Multikaonic (hyper)nuclei

Transcription

1 Multikaonic (hyper)nuclei J. Mareš Nuclear Physics Institute, Rez/Prague Γ K - (MeV) MFG (πσ,ρ) SGM DISTO FINUDA05? 50 WG08 AY02 YS07 OBELIX GFGM (πσ,πλ,ρ 2 ) DHW08 FINUDA07 WG08 OBELIX B - K (MeV) NFQCD Kyoto, 1 March, 2010 D.Gazda, E.Friedman, A.Gal, N.V.Shevchenko

2 Outline KN + K-nucleus interaction Kaonic nuclei Few-body systems (CC vs. 1C calculations) Many-body systems (RMF Lagrangian, coupling constants, K absorption) Multi-K nuclei Multi-K hypernuclei

3 K N interaction K N interaction I = 0 KN quite strongly attractive near threshold V K 100 MeV Chiral SU(3) coupled channels approach Λ(1405) is an I = 0 KN quasibound state and a πσ resonance resulting from the coupling between KN and πσ channels. Fig. π 0 Σ 0 invariant mass spectrum in the pp pk + π 0 Σ 0 reaction (ANKE) compared with a chiral dynamics calculation by Geng and Oset.

4 K N interaction Scattering data

5 K N interaction Threshold branching ratios: (A.D. Martin, Nucl. Phys. B179 (1981) 33.) γ = Γ(K p π + Σ ) = 2.36 ± 0.04 Γ(K p π Σ + ) R c = Γ(K p charged) Γ(K p all) = ± R n = Γ(K p π 0 Λ) = ± Γ(K p neutral)

6 K N interaction Kaonic hydrogen - strong interaction shift and width SIDDHARTA?

7 K atoms Exotic atom (h = π, p, K, Σ, Ξ ) opt ReV opt ImV opt (absorptive) π repulsive moderate K attractive strong p attractive strong Σ repulsive moderate

8 K atoms Phenomenological DD interaction 2µV opt = 4π(1 + µ m N )b(ρ)ρ(r), where b(ρ) = b 0 + B 0 ( ρ(r) ρ 0 ) α and b 0, B 0, α are fitted to atomic data for α > 0 + ρ 0 b(ρ) b 0, Reb 0 = 0.15 fm ( - K N scattering length) low-density limit is satisfied fits yield Re(b 0 + B 0 ) > 0 for ρ ρ 0 strong attraction in the nuclear interior RMF for kaonic atoms: V K + S + V repulsive potential V K S V attractive potential potential cannot describe the K behavior at low ρ therefore: RMF for ρ ρ 0 + DD for ρ 0 and matching at r M r M - low enough that K atom data test V RMF and high enough that RMF approach valid

9 K atoms Phenomenology (DD or RMF):

10 K atoms Phenomenology (DD or RMF):

11 K nucleus interaction Chiral SU(3) dynamics + coupled channels : chiral model for KN interactions near threshold N. Kaiser, P.B.Siegel, W. Weise, NPA594 (1995) 325; T. Waas, N. Kaiser, W.Weise, PLB 365 (1996) 12; PLB 379 (1996) 34 Λ(1405) generated dynamically through coupled Lippmann-Schwinger equations for the meson-baryon t matrix 1 solving t = v + v E H 0 t for coupled channels (K p, K 0 n, π 0 Λ, π + Σ, π 0 Σ 0, π Σ + ) V K (ρ 0 ) (100 ± 20) MeV selfconsistent treatment of kaon propagation in the nuclear medium (M. Lutz, PLB 426 (1998) 12) t med 1 = v + v E H 0 Π i t Π K = 2m K V K opt t(ρ)ρ, Π N = 2m N Vopt N V 0 ρ/ρ 0 LS equation t KN V K opt Π K LS equation V K (ρ 0 ) (50 60) MeV

12 K nucleus interaction

13 K nucleus interaction (K, N) reactions on 12 C T. Kishimoto et al, PTP 118, (2007) 181 Fig. Missing mass spectra (left) and χ 2 contour plots (right) for the inclusive reactions (K, n) (upper panel) and (K, p) (lower panel) at p K = 1 GeV/c on 12 C X V.K. Magas et al, arxiv: [nucl-th], A. Ramos et al, arxiv: [nucl-th]

14 K nucleus interaction Λ-hypernuclear production in (Kstop, π) reactions V. Krejčiřík, A. Cieplý, arxiv: [nucl-th] (also talk of G. (2009)) sensitivity to the K wave function

15 K nuclear states K-nucleus interaction strongly attractive and absorptive kaonic atom level shifts and widths? optical potential depth: ReV opt ( ) MeV phenomenological models ReV opt (50 60) MeV chiral models of K-nuclear states? sufficiently narrow to allow identification by experiment

16 K nuclear states K-nucleus interaction strongly attractive and absorptive kaonic atom level shifts and widths? optical potential depth: ReV opt ( ) MeV phenomenological models ReV opt (50 60) MeV chiral models of K-nuclear states? sufficiently narrow to allow identification by experiment

17 K nuclear states?

18 Motivation Kaon propagation in the nuclear medium

19 Motivation heavy ion collisions (G.C. Li, C.H. Lee, G.E. Brown, NPA 625 (1997) 372) p + C & p + Au collisions (KaoS - W. Scheinast et al, PRL 96 (2006) ) in-medium effects, K N potential 80 MeV

20 Motivation neutron star structure Schaffner-Bielich, NPA 804 (2008) 309 Glendenning, Schaffner-Bielich, PRC 60 (1999) kaon condensation could occur at ρ 3ρ 0, (ω K 200 MeV)

21 Motivation neutron stars weak interactions e K + ν e (ω K 200 MeV) condensation could occur at ρ 3ρ 0 HI collisions strong interaction time scales B K m K + m N m Λ 320 MeV K s the relevant degrees of freedom for self-bound strange hadronic systems B K m K + m N m Σ 240 MeV precursor phenomena to kaon condensation (only KNN ΛN) Does B K in multi- K systems increase enough?

22 Motivation neutron stars weak interactions e K + ν e (ω K 200 MeV) condensation could occur at ρ 3ρ 0 HI collisions strong interaction time scales B K m K + m N m Λ 320 MeV K s the relevant degrees of freedom for self-bound strange hadronic systems B K m K + m N m Σ 240 MeV precursor phenomena to kaon condensation (only KNN ΛN) Does B K in multi- K systems increase enough?

23 Status Quo (2N) K, (3N) K, (4N) K, (8N) K (Akaishi, Yamazaki, Doté et al.... ) large polarization effects ρ (4 8) ρ 0 B K 100 MeV, Γ K (20 35) MeV K capture in Li and 12 C (FINUDA, PRL (2005)): B = 115 ± 6 ± 4 MeV, Γ = 67 ± 14 ± 3 MeV K pn ΛN + FSI (Magas et al., PRC (2006)) K pp Faddeev calculations: B = (50 70) MeV, Γ = (60 100) MeV Shevchenko, Gal and Mares; Ikeda and Sato K pp variational calculations: B = (20 80) MeV, Γ = (40 85) MeV Dote, Hyodo and Weise; Wycech and Green K stopped in 6 Li K ppn cluster, B = 58 ± 6 MeV, Γ 30 MeV vs. vs. (FINUDA, PLB (2007) vs. Magas et al., arxiv: ) p annihilation on 4 He (Obelix, LEAR) K pp : B 160 MeV, Γ 24 MeV K ppn: B = 121±15 MeV,Γ<60MeV (Bendiscioli et al., NPA (2007)) pp K + Λp (DISTO) K pp : B = 105±118 MeV (T. Yamazaki et al EXA08, arxiv: [nucl-ex])??

24 K pp quasibound state Coupled-channel calculations of a KNN πσn system 3-body Faddeev equations (in AGS form): U 11 = + T 2 G 0 U 21 + T 3 G 0 U 31 U 21 = G T 1 G 0 U 11 + T 3 G 0 U 31 U 31 = G T 1 G 0 U 11 + T 2 G 0 U 21, U ij describe elastic and re-arrangement processes: U 11 : 1 + (23) 1 + (23) U 21 : 1 + (23) 2 + (31) U 31 : 1 + (23) 3 + (12) KN strongly coupled with πσ via Λ(1405) πσ channel included particle channels α: 1 : ( KNN) 2 : (πσn) 3 : (πnσ) i = 1 NN ΣN ΣN i = 2 KN πn πσ i = 3 KN πσ πn

25 K pp quasibound state Table: Calculated K pp binding energies and widths (in MeV) single channel coupled channel AY DHW SGM IS WG B Γ Table: Results of different calculations of the three-body pole energy E K pp in MeV, with respect to the K pp threshold: real and complex KNN one-channel (first two columns), and full coupled-channel calculations (third column) using the best set of KN πσ parameters. Fourth column: complex KNN one-channel calculation with AY set. Fifth column: Akaishi-Yamazaki result E1 best real E1 best complex E2 best coupled E1 AY complex E (AY) i i i i 30.5

26 RMF Methodology Many-body nuclear systems Relativistic mean field model for a system of nucleons, K mesons, and hyperons interacting through the exchange of σ, σ, ω, ρ, φ and photon fields: L = L RMF + L K + L Y where L RMF = standard relativistic mean field lagrangian density L K = (D µk) (D µ K) mk 2 K K g σk m K σ K K g σ K m K σ K K, L Y = ψ Y [id/ (m Y g σy σ g σ Y σ )]ψ Y, with covariant derivative: D µ = µ + i g ωk ω µ + i g ρk I ρµ + i g φk φ µ + i e (I Y )Aµ.

27 RMF Methodology Many-body nuclear systems Relativistic mean field model for a system of nucleons, K mesons, and hyperons interacting through the exchange of σ, σ, ω, ρ, φ and photon fields: L = L RMF + L K + L Y where L RMF = standard relativistic mean field lagrangian density L K = (D µk) (D µ K) mk 2 K K g σk m K σ K K g σ K m K σ K K, L Y = ψ Y [id/ (m Y g σy σ g σ Y σ )]ψ Y, with covariant derivative: D µ = µ + i g ωk ω µ + i g ρk I ρµ + i g φk φ µ + i e (I Y )Aµ.

28 RMF Methodology Many-body nuclear systems Relativistic mean field model for a system of nucleons, K mesons, and hyperons interacting through the exchange of σ, σ, ω, ρ, φ and photon fields: L = L RMF + L K + L Y where L RMF = standard relativistic mean field lagrangian density L K = (D µk) (D µ K) mk 2 K K g σk m K σ K K g σ K m K σ K K, L Y = ψ Y [id/ (m Y g σy σ g σ Y σ )]ψ Y, with covariant derivative: D µ = µ + i g ωk ω µ + i g ρk I ρµ + i g φk φ µ + i e (I Y )Aµ.

29 RMF Methodology baryons (nucleons, hyperons): [ iα j j + (m B g σb σ g σ B σ )β + g ωb ω + g ρb I 3 ρ + g φb φ + e(i Y )A]ψ B = εψ B mesons: ( 2 + mσ)σ 2 = g σn ρ s + g 2 σ 2 g 3 σ 3 + g σk m K K K+g σy ρ sy ( 2 +mσ)σ 2 = g σ K m K K K+g σ Y ρ sy ( 2 + mω)ω 2 = g ωn ρ N g ωk ρ K +g ωy ρ Y ( 2 + mρ 2 )ρ = g ρn ρ 3 g ρk ρ K +g ρn ρ 3Y ( 2 + mφ 2 )φ = g φk ρ K +g φy ρ Y 2 A = e ρ p e ρ K +e ρ cy where ρ K = 2(E K + g ωk ω + g ρk ρ + g φk φ + e A)K K

30 RMF Methodology + antikaons: ( 2 E 2 K + m 2 K + Π K )K = 0 Re Π K = g σ K m K σ g σk m K σ 2 E K (g ωk ω + g ρk ρ + g φk φ + e A) (g ωk ω + g ρk ρ + g φk φ + e A) 2 Im Π K = (0.7 f 1Σ f 1Λ )W 0 ρ N (r) f 2Σ W 0 ρ 2 N (r)/ ρ 0 f iy Absorption through: kinematical suppression factors ( reduced phase space) W 0 constrained by kaonic atom data pionic conversion modes ρ N (r) KN πσ+90 MeV, πλ+170 MeV (70%, 10%) nonmesonic modes ρ 2 N (r) KNN YN+240 MeV (20%) Γ K width phase space suppression x density enhancement

31 RMF Methodology + antikaons: ( 2 E 2 K + m 2 K + Π K )K = 0 Re Π K = g σ K m K σ g σk m K σ 2 E K (g ωk ω + g ρk ρ + g φk φ + e A) (g ωk ω + g ρk ρ + g φk φ + e A) 2 Im Π K = (0.7 f 1Σ f 1Λ )W 0 ρ N (r) f 2Σ W 0 ρ 2 N (r)/ ρ 0 f iy Absorption through: kinematical suppression factors ( reduced phase space) W 0 constrained by kaonic atom data pionic conversion modes ρ N (r) KN πσ+90 MeV, πλ+170 MeV (70%, 10%) nonmesonic modes ρ 2 N (r) KNN YN+240 MeV (20%) Γ K width phase space suppression x density enhancement

32 Single-K nuclei Suppression factors used in the calculation:

33 RMF Methodology Calculations of 12 C, 16 O, 40 Ca, 90 Zr, 208 Pb L RMF NL-SH, NL-TM1(2), L-HS L Y g ωλ = 2/3g ωn ; g φλ = 2 g 3 ωn SU(6) g σλ & g σ Λ fitted to Λ hypernuclei + ΛΛ hypernuclei g ωξ = 1/3g ωn, g ρξ = g ρn, g φξ = g ωn SU(6) g σξ fitted to the V Ξ depth L K vector-meson couplings SU(3): 2g ωk = 2g ΦK = 2g ρk = g ρπ = 6.04 (g ρπ from ρ 2π) V K V 80 MeV scalar-meson couplings g σ K = 2.65 (from f 0 (980) K + K ) g σk varied to scan over wide range of B K

34 Single-K nuclei Γ K follows the dependence sf(b K ) 200 Γ K - (MeV) C O Ca Pb B - K (MeV) Fig. 1 The K decay widths Γ K in K C, K O, K Ca, and K Pb as function of the K binding energy B K. The dashed line indicates a static nuclear matter calculation.

35 Single-K nuclei Γ K for absorption only through: KN πσ 200 1N only 150 Γ K - (MeV) OK B - K (MeV) Fig. 2 The K decay width Γ K as a function of the K binding energy B K.

36 Single-K nuclei Γ K for absorption through KN πσ (80%), KNN ΣN (20%) ρ N only πσ; ρ Γ K - (MeV) OK B - K (MeV) Fig. 2 The K decay width Γ K as a function of the K binding energy B K.

37 Single-K nuclei Γ K for absorption through KN πσ, πλ (70%,10%), KNN ΣN (20%) ρ N only πσ; ρ πσ, πλ; ρ Γ K - (MeV) OK B - K (MeV) Fig. 2 The K decay width Γ K as a function of the K binding energy B K.

38 Single-K nuclei Γ K for absorption through KN πσ, πλ (70%,10%), KNN ΣN (20%) ρ N only πσ; ρ πσ, πλ; ρ πσ, πλ; ρ 2 Γ K - (MeV) OK B - K (MeV) Fig. 2 The K decay width Γ K as a function of the K binding energy B K.

39 Single-K nuclei 150 Γ K - (MeV) PbK - πσ; ρ πσ, πλ; ρ πσ, πλ; ρ B - K (MeV) Fig. 3 The K decay width Γ K as a function of the K binding energy B K. 1N absorption πσ vs. πσ + πλ difference independent of atomic number 2N absorption ρ vs. ρ 2 difference core polarization

40 Single-K nuclei Fig. 4 Nuclear density distribution ρ(r) of 40 K Ca calculated using the RMF model NL-SH.

41 Single-K nuclei C ρ _ (fm -3 ) Ca O Pb B K - (MeV) Fig. 5 Average nuclear density ρ = A 1 R ρ 2 dr as function of the K binding energy.

42 Single-K nuclei C B K - (MeV) 100 STATIC Γ K - (MeV) STATIC α ω α σ Fig. 6 The K binding energy and width in 12 K C calculated statically (open circles).

43 Single-K nuclei 200 B K - (MeV) C DYNAMICAL STATIC Γ K - (MeV) STATIC DYNAMICAL α ω α σ Fig. 6 The K binding energy and width in 12 K C calculated statically (open circles) and dynamically (solid circles).

44 Single-K nuclei 200 B K - (MeV) C ImV opt = 0 DYNAMICAL STATIC Γ K - (MeV) STATIC DYNAMICAL α ω α σ Fig. 6 The K binding energy and width in 12 K C calculated statically (open circles) and dynamically (solid circles). The dotted line shows B K for ImV opt = 0.

45 Single-K nuclei O radius (fm) p 1/2 increase of the nuclear rms radius for large B K reduced binding energy of the 1p 1/2 state due to s.o. term E n (MeV) p 3/2 1s 1/ B K - (MeV) Fig. 7 Nuclear rms radius and neutron s.p. energies for 16 K O as function of the K binding energy; for the L-HS model (open circles) and the NL-SH model (solid circles).

46 Chiral approach K nuclei Fig. 9 ImV opt in 16 K O as function of B K. ImV opt comes from chiral approach, ReV opt from RMF

47 Chiral approach K nuclei Fig. 10 Γ K as function of B K. ImV opt comes from chiral approach, ReV opt from RMF KNN YN is not included!

48 Chiral approach K nuclei B K and Γ K calculated using V opt from chiral K N amplitudes (in MeV). static calculation dynamical calculation B K Γ K B K Γ K 12 C O Ca Pb Not included: KNN YN hadron selfenergies

49 Multi- K nuclei O + κk B K (MeV) κ Fig. 8 The K binding energies as functions of the number κ of antikaons

50 Multi- K nuclei O + κk B K (MeV) κ Fig. 8 The K binding energies as functions of the number κ of antikaons

51 Multi- K nuclei O + κk B K (MeV) κ Fig. 8 The K binding energies as functions of the number κ of antikaons

52 Multi- K nuclei O + κk B K (MeV) κ Fig. 8 The K binding energies as functions of the number κ of antikaons

53 Multi- K nuclei O + κk B K (MeV) κ Fig. 8 The K binding energies as functions of the number κ of antikaons

54 Multi- K nuclei O + κk B K (MeV) K - K κ Fig. 8 The K binding energies as functions of the number κ of antikaons. saturation observed across the periodic table

55 Multi- K nuclei O+ κk B K - (MeV) σ, ω κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

56 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

57 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

58 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ σ, ω, φ, ρ, Coul σ, ω, φ, ρ, Coul, ImV opt σ, ω, φ, ρ, σ, Coul, ImV opt κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

59 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ σ, ω, φ, ρ, Coul σ, ω, φ, ρ, Coul, ImV opt σ, ω, φ, ρ, σ, Coul, ImV opt κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

60 Multi- K nuclei O+ κk B K - (MeV) σ, ω σ, ω, φ σ, ω, φ, ρ σ, ω, φ, ρ, Coul σ, ω, φ, ρ, Coul, ImV opt σ, ω, φ, ρ, σ, Coul, ImV opt saturation occurs for any boson-field composition (when ω-field present repulsion) no saturation of B K for a purely scalar interaction substantial effect of ImΠ K for B K 100 MeV κ Fig. 9 The K binding energy as a function of the number κ of antikaons.

61 Multi- K nuclei B K - (MeV) Ca + κk - saturation qualitatively independent of RMF parametrization 100 NL-SH NL-TM1 NL-TM κ Fig. 10 The K binding energy as a function of the number κ of antikaons.

62 Multi- K nuclei ρ N (fm -3 ) O + κk ρ N (fm -3 ) Pb + κk ρ K (fm -3 ) no K 2K 4K 6K 8K 10K ρ K - (fm -3 ) no K - 2K - 4K - 6K - 8K - 10K - 12K - 14K - 16K r (fm) r (fm) Fig. 11 Nuclear (ρ N ) and K (ρ K ) density distributions for various numbers κ of antikaons.

63 Multi- K nuclei Pb + κk - m * K _ (MeV) K - 2K - 4K - 6K - 8K R 8 10 r (fm) ch m K (r) almost independent of κ over a large volume of the nucleus (r 3 fm) K effective mass m K = m K g σk m K σ affected only in the region r 2-3 fm for antikaons the concept of nuclear matter is far from being realized even in 208 Pb Fig. 12 K effective mass in 208 Pb + κk. The dashed curve stands for the static case.

64 Multi- K exotic configurations B K (MeV) O + κk n + κk n + κk 0 E n (MeV) n + 8K 0 0 8n + 4K 16 O 16 O + 4K - 16 O + 8K - 0 p 1/2-20 p 1/2-40 p 3/ p 3/2-100 s 1/ s 1/2-180 Fig. 14 Neutron single-particle spetra MeV 50 MeV κ Fig. 13 K separation energy as a function of the number κ of antikaons. systems of a finite number of neutrons bound by adding few K 0 s

65 Multi- K exotic configurations O + κk - B[A,Z,κK] (MeV) n+6p 12n+4p 14n+2p 16n + κk 0 8n + κk 0 configurations unstable against charge-exchange reactions, e.g. 16n + 8 K 0 16 O+8K κ Fig. 15 Total binding energy of multistrange systems.

66 Multi- K hypernuclei We considered many-body systems consisting of the SU(3) octet N, Λ, Σ, Ξ baryons that can be made particle stable against strong interaction only Ξ N ΛΛ and Ξ 0 n ΛΛ (Q = 20 MeV) can be overcome by binding effects NΛΞ particle stable configurations (ΞN ΛΛ Pauli blocked due to Λ orbitals being filled up to Fermi surface) filling up Λ single-particle states up to the Λ Fermi level adding Ξ hyperons (Ξ 0, Ξ ) as long as both reactions: [AN, ηλ, µξ] [(A 1)N, ηλ, (µ 1)Ξ] + 2Λ [AN, ηλ, µξ] [(A + 1)N, (η 2)Λ, (µ + 1)Ξ] are kinematically blocked

67 Multi- K hypernuclei Fig. 16 The K binding energy B K in 16 O as a function of the number κ of antikaons and η of Λ hyperons.

68 Multi- K hypernuclei Fig. 17 The K binding energy B K in 208 Pb as a function of the number κ of antikaons and η of Λ hyperons.

69 Multi- K hypernuclei B K - (MeV) Pb + κk - + η Λ Λ 20Λ 50Λ 70Λ 100Λ κ Fig. 18 The K binding energy B K in 208 Pb as a function of the number κ of antikaons and η of Λ hyperons.

70 Multi- K hypernuclei B K (MeV) Ca+20Λ+2Ξ 0 +κk Zr+40Λ+2Ξ 0 +2Ξ +κk 90 Zr+40Λ+2Ξ 0 +2Ξ +κk ; VΞ = 25 MeV 208 Pb+106Λ+8Ξ 0 +18Ξ +κκ 208 Pb+106Λ+κK κ Fig. 19 The K binding energy B K in A Z + ηλ + µ 0 Ξ 0 + µ Ξ + κk as a function of the number κ of antikaons.

71 Multi- K hypernuclei Zr + 40Λ + 2Ξ 0 + 2Ξ ρ (fm 3 ) Y + 0K no Ξ (empty symbols) N K ρ (fm 3 ) N Y ρ N ρ Y ρ K - K r (fm) Fig. 20 Density distributions in multi-k hypernuclear configurations.

72 Multi- K hypernuclei

73 K + mesons in (hyper)nuclear medium O 16 O+2Λ O+8Λ 16 O+4Λ 4p 16 O+7Λ 7p 40 V K + (MeV) V K + (MeV) Zr 90 Zr+40Λ 90 Zr+40Λ+8(Ξ 0 +Ξ ) 90 Zr+40Λ+8(Ξ 0 +Ξ ), gσ Ξ =g φξ =0 * r (fm) r (fm) Fig. 21 The K + static potential in hypernuclear systems connected with 16 O and 90 Zr. presence of hyperons decreases K + repulsion

74 K + mesons in (hyper)nuclear medium V K +(r) (MeV) O 16 O + 2Λ 16 O + 8Λ 16 O + 4Λ - 4p 16 O + 7Λ - 7p 16 - O + 4K 16 - O + 8K r (fm) Fig. 22 The K + static potential in hypernuclear systems connected with 16 O. nuclei sustained by K mesons - immensely deep but short range K + potential only weakly bound K + states found for large number of K mesons

75 Summary Dynamical calculations of K nuclei across the periodic table: Γ K : phase space suppression x enhancement due to increased density Γ K 40 ± 10 MeV for B K (100, 200) MeV Substantial polarization of a (light) nucleus due to K : ρ max/ρ 0 2, ρ/ρ Calculations of (hyper)nuclear systems containing several antikaons: K binding energies + nuclear densities saturate with the number of K saturation - a robust feature of multi- K nuclei occurs for any boson-field composition (with ω meson) qualitatively independent of the RMF model occurs also in the presence of hyperons in general, B K < 200 MeV kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter

76 Summary Dynamical calculations of K nuclei across the periodic table: Γ K : phase space suppression x enhancement due to increased density Γ K 40 ± 10 MeV for B K (100, 200) MeV Substantial polarization of a (light) nucleus due to K : ρ max/ρ 0 2, ρ/ρ Calculations of (hyper)nuclear systems containing several antikaons: K binding energies + nuclear densities saturate with the number of K saturation - a robust feature of multi- K nuclei occurs for any boson-field composition (with ω meson) qualitatively independent of the RMF model occurs also in the presence of hyperons in general, B K < 200 MeV kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter

77 Status Quo

78 Status Quo František Kupka Abstract composition