J. Yamagata (Nara Women’s Univ.)

H. Nagahiro (RCNP, Osaka Univ.)

D. Jido (YITP, Kyoto Univ.)

S. Hirenzaki (Nara Women’s Univ.)

Kaon Absorption from Kaonic Atoms

andFormation Spectra of Kaonic Nuclei

Kaonic Nuclei 3He target -- Signals for kaonic nuclei even with large width 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, WeiseReaction : Yamagata, Nagahiro, Jido, Hirenzaki ; Koike, Harada(cf: K-pp system : FINUDA. Interpretation by known process ; Oset, Toki)

Our study1.1. Kaonic Nuclei : He, t targetsKaonic Nuclei : He, t targets2. Kaonic Nuclei : 16O targets3. Deeply bound Kaonic Atoms 4. Comments on Kaon Absorption

IntroductionJ-PARCJ-PARC

Yamagata, Nagahiro, Okumura, Hirenzaki, PTP114(05)301 ; Errata 114(05)905Yamagata, Nagahiro, Hirenzaki, PRC74(06)014604Yamagata, Hirenzaki, EPJA31(07)255Yamagata, Nagahiro, Kimura, Hirenzaki in preparation

Formation spectra in Green function method

Bound state by solving Klein-Gordon equation

Optical potential Chiral Unitary Model (1) T(,E)(r)　　　　　　　　　　　　 Higher order medium modifications

(2) T(=0,E)(r)　　　　　　　　　　　　　　　　　 Linear density

Phenomenological Model (1)

(2) [T. Yamazaki, Y. Akaishi, PLB535(02)70]

Our Theoretical Tools

O. Morimatsu, K. Yazaki, NPA435(85)727, NPA483(88)493O. Morimatsu, K. Yazaki, NPA435(85)727, NPA483(88)493

E. Oset and L. L. Salcedo, J. Comput. Phys. 57 (85) 361E. Oset and L. L. Salcedo, J. Comput. Phys. 57 (85) 361

[ 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]

[A. Ramos, E. Oset, NPA671(00)481][Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

Optical Potential Chiral Unitary -- T(=0,E)(r) 　　 Linear density

1. Kaonic Nuclei - Light nuclear targetsR

e V

op

t [M

eV

]Im

Vop

t [M

eV

]

r [fm] r [fm] r [fm]

K-pp K-pn K-nn

E = 0 [MeV] -50 [MeV] -100[MeV]

E. Oset, A. Ramos, Nucl. Phys. A635 (98)99 E. Oset, A. Ramos, C. Bennhold, Phys. Lett. B527(02)99

Formation Spectra -- Chiral Unitary -- T(=0,E)(r) Linear density

Tp [MeV]Tn [MeV] Tp [MeV]1s : 42.0 MeV (41.1 1s : 42.0 MeV (41.1 MeV)MeV)2p ; 19.1 MeV(46.3 2p ; 19.1 MeV(46.3 MeV)MeV)3d : 11.6 MeV(40.0 3d : 11.6 MeV(40.0 MeV)MeV)

1s : 22.6 MeV (40.4 1s : 22.6 MeV (40.4 MeV)MeV)2p ; 11.2 MeV(38.4 2p ; 11.2 MeV(38.4 MeV)MeV)

B.E. (Width)

1. Kaonic Nuclei - Light nuclear targets

3He (K-,n) KK －－

ppppKK －－

pppp t (K-,p)3He (K-,p) KK －－

pnpnKK －－

pnpnKK －－

nnnnKK －－

nnnn

Re V

op

t [M

eV

]Im

Vop

t [M

eV

]

K-pn(T(,E)(r))

r [fm]r [fm]

K-pn(T(=0,E)(r))

1. Kaonic Nuclei - Light nuclear targets

E = 0 [MeV] -50 [MeV] -100[MeV]

Linear density vs. Higher order medium modifications

Linear density vs. Higher order medium modifications

Tp [MeV]

Kpn(T(=0,E)(r)) Kpn(T(,E)(r))

Tp [MeV]

KK －－

pnpnKK －－

pnpn

1. Kaonic Nuclei

Real Kpn Real Kpn : Expected to be in between

Tn [MeV]

Chiral Unitary(T(=0,E)(r))

Tn [MeV]

AY typeT. Yamazaki, Y. Akaishi, PLB535(02)70Koike, Harada ; nucl-th/0703037

KK －－

ppppKK －－

pppp

Different origin !

1. Kaonic Nuclei

We don’t calculate structure as few body systems.

We need to evaluate 2 body absorption correctly.Chiral Unitary Model T(=0,E) --- only 1 body absorption T(,E) --- more than 3 body absorption

We assume density distribution of pp and nn system.

1. Kaonic Nuclei ( KNN systems ) – Comments on our

calculation

Real KNN states (only 1 and 2 body absorption)

Optical Potential

2. Kaonic Nuclei (16O)

Phenomenological ModelPhenomenological ModelChiral Unitary Chiral Unitary ModelModel

E = 0 [MeV] -50 [MeV] -100[MeV]

[Batty, Friedman, Gal, Phys. Rep. 287(97)385][A. Ramos, E. Oset, NPA671(00)481]

[Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

16O(In-flight K,n) PK = 930 MeV/c

[ T.Kishimoto et al., Prog. Theor. Phys. Suppl. 149 (2003)264 ]

[ Fig. taken from the seminar slide @NWU by Dr. Hayakawa ]

Comparison with

Kishimoto group’s data

Energy dependent

Chiral Unitary

Phenomenology80%:20%

2. Kaonic Nuclei (16O)

Please ask Kishimoto groupfor experimental data.

Chiral Unitary Model

Atomic StateAtomic State

3. Deeply bound Kaonic Atoms -- 12C(K-,p)

Proton hole state – Chiral Unitary Phenomenology

1s

2p 2s

Dip !!Dip !!

Dip !!Dip !!

3. Deeply bound Kaonic Atoms

1s

2p 2s

1s 2p 2s 1s 2p 2s

1212CC1212CC

120120SnSn120120SnSn

These are very interesting structures !!

Kaon absorption from Kaonic Atoms Observed ratio 1 body : 2 body = 80 : 20 for 12C The density probed by the Kaonic Atoms

4. Comments on Kaon Absorption What the data

mean?

: Overlapping density

N K

T. Yamazaki, S. Hirenzaki

PLB557(03)20

12C

Chiral Unitary Phenomenology

E=0 MeV

-100

-50

• 80 : 20 Absorption (a) from 2p state (b) from 3d state

Im Vopt : 1body abs. ( term) 2 body abs. (2 term)

Formation Spectra

We have studied1. Kaonic Nuclei (for light nuclear targets)

Kpp and Kpn (T(=0,E)(r)) -- Bound state exist in complex E plane -- Peak positions are not corresponding to the binding energyKnn (T(=0,E)(r)) no bound statesKpn (T(,E)(r)) -- Smooth spectra, no peak.

2. Kaonic Nuclei ( for 16O) We have found smooth slope in spectra. (good agreement with the latest experimental

analysis)

3. Deeply bound Kaonic Atoms We have found very interesting structure. (no experimental evidence so far)

4. 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!!

Summary