Light nuclear systems with an antikaon

Transcription

1 Light nuclear systems with an antikaon Part 1, Dense kaonic nuclei Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. K bar N potential KEK Theory Center / IPNS Akinobu Doté Part 2, Lambda(1405) K bar N-πΣ system studied with a coupled-channel Complex Scaling Method YIPQS-WCU joint international molecule-type workshop on Dense strange nuclei and compressed baryonic matter 19. Apr. YITP, Kyoto

2 Light nuclear systems with an antikaon Part 1, Dense kaonic nuclei Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. K bar N potential Part 2, Lambda(1405) K bar N-πΣ system studied with a coupled-channel Complex Scaling Method KEK Theory Center / IPNS Akinobu Doté Collaboration with Y. Akaishi (RIKEN / Nihon univ.) and T. Yamazaki (RIKEN) YIPQS-WCU joint international molecule-type workshop on Dense strange nuclei and compressed baryonic matter 19. Apr. YITP, Kyoto

3 Dense matter with strangeness F. Weber, Prog. Part. Nucl. Phys. 54, 193 (2005) Strangeness should appear with some form (Hyperon, kaon, ) in dense nuclear matter such as neutron star.

4 Dense matter with strangeness Hyperons (Λ, Σ, ) appears at ρ= 2~4 ρ 0. Relativistic Mean Field calc. G-matrix calc. (Non-relativistic) R. Knorren, M. Prakash and P. J. Ellis, Phys. Rev. C52, 3470 (1995) S. Nishizaki, Y. Yamamoto and T. Takatsuka, Prog. Theor. Phys. 703, 108 (2002)

5 Neutron star Large nuclear system with dense state and strangeness Dense kaonic nuclei Exotic small system with strangeness? K - Nucleus containing K - meson

6 History of theoretical study of kaonic nuclei 1963 K bar NN, Y. Nogami Phys. Lett. 7, 288 (1963) 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) 1997 Experimentally solved Kaonic hydrogen puzzle M. Iwasaki, et al., PRL 78, 3067(1997) 2000~ 3 HeK -, 4 HeK - Y. Akaishi and T. Yamazaki Deeply bound and quasi-stable, shrinkage 3 HeK -,, 11 CK - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki Dense, interesting structures PRC65, (2002) PLB 590, 51(2004), PRC 70, (2004) 2006~ 12 CK -,, 208 PbK - J. Mares, A. Gal; T. Muto Medium to heavy kaonic nuclei studied with RMF NPA 770, 84 (2006), NPA 804, 332 (2008) K bar NN Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, (2008))

7 Recent results of calculation of K - pp and related experiments Width (K bar NN πyn) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Akaishi, Yamazaki [2] (Variational, Phenomenological) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Exp. : DISTO [6] (Finalized) -120 Exp. : FNUDA [5] -140 [1] PRC79, (2009) [2] PRC76, (2007) [3] PRC76, (2007) [4] PRC76, (2007) [5] PRL94, (2005) [6] PRL104, (2010) Using S-wave K bar N potential constrained by experimental data. K bar N scattering data, Kaonic hydrogen atom data, Λ(1405) etc.

8 Recent results of calculation of K - pp and related experiments Width (K bar NN πyn) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) -40 Akaishi, Yamazaki [2] (Variational, Phenomenological) -60Wycech, Green [7] (Variational, phenomenological, P-wave) -80 Ikeda, Sato [4] (Faddeev, Chiral SU(3)) -100 Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Exp. : DISTO [6] (Finalized) -120 Exp. : FNUDA [5] -140 [1] PRC79, (2009) [2] PRC76, (2007) [3] PRC76, (2007) [4] PRC76, (2007) [5] PRL94, (2005) [6] PRL104, (2010) Using S-wave K bar N potential constrained by experimental data. K bar N scattering data, Including P-wave K bar N potential, Kaonic hydrogen atom data, and other effects. Λ(1405) etc. [7] PRC79, (2009)

9 History of theoretical study of kaonic nuclei 1963 K bar NN, Y. Nogami Phys. Lett. 7, 288 (1963) 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) 1997 Experimentally solved Kaonic hydrogen puzzle M. Iwasaki, et al., PRL 78, 3067(1997) 2000~ 3 HeK -, 4 HeK - Y. Akaishi and T. Yamazaki Deeply bound and quasi-stable, shrinkage PRC65, (2002) 3 HeK -,, 11 CK - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki Dense, interesting structures PLB 590, 51(2004), PRC 70, (2004) 2006~ 12 CK -,, 208 PbK - J. Mares, A. Gal; T. Muto Medium to heavy kaonic nuclei studied with RMF NPA 770, 84 (2006), NPA 804, 332 (2008) K bar NN 2010~ K bar N-πΣ ~ Λ(1405) Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials Precise study of a building block of kaonic nuclei Based on updated experimental data Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, (2008)) Y. Ikeda, T. Hyodo, D. Jido, Y. Akaishi, T. Yamazaki,

10 History of theoretical study of kaonic nuclei 1963 K bar NN, Y. Nogami Phys. Lett. 7, 288 (1963) 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) 1997 Experimentally solved Kaonic hydrogen puzzle M. Iwasaki, et al., PRL 78, 3067(1997) 2000~ 3 HeK -, 4 HeK - Y. Akaishi and T. Yamazaki Deeply bound and quasi-stable, shrinkage 3 HeK -,, 11 CK - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki Dense, interesting structures PRC65, (2002) PLB 590, 51(2004), PRC 70, (2004) 2006~ 12 CK -,, 208 PbK - J. Mares, A. Gal; T. Muto Medium to heavy kaonic nuclei studied with RMF NPA 770, 84 (2006), NPA 804, 332 (2008) K bar NN 2010~ K bar N-πΣ ~ Λ(1405) Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials More essential system to know more precisely Precise study of a building block of kaonic nuclei Based on updated experimental data Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, (2008)) Y. Ikeda, T. Hyodo, D. Jido, Y. Akaishi, T. Yamazaki,

11 History of theoretical study of kaonic nuclei 1963 K bar NN, Y. Nogami Phys. Lett. 7, 288 (1963) 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) 1997 Experimentally solved Kaonic hydrogen puzzle M. Iwasaki, et al., PRL 78, 3067(1997) 2000~ 3 HeK -, 4 HeK - Y. Akaishi and T. Yamazaki Deeply bound and quasi-stable, shrinkage 3 HeK -,, 11 CK - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki Dense, interesting structures PRC65, (2002) PLB 590, 51(2004), PRC 70, (2004) 2006~ 12 CK -,, 208 PbK - J. Mares, A. Gal; T. Muto K bar NN 2010~ K bar N-πΣ ~ Λ(1405) Medium to heavy kaonic nuclei studied with RMF Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials Precise study of a building block of kaonic nuclei Based on updated experimental data NPA 770, 84 (2006), NPA 804, 332 (2008) Revisit the past studies to show possible interesting properties of kaonic nuclei as many-body systems, though these studies include several problems Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, (2008)) Y. Ikeda, T. Hyodo, D. Jido, Y. Akaishi, T. Yamazaki,

12 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

13 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

14 What is Kaonic nucleus? Kaonic atom Nucleus ~10 fm Mainly bound by Coulomb force K - Atomic orbit Kaonic nucleus K - Bound by strong interaction Inside of nucleus The nuclear structure may be changed, if the interaction is so attractive. observed in wide mass-number range ( 4 He ~ 238 U) Deeply bound below πσ threshold (main decay channel) KNNN 0 MeV Possible to exist as a quasi-bound state with narrow width ΣπNN -103 MeV K nuclear state

15 Energy [MeV] K - p interaction and Λ(1405) 1405 Λ(1405) Excited state of Λ Mysterious state??? 1193 Σ Hyperons 1116 Λ 939 p, n

16 Mysterious state; Λ(1405) Quark model prediction calculated as 3-quark state Λ(1405) can t be well reproduced as a 3-quark state! calculated Λ(1405) observed Λ(1405) q q q N. Isgar and G. Karl, Phys. Rev. D18, 4187 (1978)

17 K - p interaction and Λ(1405) Energy [MeV] p + K - Λ(1405) Excited state of Λ Mysterious state??? 1193 Σ 1116 Λ Hyperons 939 p, n

18 K - p interaction and Λ(1405) Energy [MeV] p + K - Λ(1405) Excited state of Λ Not Mysterious 3 quark state??? state, but 1193 Σ 1116 Λ q q q 939 p,n I=0 Proton-K - bound state with 27MeV binding energy? u u d Hyperons u bar s Chiral unitary model T. Hyodo, D. Jido, E. Oset, N. Kaiser, W. Weise,

19 Kaonic hydrogen atom Atomic 1s level shift = Repulsive Precise measurement of kaonic hydrogen KpX Exp. (KEK) M. Iwasaki et al., PRL 78, 3067(1997) 14 kev 1s Coulomb potential + K bar N potential Repulsive Attractive Solved Kaonic hydrogen puzzle

20 Kaonic hydrogen atom Atomic 1s level shift = Repulsive Wave function 14 kev 1s Coulomb potential Node due to orthogonality r = K bar N potential 27 MeV Λ(1405) r The atomic state has a node to orthogonalize to the nuclear state (=Λ(1405)). Kinetic energy increases, then the atomic level is repulsively shifted. Repulsive 1s level shift doesn t contradict Λ(1405) = quasi-bound K - p.

21 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

22 A phenomenological potential AY K bar N potential Y. Akaishi and T. Yamazaki, PRC 65 (2002) , Free K bar N scattering data A.D.Martin, Nucl.Phys.B179(1981)33 a I=0 = i 0.46 fm, a I=1 = i 0.60 fm Exp. : a I=0 = i 0.68 fm, a I=1 = i 0.60 fm 2, X-ray data of kaonic hydrogen atom a K-p = ( a I=0 +a I=1 ) /2 = i 0.53 fm 3, Binding energy and decay width of Λ(1405) B.E.= -27 MeV (from K - p threshold), Γ= 40 MeV M.Iwasaki et al., Phys.Rev.Lett.78(1997)3067 I=0 K - p quasibound state Exp. : a K-p = (-0.78 ± 0.15 ± 0.03) + i (0.49 ± 0.25 ± 0.12) fm cf) Λ(1405): 27 MeV below K - +p threshold

23 A phenomenological potential AY K bar N potential Y. Akaishi and T. Yamazaki, PRC 65 (2002) I I 2 v r vd exp r / 0.66 fm, KN I I 2 v r v exp / 0.66 fm, KN, C r 1 I exp / 0.66 fm I v r v KN, C r 2 2 Not single channel, but coupled-channel potential. I=0 ch. I=1 ch. v 436 MeV, v 412 MeV, v none, I0 I0 I0 D C C 1 2 v 62 MeV, v 285 MeV, v 285 MeV. I 1 I 1 I 1 D C C 1 2 Strongly attractive in isopin-0 channel

24 Pioneering work by Akaishi and Yamazaki Method: Brueckner Hartree-Fock Effective NN interaction: Hasegawa-Nagata interaction Bare K bar N interaction: AY K bar N interaction I I 1 3 g 2 g g g 4 4 I0 I1 ppnk - (T=0) has attractive I=0 K bar N component. Deeply bound Exist as a discrete state, since Σπ-decay mode is closed. ppnk - (T=0): E(K)=108 MeV, Γ=20 MeV

25 Contraction R 1.47 fm B.E. = 70 MeV core R 1.12 fm B.E. = 86 MeV core Due to the shrinkage, a kaonic nucleus gains the binding energy. K - causes drastic change of nuclear structure? Many-body dynamics is important??

26 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

27 Kaonic nuclei studied with AMD Antisymmetrized Molecular Dynamics Single-nucleon wave fn. = Gauss packet 3/ Zi i exp i i r Antisymmetrization det i a Parity and angular-momentum projections Fully microscopic treatment. No assumption on nuclear structure. deformation, axial symmetry, existence of cluster Both of shell-like and cluster-like structures can be described with one framework. PJPP { Z i } are determined by energy variation. (Frictional cooling method) PP is employed as a trial wave func, due to calculational cost. Great success in the study of light stable/unstable nuclei which have various structures.

28 Essence of AMD Both of shell-like and cluster-like structures are described with various configuration of Gauss packets. Gaussian wave packet det Cooling The structure is determined by only the energy-variation. det det det det 0p 0s Shell Cluster

29 Kaonic nuclei studied with AMD K - meson = a seed of strong attraction How will A-nucleons system be, if a K - meson is put into the nuclear system? p Kaonic Normal nucleus???????? n Question How does A+1-body system self-organize? AMD could give an answer, because it treats the system in a fully microscopic way.

30 Improve the AMD for kaonic nuclei I=0 K bar N potential plays a key role in kaonic nuclei. p K V ( I 0) bar K N Charge-mixed single-particle state N a proton b i i i neutron n K 0 K x K y K K bar N potential causes a charge-mixing in the charge-base treatment such as AMD. + Charge projection 0 Systematic study of kaonic nuclei!

31 Wave function Essence of - 0 K p/k n mixing Nucleon s wave function n i C exp r i 2 Z i i or i 1 1 p n 2 2 p-n mixing i N a proton b neutron K x K y K Total wave function det[ ] K P 0 Anti-kaon s wave function K 2 k K K Z K C exp r K 1 K o 1 K K K -K mixing K Charge projection P exp ˆ M d i TZ M as a trial function

32 J & T projections (VBP) P J MK P T TzTz ' : Eigen state of angular momentum J and isospin T P P d D ( ) R ( ) J T J* MK TzTz ' Ang MK Ang Ang Ang d D ( ) R ( ) T* iso TzTz ' iso iso iso J projection T projection R Ang ( ) exp i J z exp i J y exp i J z Riso( ) exp i T z exp it y exp i T z Various quantities are calculated with MK TzTz '. P J P T

33 Note on the extended framework By expressing a nucleon and a kaon with superposition of wave packets, we can represent the difference between their distributions. Ex) Nucleon: 2 packets, Kaon: 5 packets By the charge-number projection, we can remove unnecessary charge states. Ex) ppnk - (p+n)(p+n)(p+n)(k - +K 0 ) = pppk 0 We can extract only charge 1 state by the charge number projection. + pppk - + ppnk 0 + ppnk - + pnnk 0 + pnnk - + nnnk 0 + nnnk - Charge

34 Hamiltonian Hˆ Tˆ Vˆ Vˆ Vˆ Tˆ NN KN Coulomb G G-matrix method Effective interaction Bare NN int = Tamagaki potential (OPEG) Bare K bar N int = AY potential Vˆ NN, Vˆ KN NN/K bar N effective interactions have a 10-range Gaussian form. A 10 NN NN ˆ X ˆ, ˆ exp r r Vˆ v v P X v b 2 2 NN ij ij a i j a i j X E, E, O, O a1 A 10 KN KN ˆ, ˆ ˆ I exp r r Vˆ v v P v b 2 2 KN Ki Ki I a i j a i1 I 0,1 a1

35 According to the study with Collaboration with Akaishi-san and Yamazaki-san Antisymmetrized Molecular Dynamics Total system is treated in a fully microscopic way. + G-matrix NN repulsive core is adequately smoothed out, based on conventional nuclear physics. + Phenomenological K bar N interaction Strongly attractive, especially in I=0 channel Kaonic nuclei has interesting properties

36 AMD + G-matrix + AY K bar N interaction studies revealed 1. E(K) > 100 MeV for various light nuclei 2. Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - 3. Highly dense state is formed in K bar nuclei. maximum density > 4ρ 0 averaged density 2~4ρ 0 4. Proton satellite in pppk - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

37 E(K) [MeV] AMD + G-matrix + AY K bar N interaction studies revealed 1. E(K) > 100 MeV for various light nuclei Nucleus-K - threshold Drastic change of the structure of 8 Be, isovector deformation in 8 BeK Highly dense state is formed in K bar nuclei. maximum density > 4ρ 0 averaged density 2~4ρ Proton satellite in pppk ppnk pppk pppnk 6BeK 8BeK 9BK Σπ threshold Width (Σπ, Λπ) (simple AMD) A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

38 AMD + G-matrix + AY K bar N interaction studies revealed Binding energy of K - = 104 MeV 1. E(K) > 100 MeV for various light nuclei 2. Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - Density (/fm^3) Highly dense state is formed in K bar nuclei. maximum density 8 BeK > 4ρ - 0 averaged density 2~4ρ 0 Rrms = fm β = Central density = /fm^3 4.5 normal density 4. Proton satellite in pppk - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

39 AMD + G-matrix + AY K bar N interaction studies revealed Isovector deformation 1. E(K) > 100 MeV for various light nuclei 2. Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - 3. Highly dense state is formed in K bar nuclei. maximum density > 4ρ 0 averaged density 2~4ρ 0 4. Proton satellite in pppk - V V V KN KN I 0 I 1 K p V K n A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

40 AMD + G-matrix + AY K bar N interaction studies revealed 1. E(K) > 100 MeV for various light nuclei 2. Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - 3. Highly dense state is formed in K bar nuclei. maximum density > 4ρ 0 averaged density 2~4ρ 0 4. Proton satellite in pppk - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

41 AMD + G-matrix + AY K bar N interaction studies revealed 1. E(K) > 100 MeV for various light nuclei pppk - 2. Drastic change of the structure of 8 Be, isovector deformation in 8 BeK - 3. Highly dense state is formed in K bar nuclei. maximum density > 4ρ Proton satellite 0 averaged density 2~4ρ 0 4. Proton satellite in pppk - A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004)

42 Nuclear density distribution ppnk - pppk - pppnk - 3 fm ρ ave = 3.1ρ 0 ρ ave = 3.9ρ 0 ρ ave = 2.5ρ 0 6 BeK - 9 BK - 4 fm ρ ave = 2.2ρ 0 ρ ave = 1.9ρ 0

43 Saturation of nucleon number around K -? ppnk - One-center like Two-center like Nucleons Strange structure Kaon 1 ( ) 5 K MAX Single K - meson can interact with limited numbers of nucleons? Saturation of E(K)

44 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

45 According to AMD+G-matrix+Pheno. K bar N pot. study, One K - meson causes lots of interesting phenomena in nuclei. Drastic change of nuclear structure Dense state Strange structure Two K - mesons??? Double kaonic nucleus AMD for Double kaonic nuclei Wave func.: det NN N S[ KK] V 0 : K bar K bar potential is switched off. KK Symmetrized since K - meson is boson.

46 Double kaonic nucleus - ppnk - K fm 4 fm 4 fm E(K) = 110 MeV E(2K) = 213 MeV Density [fm -3 ] Density [fm -3 ] Density [fm -3 ] ppn Total B.E. = 6.0 MeV Central density = 0.14 fm -3 R rms = 1.59 fm ppnk - Total B.E. = 118 MeV Central density = 1.5 fm -3 R rms = 0.72 fm ppnk - K - Total B.E. = 221 MeV Central density = 3.0 fm -3 R rms = 0.69 fm T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)

47 Double kaonic nucleus - ppnk - K fm 4 fm 4 fm E(K) = 110 MeV E(2K) = 213 MeV Density [fm -3 ] Density [fm -3 ] Density [fm -3 ] ppn Total B.E. = 6.0 MeV Central density = 0.14 fm -3 R rms = 1.59 fm ppnk - Double kaonic nuclei Total B.E. = 118 MeV Central density = 1.5 fm -3 R rms = 0.72 fm ppnk - K - Total B.E. = 221 MeV Central density = 3.0 fm -3 R rms = 0.69 fm T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)

48 Dense kaonic nuclei Introduction Phenomenological K bar N potential and study with a simple model Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Double kaonic nuclei Summary and Remarks

49 Summary The excited hyperon Λ(1405) is considered to be a quasi-bound state of K - and proton. 1. Low energy scattering data (I=0 K bar N scattering length) 2. Kaonic hydrogen atom data (K - p scattering length) 3. Λ(1405) : B. E. (K - p) = 28 MeV, Γ(πΣ) = 40 MeV Very attractive K bar N potential in I=0 channel According to the systematic study of light kaonic nuclei ( 3 HeK - ~ 11 CK - ) with Antisymmetrized Molecular Dynamics + G-matrix + a phenomenological K bar N interaction, 1. Kaonic nuclei are deeply bound below πσ threshold! Binding energy of K - > 100 MeV 3. Dense state is formed in kaonic nuclei, against the nuclear saturation property. (averaged density: 2~ 4 ρ 0 ) 2. Strong attraction of K - changes nuclear structure drastically! 4. Interesting structures isovector 8 BeK - proton K - ppp

50 Theoretical studies of nuclear system with anti-kaons Light nuclei with a single antikaon 3 HeK - ~ 11 CK - studied with AMD + G-matrix + AY potential E(K) 100MeV Light nuclei with double antikaons 3 HeK - K - etc studied with AMD + G-matrix + AY potential E(2K) 200MeV Medium to heavy nuclei with multi-antikaons Studied with Relativistic Mean Field - D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, (2007); PRC77, (2008) - T. Muto, T. Maruyama and T. Tatsumi, PRC79, (2009) Repulsive K bar K bar interaction Saturation for the number of antikaons Central nuclear density and Separation energy of anti-kaon (or Kaon s binding energy / kaon) are saturated. Nuclear matter with antikoans Neutron star, kaon condensation

51 Remarks Questions to Deeply Bound Kaonic Nuclei The phenomenological K bar N potential is all right? πσ-πσ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. AY potential The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed?? Chiral SU(3) K bar N πσ ηλ KΞ Independent-pair assumption still holds??? Two nucleon absorption? 2 KNN YN N It should be terribly large at high density. So, such kaonic nuclei can t survive?

52 Thank you very much!