1. Light nuclear systems with an antikaon KEK Theory Center / IPNS KEK Theory Center / IPNS Akinobu Doté Part 1, “Dense kaonic nuclei” Revisit the study of kaonic nuclei with Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. K bar N potential AMD+G-matrix+Phen. K bar N potential Part 2, “Lambda(1405)” K bar N-πΣ system studied with K bar N-πΣ system studied with a coupled-channel Complex Scaling Method a coupled-channel Complex Scaling Method YIPQS-WCU joint international molecule-type workshop on “Dense strange nuclei and compressed baryonic matter” 19. Apr. ‘11 @ YITP, Kyoto

2. Light nuclear systems with an antikaon KEK Theory Center / IPNS KEK Theory Center / IPNS Akinobu Doté Part 1, “Dense kaonic nuclei” Revisit the study of kaonic nuclei with Revisit the study of kaonic nuclei with AMD+G-matrix+Phen. K bar N potential AMD+G-matrix+Phen. K bar N potential Part 2, “Lambda(1405)” K bar N-πΣ system studied with K bar N-πΣ system studied with a coupled-channel Complex Scaling Method a coupled-channel Complex Scaling Method YIPQS-WCU joint international molecule-type workshop on “Dense strange nuclei and compressed baryonic matter” 19. Apr. ‘11 @ YITP, Kyoto Collaboration with Y. Akaishi (RIKEN / Nihon univ.) and T. Yamazaki (RIKEN)

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

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

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

6. History of theoretical study of kaonic nuclei Phys. Lett. 7, 288 (1963) 1963 K bar NN, Y. Nogami 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) PRC65, 044005 (2002) 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 PLB 590, 51(2004), PRC 70, 044313 (2004) 1997 Experimentally solved “Kaonic hydrogen puzzle” M. Iwasaki, et al., PRL 78, 3067(1997) a prototype of kaonic nuclei Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials K bar NN Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, 055202 (2008)) 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)

7. Width (K bar NN→πYN) [MeV] Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Akaishi, Yamazaki [2] (Variational, Phenomenological) Akaishi, Yamazaki [2] (Variational, Phenomenological) Exp. : FNUDA [5] Exp. : DISTO [6] (Finalized) Exp. : DISTO [6] (Finalized) Using S-wave K bar N potential constrained by experimental data. … K bar N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010) Recent results of calculation of K - pp Recent results of calculation of K - pp and related experiments

8. Width (K bar NN→πYN) [MeV] Exp. : FNUDA [5] Exp. : DISTO [6] (Finalized) Exp. : DISTO [6] (Finalized) Using S-wave K bar N potential constrained by experimental data. … K bar N scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) Shevchenko, Gal, Mares [3] (Faddeev, Phenomenological) [1] PRC79, 014003 (2009) [2] PRC76, 045201 (2007) [3] PRC76, 044004 (2007) [4] PRC76, 035203 (2007) [5] PRL94, 212303 (2005) [6] PRL104, 132502 (2010) Recent results of calculation of K - pp Recent results of calculation of K - pp and related experiments Akaishi, Yamazaki [2] (Variational, Phenomenological) Akaishi, Yamazaki [2] (Variational, Phenomenological) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Ikeda, Sato [4] (Faddeev, Chiral SU(3)) Wycech, Green [7] (Variational, phenomenological, P-wave) Wycech, Green [7] (Variational, phenomenological, P-wave) [7] PRC79, 014001 (2009) Including P-wave K bar N potential, and other effects. Including P-wave K bar N potential, and other effects. Doté, Hyodo, Weise [1] (Variational, Chiral SU(3)) Doté, Hyodo, Weise [1] (Variational, Chiral SU(3))

9. History of theoretical study of kaonic nuclei Phys. Lett. 7, 288 (1963) 1963 K bar NN, Y. Nogami 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) PRC65, 044005 (2002) 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 PLB 590, 51(2004), PRC 70, 044313 (2004) 1997 Experimentally solved “Kaonic hydrogen puzzle” M. Iwasaki, et al., PRL 78, 3067(1997) 2010~ K bar N-πΣ ~ Λ(1405) Precise study of a building block of kaonic nuclei Based on updated experimental data a prototype of kaonic nuclei Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials K bar NN Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, 055202 (2008)) 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) Y. Ikeda, T. Hyodo, D. Jido, … Y. Akaishi, T. Yamazaki, …

10. History of theoretical study of kaonic nuclei Phys. Lett. 7, 288 (1963) 1963 K bar NN, Y. Nogami 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) PRC65, 044005 (2002) 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 PLB 590, 51(2004), PRC 70, 044313 (2004) 1997 Experimentally solved “Kaonic hydrogen puzzle” M. Iwasaki, et al., PRL 78, 3067(1997) 2010~ K bar N-πΣ ~ Λ(1405) Precise study of a building block of kaonic nuclei Based on updated experimental data a prototype of kaonic nuclei Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials K bar NN Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, 055202 (2008)) 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) Y. Ikeda, T. Hyodo, D. Jido, … Y. Akaishi, T. Yamazaki, … More essential system to know more precisely More essential system to know more precisely

11. History of theoretical study of kaonic nuclei Phys. Lett. 7, 288 (1963) 1963 K bar NN, Y. Nogami 1985 Quasi-stable kaonic nuclei, S. Wycech NPA 450, 399 (1986) PRC65, 044005 (2002) 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 PLB 590, 51(2004), PRC 70, 044313 (2004) 1997 Experimentally solved “Kaonic hydrogen puzzle” M. Iwasaki, et al., PRL 78, 3067(1997) 2010~ K bar N-πΣ ~ Λ(1405) Precise study of a building block of kaonic nuclei Based on updated experimental data a prototype of kaonic nuclei Detailed study of a prototype of kaonic nuclei Studied with various approaches and potentials K bar NN Variational calc. / Faddeev Phen. pot. / chiral-based pot. Skyrme model (T. Nishikawa and Y. Kondo, PRC77, 055202 (2008)) 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) Y. Ikeda, T. Hyodo, D. Jido, … Y. Akaishi, T. Yamazaki, … Revisit the past studies to show “possible” interesting properties of kaonic nuclei as many-body systems, though these studies include several problems… Revisit the past studies to show “possible” interesting properties of kaonic nuclei as many-body systems, though these studies include several problems…

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

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

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

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

16. Mysterious state; Λ(1405) Quark model prediction … calculated as 3-quark state N. Isgar and G. Karl, Phys. Rev. D18, 4187 (1978) q q q Λ(1405) can’t be well reproduced as a 3-quark state! Λ(1405) can’t be well reproduced as a 3-quark state! observed Λ(1405) calculated Λ(1405)

17. 939p, n 1116 Λ 1193 Σ Λ(1405) 1405 Energy [MeV] Hyperons Excited state of Λ Mysterious state??? p + K - 1432 K - p interaction and Λ(1405)

18. 939p,n 1116 Λ 1193 Σ Λ(1405) 1405 Energy [MeV] Hyperons Excited state of Λ Mysterious state??? p + K - 1432 Not 3 quark state, but I=0 Proton-K - bound state with 27MeV binding energy? with 27MeV binding energy? Not 3 quark state, but I=0 Proton-K - bound state with 27MeV binding energy? with 27MeV binding energy? q q q u bar s u u d K - p interaction and Λ(1405) Chiral unitary model T. Hyodo, D. Jido, E. Oset, … N. Kaiser, W. Weise, …

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

20. Kaonic hydrogen atom Atomic 1s level shift = Repulsive 1s 14 keV Coulomb potential ＝ K bar N potential 27 MeV Λ(1405) Wave function r r The atomic state has a node to orthogonalize to the nuclear state (=Λ(1405)). Node due to orthogonality 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 Introduction Phenomenological K bar N potential Phenomenological K bar N potential and study with a simple model and study with a simple model Kaonic nuclei studied with Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Antisymmetrized Molecular Dynamics Double kaonic nuclei Double kaonic nuclei Summary and Remarks Summary and Remarks

22. A phenomenological potential … AY K bar N potential 1, Free K bar N scattering data 3, Binding energy and decay width of Λ(1405) M.Iwasaki et al., Phys.Rev.Lett.78(1997)3067 2, X-ray data of kaonic hydrogen atom A.D.Martin, Nucl.Phys.B179(1981)33 Exp. : a I=0 = -1.70 + i 0.68 fm, a I=1 = 0.37 + i 0.60 fm a I=0 = -1.76 + i 0.46 fm, a I=1 = 0.37 + i 0.60 fm B.E.= -27 MeV (from K - p threshold), Γ= 40 MeV cf) Λ(1405): 27 MeV below K - +p threshold a K-p = ( a I=0 +a I=1 ) /2 = -0.70 + i 0.53 fm Exp. : a K-p = (-0.78 ± 0.15 ± 0.03) + i (0.49 ± 0.25 ± 0.12) fm I=0 K - p quasi- bound state Y. Akaishi and T. Yamazaki, PRC 65 (2002) 044005

23. Y. Akaishi and T. Yamazaki, PRC 65 (2002) 044005 Strongly attractive in isopin-0 channel I=0 ch. I=1 ch. Not single channel, but coupled-channel potential. A phenomenological potential … AY K bar N potential

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 Deeply bound Exist as a discrete state, since Σπ-decay mode is closed. ppnK - (T=0): E(K)=108 MeV, Γ=20 MeV Deeply bound Exist as a discrete state, since Σπ-decay mode is closed. ppnK - (T=0): E(K)=108 MeV, Γ=20 MeV ppnK - (T=0) has attractive I=0 K bar N component. ppnK - (T=0) has attractive I=0 K bar N component.

25. “Contraction” B.E. = 70 MeV 86 B.E. = 86 MeV 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 Introduction Phenomenological K bar N potential Phenomenological K bar N potential and study with a simple model and study with a simple model Kaonic nuclei studied with Kaonic nuclei studied with Antisymmetrized Molecular Dynamics Antisymmetrized Molecular Dynamics Double kaonic nuclei Double kaonic nuclei Summary and Remarks Summary and Remarks

27. Kaonic nuclei studied with AMD A ntisymmetrized M olecular D ynamics Single-nucleon wave fn. = Gauss packet Antisymmetrization Parity and angular-momentum projections { Z i } are determined by energy variation. ( Frictional cooling method ) is employed as a trial wave func, due to calculational cost. 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. Great success in the study of light stable/unstable nuclei which have various structures.

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

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

30. Improve the AMD for kaonic nuclei K bar N potential causes a charge-mixing in the charge-base treatment such as AMD. pn I=0 K bar N potential plays a key role in kaonic nuclei. + Charge projection Charge-mixed single-particle state Systematic study of kaonic nuclei!

31. Wave function Total wave function Nucleon’s wave function p-n mixing Anti-kaon’s wave function mixing Charge projection as a trial function Essence of mixing

32. J & T projections (VBP) Various quantities are calculated with. J projection T projection : Eigen state of angular momentum J and isospin 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 + pppK - + ppnK 0 + ppnK - + pnnK 0 + pnnK - + nnnK 0 + nnnK - Charge 3 2 1 0 We can extract only charge 1 state by the charge number projection.

34. Hamiltonian G-matrix method Effective interaction Bare NN int = Tamagaki potential (OPEG) Bare K bar N int = AY potential NN/K bar N effective interactions have a 10-range Gaussian form.

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

36. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 -

37. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 - Nucleus-K - threshold Σπ threshold (simple AMD) Width ( Σπ, Λπ )

38. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 - Rrms = 1.42 fm β = 0.55 Central density = 0.76 /fm^3 8 BeK - Density (/fm^3) 0.0 0.41 0.83 4.5 normal density Binding energy of K - = 104 MeV

39. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 - Isovector deformation

40. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 2 ～ 4ρ 0 averaged density 2 ～ 4ρ 0 4.Proton satellite in pppK -

41. AMD + G-matrix + AY K bar N interaction studies revealed … A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. 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 - pppK - Proton satellite

42. Nuclear density distribution ppnK - pppK - pppnK - 6 BeK - 3 fm 9 BK - 4 fm ρ ave = 3.1ρ 0 ρ ave = 3.9ρ 0 ρ ave = 2.5ρ 0 ρ ave = 2.2ρ 0 ρ ave = 1.9ρ 0

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

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

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

46. Double kaonic nucleus - ppnK - K - - Total B.E. = 118 MeV Central density = 1.5 fm -3 R rms = 0.72 fm ppnK - Density [fm -3 ] 0.00 0.75 1.50 E(K) = 110 MeV 4 fm Total B.E. = 221 MeV Central density = 3.0 fm -3 R rms = 0.69 fm ppnK - K - Density [fm -3 ] 0.0 1.5 3.0 E(2K) = 213 MeV 4 fm Total B.E. = 6.0 MeV Central density = 0.14 fm -3 R rms = 1.59 fm ppn 4 fm Density [fm -3 ] 0.00 0.14 T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)

47. Total B.E. = 221 MeV Central density = 3.0 fm -3 R rms = 0.69 fm ppnK - K - Total B.E. = 118 MeV Central density = 1.5 fm -3 R rms = 0.72 fm Total B.E. = 6.0 MeV Central density = 0.14 fm -3 R rms = 1.59 fm Double kaonic nucleus - ppnK - K - - Density [fm -3 ] 0.0 1.5 3.0 Density [fm -3 ] 0.00 0.75 1.50 E(2K) = 213 MeV 4 fm ppnK - ppn 4 fm E(K) = 110 MeV 4 fm Density [fm -3 ] 0.00 0.14 Double kaonic nuclei T. Yamazaki, A. Doté and Y. Akaishi, PLB578, 167(2004)

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

49. Summary The excited hyperon Λ(1405) is considered to be a quasi-bound state of K - and proton. According to the systematic study of light kaonic nuclei ( 3 HeK - ~ 11 CK - ) with Antisymmetrized Molecular Dynamics + G-matrix + G-matrix + a phenomenological K bar N interaction, + a phenomenological K bar N interaction, 1.Kaonic nuclei are deeply bound below πΣ threshold! Binding energy of K - > 100 MeV 1.Kaonic nuclei are deeply bound below πΣ threshold! Binding energy of K - > 100 MeV 2. Strong attraction of K - changes nuclear structure drastically! 2. Strong attraction of K - changes nuclear structure drastically! Dense state 3. Dense state is formed in kaonic nuclei, against the nuclear saturation property. 2 ～ 4 ρ 0 (averaged density: 2 ～ 4 ρ 0 ) Dense state 3. Dense state is formed in kaonic nuclei, against the nuclear saturation property. 2 ～ 4 ρ 0 (averaged density: 2 ～ 4 ρ 0 ) 4. Interesting structures isovector deformation @ 8 BeK - proton satellite @ K - ppp 4. Interesting structures isovector deformation @ 8 BeK - proton satellite @ K - ppp 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

50. Theoretical studies of nuclear system with anti-kaons Medium to heavy nuclei with multi-antikaons Nuclear matter with antikoans Neutron star, kaon condensation… - T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009) - D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76, 055204 (2007); PRC77, 045206 (2008) 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 Studied with Relativistic Mean Field 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.

51. The phenomenological K bar N potential is all right?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. Questions to Deeply Bound Kaonic Nuclei Two nucleon absorption?Two nucleon absorption? It should be terribly large at high density. So, such kaonic nuclei can’t survive? Remarks The G-matrix treatment is adequate?The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed?? “Independent-pair assumption” still holds??? K bar NπΣηΛKΞ Chiral SU(3) AY potential

52. Thank you very much!