) for low-lying states (2)
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12
114.1 129.3 167.0 215.5 269.1 325.1 382.4
1/2+(Τ=0)0.0005/2+(Τ=0)0.7271/2−(Τ=0)1.312
3/2+(Τ=1)3.082+5/2+(Τ=1)3.1513/2−(Τ=0)3.2231/2−(Τ=0)3.3313/2−(Τ=1)5.772
PSfrag replacements
Scattering Angle θLab (deg)
Momentum Transfer q (MeV/c)
Cro
ssSe
ctio
ndσ/dΩ
(µb/
sr)
19F (K−, π−) 19Λ
F pK = 1.80 GeV/c
20
KEK Aug. 4, 2015M1 and E2 transitions of 18F
1+
3+
5+
0+
2+
0−
2−
1−
E2 20.31) (16.77)
E2 18.61) (16.62)
E2 15.78) (22.39) E2 31.61)
(45.56)
M1 6.88) (3.79)
M1 0.12) (0.38)
M1 17.02) (19.72)
M1 0.0159) (0.0042)
3−4+
Cal. (Exp.)
B(M1) µ2NB(E2) e2 fm4
Cal. (Exp.)
J+, T =0 J+, T =1
J−, T =0
Adjusting effective chargesto reproduce the experimentalE2 transition strengths
21
KEK Aug. 4, 2015E1 transitions of 18F
1+
3+
5+
0+
2+
0−
2−
1−
1.89×10−5)(1.81×10−5)
3−4+
Cal. (Exp.)
B(E1) e2 fm2
J+, T =0
J+, T =1
J−, T =0
5.61×10−7)(5.10×10−6)
3.68×10−6)(2.45×10−5)
7.51×10−5)(6.00×10−5)
2.44×10−7)(2.05×10−5)
2.25×10−4)(2.55×10−4)
Adjusting effective chargesto reproduce the experimentalE1 transition strengths
22
KEK Aug. 4, 2015E2, M1 and E1 transitions of 19
ΛF
1/2+
5/2+
7/2+ 1/2−
3/2−5/2−
0.06
0.33
J+, T =0 J+, T =1 J−, T =0
3/2+
9/2+
11/2+
0.92
17.1
3
4.35
17.4
2
19.7
7
2.02
1.67
18.4
15/2+
0.35
5.05
11.5
6
0.34
1.39 0.
07
6.25
0.12
0.51
6.54
15.9
10.52
0.01
0.04
0.30
0.29
32.8
031
.56
9.71
0.11
0.08
0.10
0.040.42
2.88
1.86
×10−5
6.32
×10−6
4.72
×10−8
2.09
×10−6
3.74
×10−7
3/2+
1/2+
B(E1) e2 fm2
B(M1) µ2N
B(E2) e2 fm4
23
KEK Aug. 4, 2015Summary
As a typical gate to medium-heavy sd-shell hypernuclei, we havecalculated the energy levels, the production cross sections andelectro-magnetic transition strengths of 19
ΛF by using the
multi-configuration shell model.
1/2+ (0.000)
3/2+ (0.419)
5/2+ (0.727)
7/2+ (1.289)
1/2+ (1.317)1/2− (1.311)
1+ (0.000)
3+ (0.917)
0− (1.107)0+ (1.063)
Cal. MeV
Cal. MeV
M1 0.33 µ2Ν
E2
E2 E1M1 M1
ΛN spin-spin interaction
E13 : 19ΛF spectroscopy
18F19ΛF
The first study of sd-shell hypernuclei
19F (K−, π− )∆E(3/2+ − 1/2+g.s.) = 0.419 MeVB(M1; 3/2+→1/2+g.s.) = 0.33 µ2
NHowever the cross section of 3/2+states is the small value ofdσ/dΩ = 0.29 µb/srin 19F(K−, π−)19
ΛF with
pK= 1.80 GeV/c and θLab = 6.
24
KEK Aug. 4, 2015
M1 M1
E2 M1
E2
M1
E2
1/2+ (0.000)
3/2+ (0.419)
5/2+ (0.727)
7/2+ (1.289)
1/2+ (1.317)1/2− (1.311)
1+ (0.000) (0.000)
3+ (0.937) (0.917)
0− (1.081) (1.107)0+ (1.042) (1.063)
Cal. MeV
Cal. MeV
0.33 µ2Ν
ΛN spin-spin interaction
E13 : 19ΛF spectroscopy (Shell-model calculation)
18F19ΛF
The first study of sd-shell hypernuclei
19F (K−, π− )
1.86×10−5
0.35
4.35
17.13
6.32×10−6
19.77
11.56
5.05
B(E1)B(M1)B(E2)
e2 fm
4 µ2N
Exp. MeV
E1 E1
e2 fm
2
25
KEK Aug. 4, 2015
Backup
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different incident momemta (a)
−20
−15
−10
−5
0
5
10
0 500 1000 1500 2000
0sΛ
0pΛ
sdΛ
1/2+
1/2+ 1/2+(Τ=1)1/2+
1/2+(Τ=1)
3/2−
3/2−
3/2−(Τ=1)
1/2+ 1/2+
1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 0.80 GeV/c, θLab= 2
q = 51–74 MeV/c−20
−15
−10
−5
0
5
10
0 50 100 150 200 250
0sΛ
0pΛ
sdΛ
1/2+
1/2+ 1/2−(Τ=1) 1/2−
1/2−(Τ=1)
3/2− 3/2−
3/2−
1/2+ 1/2+
1/2+(Τ=1)
1/2+
3/2−(Τ=1)
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.10 GeV/c, θLab= 2
q = 83–107 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
1
KEK Aug. 4, 2015Cross sections of 19F(K−, π−) at different incident momemta (b)
−20
−15
−10
−5
0
5
10
0 50 100
0sΛ
0pΛ
sdΛ
1/2+ 5/2+
5/2+ 1/2+ 1/2+
1/2+(Τ=1)
3/2− 3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
1/2+ 1/2+
1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
FH
yper
nucl
earE
nerg
yEΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.50 GeV/c, θLab= 2
q = 111–134 MeV/c−20
−15
−10
−5
0
5
10
0 50 100 150 200
0sΛ
0pΛ
sdΛ
5/2+
5/2+ 1/2+
3/2− 3/2−
1/2− 3/2−
3/2−(Τ=1)1/2−(Τ=1)
3/2− 1/2−
1/2+ 1/2+
1/2+(Τ=1)
1/2+
PSfragreplacem
ents
19F (K−, π−) 19Λ
F
Hyp
ernu
clea
rEne
rgy
EΛ
(MeV
)
Cross Section d2σ/dΩdE (µb/sr/MeV)
pK = 1.80 GeV/c, θLab= 2
q = 126–149 MeV/c
: J+core ⊗ j+Λ
, : J+core ⊗ j−Λ
, : J−core ⊗ j+Λ
, : J−core ⊗ j−Λ
2
KEK Aug. 4, 2015Cross section of 19F(γ, K+)32 T. Motoba / Nuclear Physics A 914 (2013) 23–33
Fig. 8. Excitation spectrum for the 19F(γ ,K+)19Λ
O reaction calculated in DWIA at Eγ = 1.3 GeV and θLabK
= 3 .
Another series of peaks marked by B1 and B2 are based on the second lowest proton p−11/2 hole
(the 0− state at 6.88 MeV [29]) coupled with sΛ and pΛ, respectively.
6. Concluding remarks
Encouraged by the precision measurements of the (e, e′K+) experiments performed at the
Jefferson Laboratory and also by the remarkable success of the theoretical predictions, we
have extended the calculation of hypernuclear photo-production cross section to typical sd- and
fp-shell cases. Because of the sizable momentum transfer and the spin-flip dominance in the ele-
mentary amplitudes, first we have demonstrated that high-spin series of unnatural parity states in
hypernuclei are selectively excited for jj -closed-shell targets. In fact, the predictions done some
years ago for 28Si(γ ,K+)28ΛAl have been remarkably confirmed by the recent 28Si(e, e′K+)28
ΛAl
experiment.
Secondly, when an LS-closed target is employed, a series of high-spin natural parity states
are shown to be preferentially excited. In both cases, it is also interesting to predict subseries of
peaks, the characters of which are clearly related to the conversion of inner core protons.
As the unique character of the strangeness photo-production process appears more clearly in
medium-heavy systems, we emphasize the merit of using the (e, e′K+) reaction on medium-mass
nuclear targets so as to extract the hyperon single-particle energies with the remarkable precision
of a few hundred keV. As hypernuclear structures beyond p-shell have not been studied so far in
detail, we emphasize that sub-MeV reaction spectroscopy of sd- and fp-shell hypernuclei surely
opens interesting opportunities in understanding the dynamical interplay between a hyperon and
a variety of nuclear core excitations.
Acknowledgements
This report is based on the long collaboration with P. Bydžovsky, M. Sotona, K. Itonaga,
K. Ogawa and O. Hashimoto. The author would like to dedicate this paper to the memory of
3