KEK JPARC 分室、JAEA...

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

)


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

)



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

)



q = 200–208 MeV/c

: 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

)



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

)



q = 324–332 MeV/c

: 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

)



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

)



q = 164–182 MeV/c

: J+core ⊗ j+Λ




16


−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

)



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

)



q = 267–276 MeV/c

: J+core ⊗ j+Λ




17


−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

)



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

)



q = 381–387 MeV/c

: 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


E13 : 19ΛF spectroscopy

18F19ΛF


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


E13 : 19ΛF spectroscopy (Shell-model calculation)

18F19ΛF


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

)



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

)



q = 83–107 MeV/c

: 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

)



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

)



q = 126–149 MeV/c

: 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

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