1. 1.Introduction 2.Exotic properties of K nuclei 3.To go forward (Future plan) 4.Summary Dense K nuclei - To go forward - KEK Nuclear workshop @ KEK, ’06.Aug.3 A. Dote （ KEK ） ´ Y. Akaishi (Nihon univ.) T. Yamazaki (RIKEN) W. Weise (TU Muenchen)

2. Introduction What are kaonic nuclei (K nuclei)? K - meson is bound in a nucleus by strong interaction. cf) Kaonic atom K - meson is around a nucleus, bound by Coulomb interaction. K nuclei can exist as discrete states, since K - meson is deeply bound below Σπ threshold. KNNN… ΣπNN… K nuclear state

3. Deeply bound; Binding energy of K - > 100 MeV Discrete state; Below Σπ threshold Very attractive I=0 KN interaction makes …... Deeply bound kaonic nuclei 1.free KN scattering data 2.1s level shift of kaonic hydrogen atom 3.binding energy and width of Λ(1405) Phenomenological KN potential (AY KN potential) Strongly attractive. Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 = K - + proton

4. My motivation Only one K - meson can drastically change the nuclear structure? Only one K - meson can drastically change the nuclear structure? Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 8 Be + K - … Akaishi’s special lecture held in Kyoto university in ’00.

5. Exotic features of K nuclei Fully microscopic treatment No assumption on nuclear structure; cluster, deformation … System self-organizes only following energy variation. p n Normal nucleus p n K-K- normal nucleus ? ?? ? ? ? Kaonic nucleus What kind of structure does A+1 system favor? Antisymmetrized Molecular Dynamics （ AMD ） K - meson = a seed of strong attraction

6. ☆ Improve AMD for K nuclei mixing + Charge projection of total wave function Single nucleon/kaon wave function

7. Hamiltonian in AMD calculation : effective NN int. Tamagaki potential (OPEG) : effective KN int. AY KN potential G-matrix method Y. Akaishi and T. Yamazaki, PRC 52 (2002) 044005 Deep potential Y. Akaishi T. Yamazaki A. Dote W. Weise Shallow potential E. Oset H. Toki A. Gal vs Akaishi-san’s talkProf. Oset’s talk

8. A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590 (2004) 51; PRC 70 (2004) 044313. AMD 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 nuclei. maximum density > 4ρ 0 averaged density 2 ～ 4ρ 0 4.Proton satellite in pppK - Rrms = 2.46 fm β = 0.63 Central density = 0.10 /fm^3 8 Be Density (/fm^3) 0.0 0.10 0.20 Nucleus-K - threshold Σπ threshold (simple AMD) Width (Σπ, Λπ) 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 Isovector deformation pppK - Proton satellite

9. Various shapes of K nuclei ppnK - pppK - pppnK - 6 BeK - 3 fm 9BK-9BK- 4 fm 8.8ρ 0 9.2ρ 0 7.6ρ 0 5.4ρ 0 4.1ρ 0 1.141.67 1.78 2.552.53 4 fm 4.1ρ 0 Single K - meson can interact with limited numbers of nucleons? Saturation of E(K)

10. ① Deeply bound and Dense ③ Isovector deformation ④ proton satellite pppK - ② Drastic change of structure 8 Be 8 BeK -

11. Various groups are trying to search for deeply bound kaonic nuclei in various way. T. Suzuki, M.Iwasaki et al; 4 He(stopped K -, n or p) @ KEK ppnK - : B.E. = 169MeV, pnnK - : B.E. = 195MeV H. Fujioka, T. Nagae et al; ppK - @ DAΦNE ppK - : B.E. = 116MeV Kishimoto et al; 16 O(inflight K -, n) 15 OK - @ BNL N.Herrmann et al; Invariant-mass method (heavy-ion collision) @ GSI ppnK - : B.E. ～ 150MeV (preliminary) K. Suzuki et al; proton induced reaction @ GSI J-PARC

12. The technique of conventional nuclear physics Phenomenological KN interaction Experimental results are coming up. K nucleus has very exotic properties! Truth To go forward

13. 1, Short-range repulsive core part of NN interaction The repulsive core part of the effective NN potential derived by G-matrix method is too much smoothed out for the study of kaonic nuclei? “Beyond the conventional nuclear physics” 3, Mystery of two-body absorption (KNN --> YN) … large decay width at high density K nuclei can survive? 2, Using more theoretical KN interaction Energy- and density-dependence I=1 P-wave interaction … Attractive below Σ(1385). … Large contribution at high density? Additional attraction to deeply bound kaonic nuclei To go forward … Collaborating with W. Weise This part is undergoing… This part is undergoing…

14. Summary  Kaonic nuclei have interesting properties! The AMD study with AY KN interaction showed … K - is deeply bound by ～ 100 MeV and forms highly dense state. Strange structures appear in K nuclei. Drastic change of 8 Be structure, Isovector deformation in 8 BeK -, Proton satellite in pppK -.

15.  Study more various K nuclei  Double K nuclei?  Other type of KN interaction? Many experiments will start, or started. T. Suzuki, Iwasaki et al; 4 He(stopped K -, n or p) @ KEK Fujioka, Nagae et al; ppK - @ DAΦNE Kishimoto et al; 16 O(inflight K -, n) 15 OK - @BNL Herrmann et al; Invariant-mass method (heavy-ion collision) @ GSI K. Suzuki et al; proton induced reaction @ GSI J-PARC I=1 p-wave KN interaction … suggested by S. Wycech et al. nucl-th/0501019 Collaborate with W. Weise  Study K nuclei from the viewpoint of quarks Collaborate with Y. Kanada-En’yo and O. Morimatsu Λ(1405) = qqq-qq, ppK - = 7qq, ppnK - = 10qq (undeca-quarks state) - --  Apply our wave function to the study of reaction Dense or not? (S. Hirenzaki and J. Yamagata) Future plans

16. Kaonic nucleus K nuclei… Exotic system ! … related to various fields!! KN interaction Cold and Dense Kaonic atom Λ （１４０５） Interesting structure … Nuclear structure Kaon condensation (Strange) Quark matter Chiral symmetry restoration