Electroproduction of
medium-heavy L-hypernuclei
Toshio MOTOBA （Osaka E-C)
major part done in collaboration with
P. Bydzovsky ( Prague)
M. Sotona ( Prague)
K. Itonaga ( Gifu )
K. Ogawa ( Chiba )
O. Hashimoto ( Tohoku )
JSPS Core-to-Core Seminar
EU SPHERE Network Meeting
September 4-6, 2010, Villa Lanna, Prague
1
CONTENTS
1. Basic motivationｓ for medium-heavy
systems
2. Go to sd-shell: “Simplest” target (19F)
and the (d5/2)6 model to demonstrate the
present theoretical treatments.
3. Realistic predictions for photo-production
reaction with a typical target 28Si(g, K+)L28Al
4. Extension of the approach to produce
heavier hypernuclei around A=40-52
5. Outlook
2
1. Basic motivation:
Why medium-heavy hypernuclei ?
(1)
The great success of Hall A and Hall C
experiments at Jlab:
-- sub-MeV ( G= approx. 0.5 MeV)
-- predictions for p-shell confirmed
encourages
extension of high-resolution reaction
spectroscopy to heavier hypernuclei:
3
(K-,p-)
(p＋,K+)
played a great role of
exciting high-spin series
G = 1.5 MeV (best)
(e,e’K+), (g, K+)
Motoba. Sotona, Itonaga,
Prog.Theor.Phys.S.117(1994)
T.M. Mesons & Light Nuclei
(2000) updated w/NSC97f.
------------------------------JLab Exp’t : G = 0.5 MeV
4
Theor. prediction vs. (e,e’K+) experiments
Theory
Motoba. Sotona, Itonaga,
Prog.Theor.Phys.Sup.117 (1994)
T.M. Mesons & Light Nuclei (2000)
updated w/NSC97f.
-------------------- Sotona’s Calc.----
Hall C (up) T. Miyoshi et al.
P.R.L.90 (2003) 232502. G=0.75 MeV
Hall A (bottom), J.J. LeRose et al.
N.P. A804 (2008) 116. G=0.67 MeV
5
Why medium-heavy hypernuclei ?
motivation (2)
Unique characteristics of the (e,e’K+), (g, K+)
process are based on the basic Properties
of elementary amplitudes for g p → LK+ :
--- sizable momentum transfer to
excite high-spin states, like (p＋,K+)
--- spin-flip dominance of the operator,
leading to unnatural parity states
6
Comparison of the recoil momentum
qL=350-420 MeV/c at Eg=1.3 GeV
7
Elementary amplitudes (2CM): gpLK+
8
Lab ds/dW for photoproduction (2Lab)
9
These characteristic merits of the
+
gp → L K process(ability to excite
high-spin unnatural-parity states)
should be realized better in
heavier systems involving
large jp and large jL
(e,e’K+)
d3s/dEe dWe dWK = G x ds/dWK
G : virtual photon flux (kinematics)
Hereafter we discuss ds/dWK for
AZ
(g,K+)LAZ’
10
2. Go to sd-shell:
2-1. Simplest sd-shell target
Choose 19F(1/2+) target
for demonstration of the hypernuclear
photoproduction
(asking the feasibility as a practical target )
11
2
2
2
2
Choose 19F(1/2+) target for demonstration
0d3/2
1s1/2
1s1/2
1s1/2
0d5/2
0d5/2 0p1/2
0p1/2 0p3/2
0d5/2
0p1/2
0p3/2
外側の
0d3/2
軌道
16
0p1/2
O
0p3/2
0s1/2
0d5/2
0p1/2
0p3/2
0s1/2
E
0p3/2 0s1/2
0d3/2
0s1/2 0d
1s1/2
3/2
0d3/2
1s1/2
0d5/2
1s1/2 0d
0d5/2 0p
0p8MeV
0p3
1/2
0d3/2
0d3/2
1s1/2
1s1/2
0d5/2
0d5/2
0p1/2
0p1/2
0p3/2
0p3/2 0s
-2.5MeV
0s
1/2
1s1/2
0d5/2
0p1/2
0p3/2
0s1/2
-13MeV
0s1/2
閉殻
0p3/2
0s1/2
0d3/2
Λ粒子の生成軌道
中性子の軌道
neutron
陽子の軌道
proton
L (DDHF)
Partial contributions
Conversion of 1s1/2-proton(nb/sr)
35
1s1/2軌道からの生成断面積
60
30
d
20
10
0
-15
-10
-5
0
5
10
15
ハイパー核励起エネルギー〔ＭｅＶ〕
20
生成断面積〔μb／ｓｒ〕
50
40
-20
1s1/2 軌道から
0d5/2 軌道から
30
p
生成断面積〔 μb/ sr〕
s
Cf. a trial calculation:
If the last odd proton
were in 0d5/2, then
25
20
15
10
5
0
-13
-2.5 -2.3
8.3
エネルギー　〔MeV〕
8.4
8.5
Partial contributions
Conversion from 1p3/2
Conversion from 0p1/2
p
20
15
10
s
-10
-5
0
5
10
15
ハイパー核励起エネルギー〔ＭｅＶ〕
20
35
d
30
生成断面積〔μb/sr〕
25
-15
40
30
d
-20
0p3/2軌道からの生成断面積
35
25
p
20
15
10
s
5
5
0
0
-20
-15
-10 -5
0
5
10
15
ハイパー核励起エネルギー〔ＭｅＶ〕
20
生成断面積〔μb/sr〕
0p1/2軌道からの生成断面積
19F(g,K+)
L
19O
SUM γ線によるハイパー核Λ19Oの生成断面積
of the partial contributions
60
合計
1s1/2
0p1/2
50
40
30
20
生成断面積〔μb/sr〕
0p3/2
10
0
-20
-15
-10
-5
0
5
10
ハイパー核励起エネルギー〔ＭｅＶ〕
15
20
As a “closed core (18O)”+ L , cf. SO-splitting(0p)=152+-54 keV(C13)
2-1. Single-j model for
28
the Si target
A typical example of medium-heavy
target :28Si: (d5/2)6
to show characteristics of
the (g,K+) reaction with DDHF w.f.
( Spin-orbit splitting:
consistent with L7Li, 9Be,13C, 89Y )
16
Theor. x-section for (d5/2)6 (g,K+) [ ｊh-ｊL]J
17
XS(J)
DWIA
(65%)
vs.
PWIA
18
ds/dW(qK): angular dependence
19
[ j<-1 j>L]
20
3. Realistic prediction for
28Si
(g,K+) L28Al
By fully taking account of
-- full p(sd)6.n(sd)6 configurations,
-- fragmentations when a proton is converted,
-- 27Al core nuclear excitation
-- K+ wave distortion effects
 Comparison with the 28Si (e,e’K+) exp.
21
proton-state fragmentations should
be taken into account to be realistic
22
Proton pickup from 28Si(0+):(sd)6 =(d5/2)4.1(1s1/2)0.9(d3/2)1.0
23
23
Peaks can be classified by the characters
24
•
25
Peak energies: 28LSi vs. 28LAl
H.Hotchi et al, PRC 64(2001) vs.
28Si(p+,K+)28 Si
L
j
L
s
p
O.Hashimoto et al, NP A804(2008)
28Si(e,e’K+)28 Al
L
EL=-BL (Ex )
(as read on the
Sendai08 poster)
-16.6+-0.2 (GS)
-17.85 ?? (GS)
-16.6 (GS)
-15.7 ?
-13.0 ?
-10.8 ?
-11.9+-0.4 (Ex=4.7)
-7.0+-0.2 (Ex=9.6)
- 6.88 +- ?? (Ex=11)
-4.3+-0.2 (Ex=12.4)
d
+1.0+-0.8 Ex=17.6)
(g,K+)
-8.1
CAL
( Ex=8.5)
-5.6, -4.0
+ 1.35 +/- (Ex=19.2)
+0.9 (Ex=17.5)
26
26
4. Extend to heavier
nuclear Targets
52Cr:
(f7/2)4 assumed
40Ca: (sd-shell LS-closed)
27
Well-separated series of peaks
due to large q and spin-flip dominance:
j>=l+1/2, j<=l-1/2
28
52Cr
( j> dominant target case)
typical unnatural-parity high-spin states
29
40Ca
( LS-closed shell case):
high-spin states with natural-parity (2+,3-,4+)
30
6. SUMMARY
31
.
was made.
３) Realistic prediction for the
target
The calculation is in good agreement with the
recent JLab exp. The predictions are made also
for 40Ca and 52Cr.
28Si
4) Almost all predictions for the p-shell targets have
been confirmed by the recent Jlab exp.(Hall A, C).
5) Medium-mass hypernuclear production by
(e,e’K+) provide us with good opportunities in
understanding the details of the hyperon motion
in nuclear matter.(L-s.p.e. to establish “textbook”,
Rotation/Vib.-L coupling, Auger effect, mL ,
eeff (L), etc )
32
Single-particle energies of L
33
89Y
SO splitting in
vs.
Nijmegen models
34
35
Additional part:
Demonstration of
p-Shell Targets:
(Full shell model cal.)
7Li, 9Be,10B, 12C, 14N, 16O
36
16O
target:
Prediction
Motoba-SotonaItonaga, P.T.P.
Suppl.117 (1994)
Hall A Exp:
J.J.LeRose et al.,
Nucl.Phys.
A804, 116
(2008)
37
10B
target:
Prediction
Motoba-SotonaItonaga, P.T.P.
Suppl.117 (1994)
compared
with
x
other theoretical
calculations for
(K-,p-)
(p+,K+)
38
9Be
target:
Prediction
Motoba-SotonaItonaga, P.T.P.
Suppl.117 (1994)
Hall A Exp:
c
J.J.LeRose et al.,
Nucl.Phys.
A804, 116
(2008)
39
40
41
Comparison with new
exp. data JLab Hall C
Hashimoto et al.,
Nucl. Phys. A804 (2008)
Major peaks:
as redicted
Satellite
peaks ?
Wait for
the final
report.
42
Left：Hotchi et al., PRC 64 (2001) Λ51V, Λ89Y,
R:Hasegawa et al., PRC 53 (1996) Λ139La, Λ208Pb
43
..
44
All the existing exp.data can be explained.
Genuine hypernucear states confirmed !
For further example,
Brief look at the results of
the detailed analysis for
89Y(p+,K+) 89
LY
46
1. Introduction / Motivation
47
L spin-orbit splitting
in heavy hypernuclei as
deduced from DWIA analyses
89
89
+
+
of the Y(p ,K ) L Y reaction
T. Motoba (Osaka E-C U.)
D.E. Lanskoy (Moscow State U.)
D.J. Millener (Brookhaven Nat. Lab.)
Y. Yamamoto (Tsuru U.)
Nucl. Phys. A804 (2008)
48
All the 2p-1h configurations adopted
49
CONCLUSION
(1)Reproduce cross section ratios among a
series of pronounced peaks and sub-peaks.
50
Λ s.p.e.
vs.
DDHF
Mfcal
based
on
realistic
interactions
51
Peak energies: 28LSi vs. 28LAl
H.Hotchi et al, PRC 64(2001) vs.
j
L
28Si(p+,K+)28 Si
L
s
-16.6+-0.2 (gs)
O.Hashimoto et al, NP A804(2008)
28Si(e,e’K+)28 Al
L
EL=-BL (Ex )
-18.5 ?? (gs)
-16.6
- 7.5+- ?? (11)
-15.7,
-14.1,-12.3
-8.1
-11.9+-0.4 (4.7)
p
d
-7.0+-0.2 (9.6)
(g,K+)
CAL
-4.3+-0.2 (12.4)
-5.6, -4.0
+1.0+-0.8 (17.6)
+0.9
52
Kinematics for electroproduction process
e(pe) + p(pp)  e’(pe’)+K+(pK) + L(pL)
A(pA)
HN(pH)
53
Express
the
amplitudes
in
{S2} frame
spinnonflip
term (f )
and
3 spin-flip
terms
(g ‘s)
54
Typical 4 amplitudes
(among 16 sets)
AW2:
Adelseck-Wright,
P.R. C 38 (1988)
AS1:
Adelseck-Shagai,
P. R. C 40 (1990)
C4:
William-JI-Cotanch,
P.R. C 46 (1992)
SL-A:
Mizutani et al.
P.R. C 58 (1998)
55
Polarizations
much
different
from each
other.
need more
exp. data
56
Basic Properties of
Elementary Amplitudes for
g+p→L
+
K
(Physical contents: discussed by Bydzovsky)
(e,e’K+)
d3s/dEe dWe dWK = G x ds/dWK
G: virtual photon flux (kinematics)
Hereafter we discuss ds/dWK for A (g,K+)LA
57
•
58