1. Kaon Absorption from Kaonic Atoms and
Formation Spectra of Kaonic Nuclei
J. Yamagata (Nara Women’s Univ.)
H. Nagahiro (RCNP, Osaka Univ.)
D. Jido (YITP, Kyoto Univ.)
S. Hirenzaki (Nara Women’s Univ.)

2. Introduction Kaonic Nuclei Our study J-PARC 3He target
-- Signals for kaonic nuclei even with large width?
( only a few subcomponents )
Theoretical Study ( Kpp bound states )
Structure : Akaishi, Yamazaki, Dote ; N. V. Shevchenko, A. Gal, J. Mares；
Ikeda, Sato; Dote, Weise
Reaction : Yamagata, Nagahiro, Jido, Hirenzaki ; Koike, Harada
(cf: K-pp system : FINUDA. Interpretation by known process ; Oset, Toki)
Our study
Kaonic Nuclei : He, t targets
Kaonic Nuclei : 16O targets
Deeply bound Kaonic Atoms
Comments on Kaon Absorption
J-PARC
Yamagata, Nagahiro, Okumura, Hirenzaki,
PTP114(05)301 ; Errata 114(05)905
Yamagata, Nagahiro, Hirenzaki,
PRC74(06)014604
Yamagata, Hirenzaki, EPJA31(07)255
Yamagata, Nagahiro, Kimura, Hirenzaki
in preparation

3. Our Theoretical Tools Formation spectra in Green function method
Bound state by solving Klein-Gordon equation
Optical potential
Chiral Unitary Model
(1) T(r,E)r(r)
　　　　　　　　　　　　 Higher order medium modifications
(2) T(r=0,E)r(r)
　　　　　　　　　　　　　　　　　 Linear density
Phenomenological Model
(1)
(2) [T. Yamazaki, Y. Akaishi, PLB535(02)70]
O. Morimatsu, K. Yazaki, NPA435(85)727, NPA483(88)493
E. Oset and L. L. Salcedo, J. Comput. Phys. 57 (85) 361
[A. Ramos, E. Oset, NPA671(00)481]
[Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]
[ E. Oset, A. Ramos, Nucl. Phys. A635 (98)99]
[ E. Oset, A. Ramos, C. Bennhold, Phys. Lett. B527(02)99]
[Batty, Friedman, Gal, Phys. Rep. 287(97)385]

4. 1. Kaonic Nuclei - Light nuclear targets
Optical Potential
Chiral Unitary -- T(r=0,E)r(r)　　 Linear density
E. Oset, A. Ramos, Nucl. Phys. A635 (98)99
E. Oset, A. Ramos, C. Bennhold, Phys. Lett. B527(02)99
K-pp
K-pn
K-nn
Re Vopt [MeV]
E = 0 [MeV]
-50 [MeV]
-100[MeV]
Im Vopt [MeV]
r [fm]
r [fm]
r [fm]

5. 1. Kaonic Nuclei - Light nuclear targets
Formation Spectra　-- Chiral Unitary -- T(r=0,E)r(r)　 Linear density
3He (K-,n)
K－pp
3He (K-,p)
K－pn
t (K-,p)
K－nn
1s : 42.0 MeV (41.1 MeV)
2p ; 19.1 MeV(46.3 MeV)
3d : 11.6 MeV(40.0 MeV)
1s : 22.6 MeV (40.4 MeV)
2p ; 11.2 MeV(38.4 MeV)
Tn [MeV]
Tp [MeV]
Tp [MeV]
B.E. (Width)

6. 1. Kaonic Nuclei - Light nuclear targets
Linear density vs. Higher order medium modifications
K-pn(T(r=0,E)r(r))
K-pn(T(r,E)r(r))
Re Vopt [MeV]
E = 0 [MeV]
-50 [MeV]
-100[MeV]
Im Vopt [MeV]
r [fm]
r [fm]

7. 1. Kaonic Nuclei
K－pn
Linear density vs. Higher order medium modifications
Kpn(T(r=0,E)r(r))
Kpn(T(r,E)r(r))
Tp [MeV]
Tp [MeV]
Real Kpn : Expected to be in between

8. 1. Kaonic Nuclei K－pp Chiral Unitary (T(r=0,E)r(r)) AY type
T. Yamazaki, Y. Akaishi, PLB535(02)70
Koike, Harada　; nucl-th/
Chiral Unitary
(T(r=0,E)r(r))
AY type
Different origin !
Tn [MeV]
Tn [MeV]

9. Kaonic Nuclei ( KNN systems ) – Comments on our calculation
We don’t calculate structure as few body systems.
We need to evaluate 2 body absorption correctly.
Chiral Unitary Model
T(r=0,E) --- only 1 body absorption
T(r,E) more than 3 body absorption
We assume density distribution of pp and nn system.
Real KNN states (only 1 and 2 body absorption)

10. 2. Kaonic Nuclei (16O) Optical Potential Chiral Unitary Model
Phenomenological Model
[A. Ramos, E. Oset, NPA671(00)481]
[Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]
[Batty, Friedman, Gal, Phys. Rep. 287(97)385]
E = 0 [MeV]
-50 [MeV]
-100[MeV]

11. Please ask Kishimoto group
Energy dependent
2. Kaonic Nuclei (16O)
Chiral Unitary
16O(In-flight K,n) PK = 930 MeV/c
Please ask Kishimoto group
for experimental data.
Phenomenology
80%:20%
Comparison with
Kishimoto group’s data
[ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003)264 ]
[ Fig. taken from the seminar by Dr. Hayakawa ]

12. 3. Deeply bound Kaonic Atoms -- 12C(K-,p)
Chiral Unitary Model
Atomic State

13. 3. Deeply bound Kaonic Atoms
Proton hole state –
12C
Chiral Unitary
Phenomenology 1s 2p 1s 2s 2p 2s
Dip !!
Dip !! 1s 2p
120Sn 2s 1s 2p 2s
These are very interesting structures !!

14. 4. Comments on Kaon Absorption
What the data mean?
Kaon absorption from Kaonic Atoms
Observed ratio 1 body : 2 body = 80 : 20 for 12C
The density probed by the Kaonic Atoms
: Overlapping density N K K
12C
Chiral Unitary
Phenomenology p
T. Yamazaki,
S. Hirenzaki
PLB557
(03)20

15. Im Vopt : 1body abs. (r term) 2 body abs. (r2 term)
Formation Spectra
E=0 MeV
-100
-50
80 : 20
Absorption
(a) from 2p state
(b) from 3d state

16. Summary We have studied Kaonic Nuclei (for light nuclear targets)
Kpp and Kpn (T(r=0,E)r(r))
-- Bound state exist in complex E plane
-- Peak positions are not corresponding to the binding energy
Knn (T(r=0,E)r(r))  no bound states
Kpn (T(r,E)r(r)) -- Smooth spectra, no peak.
Kaonic Nuclei ( for 16O)
We have found smooth slope in spectra.
(good agreement with the latest experimental analysis)
Deeply bound Kaonic Atoms
We have found very interesting structure.
(no experimental evidence so far)
Comments on Kaon Absorption
The strong K-atomic state dependence of the nuclear density probed by atomic kaon. (meanings of the observed ratio of 1 to 2 body abs.)
 evaluation of 2 body absorption is very important!!