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K 凝縮ハイパー核の構造と安定性

「ストレンジネスとエキゾティクス・理論の課題」研究会 ( 志摩ビーチホテル , 2007 / 3/1 - 3/3 ）. K 凝縮ハイパー核の構造と安定性. 武藤　巧 ( 千葉工大 ). 1. Introduction. K 凝縮原子核 (KCN) を実験室で生成する可能性. 2. Formulation. Chiral symmetry for kaon-baryon interaction + effective interactions between baryons. 3. Numerical results.

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K 凝縮ハイパー核の構造と安定性

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  1. 「ストレンジネスとエキゾティクス・理論の課題」研究会 ( 志摩ビーチホテル, 2007 / 3/1 - 3/3） K凝縮ハイパー核の構造と安定性 武藤　巧 (千葉工大) 1. Introduction K凝縮原子核 (KCN) を実験室で生成する可能性 2. Formulation Chiral symmetry for kaon-baryon interaction + effective interactions between baryons 3. Numerical results ・KCN の構造・崩壊（A=20 ）におけるハイペロン混在の効果 ・構造（バリオン数密度, バリオン混在度, 束縛エネルギー) ・K -分布, バリオン分布に対する一様分布の妥当性 4. Summary and concluding remarks

  2. 1. Introduction Deeply bound kaonicnuclear states の存在可能性 [ Y.Akaishi and T.Yamazaki, Phys.Rev. C65 (2002) 044005. ] [A. Dote, H. Horiuchi et al., Phys. Lett. B 590 (2004) 51; Phys.Rev. C70 (2004) 044313. ] ー K nuclear clusters [T.Yamazaki, A. Dote and Y.Akaishi, Phys.Lett. B 587 (2004) 167. ] Cold and dense matter の実験室での実現 K 凝縮状態(無限系) との関連 ・KCN の構造・崩壊（A=20 ）におけるハイペロン混在の効果 ・構造（バリオン数密度, バリオン混在度, 束縛エネルギー) ・K -分布, バリオン分布に対する一様分布の妥当性

  3. 2. Formulation ----- (anti)kaon condensation in the laboratory ----- Kaon-condensed nucleus (KCN) Initial system K- mesons ( A: baryon number Zー|S|: electromagneticcharge |S| : strangeness ) ( |S| : the number of K-) + Target nucleus ( A: mass number, Z: atomic number) uniform density Systematic study of KCNby giving A, Z,|S|fromO(1)toO(100) (liquid drop picture) [ total energy of the KCN ] ( T= 0 ) surface energy Coulomb energy volume part =1 MeV/fm2

  4. Volume part of the energy ・Chiral symmetry effective chiral Lagrangian Classical kaon field Θ:chiral angle μ: chemical potential k: momentum S-wave K- - baryon int. (p, Λ, n, Σー) baryons ・ KN-sigma term (scalar int.) (Explicit χSB breaking) ・ Tomozawa-Weinberg term (vector int.) ・Nonrelativistic baryon-baryon effctive interactions in hyperonic matter [ S. Balberg and A. Gal, Nucl. Phys. A625 (1997), 435. ] ・Saturation property, ・ Incompressibility K=306 MeV ・ hyperon potential depths repulsive case VΛ= -27 MeV at  0.16 fm-3 = 23.5 MeV at  0.16 fm-3

  5. Volume part of energy density Baryon kinetic energy YN mass difference Baryon potential energy Kaon-baryon interaction and free kaons ・Strangeness conservation ・Charge conservation ・Baryon number conservation ・Chemical equilibrium for strong processes

  6. 3. Numerical results < a possibility of density isomer > noncondensed state with Λ or Σ- mixing K- condensed state with Λ mixing K- condensed state with Λ, Σ- mixing initial free K-, N system Ξ- の効果: 高密度領域で Σ- の代わりに混在する可能性 free Λ, N system

  7. K- condensed state with nucleons only Hyperon-mixed case (I) noncondensed state with Λ or Σ- mixing (II) K- condensed state with Λ mixing (III) K- condensed state with Λ, Σ- mixing free Λ, N system (I) (I) (II) (III) 8.3ρ0

  8. ハイペロン混在の効果 Energy minimum の位置は, 主として (1) classical K-(free kaon + kaon-baryon 引力) からの寄与 (2) Baryon potentialの寄与 の密度 ρB 依存性で決まる。 Mixing of hyperons ・(1)Kaon-baryon 引力がより強められる。 ・(2) ハイペロンの混在により核子の密度が相対的に小さくなる。 高密度での核子間斥力を避ける機構 (ハイペロンの混在によるバリオン運動エネルギーの減少効果は小さい。) High density and low energy state ができる。

  9. ・large strangeness fraction ：|S| / A 0.7 Properties of the kaon-condensed nucleus (density isomer) Kaon condensates + hyperons ・Highly dense and compact object RA〜0.6 A1/3 ( RA〜1.2 A1/3 for ordinary nuclei) ・Positive charge by proton is compensated by negative charge by K- Coulomb repulsion effect is small. ・decay modes: weak processes Long lifetime

  10. ・K -分布, バリオン分布に対する一様分布の妥当性 S 波 K 凝縮 K- の運動量 k = 0 (運動量空間での凝縮) (無限系) ・K- 凝縮, バリオン系は空間的に一様分布 ・ストレンジネス数|S| が充分に大きい　　　 Classical kaon field [ Toshiki Maruyama, T. Tatsumi, T. Muto, preliminary result ] (有限系) K- field proton density neutron density Thomas-Fermi approx. in the RMF model

  11. 4. Summary and concluding remarks Highly dense and compact object with kaon condensates ・高密度・低エネルギー状態の形成には Hyperon-mixing効果が重要 ・ density isomer state の形成には 　たくさんの (negative) strangeness ( |S|=O(A) )を核内に閉じ込める必要。 ・decay mode は weak processes 長寿命 Kaon condensates とhyperon との共存により, EOS が著しく軟化 Consistency with neutron-star mass observation [ S. E. Thorsett, D. Chakrabarty, Astrophys.J. 512(1999) 288.] [D. J. Nice et al., Astrophys.J. 634 (2005) 1242. ] ・非常に高密度領域でのバリオン間の斥力効果の不定性

  12. Future problems Realistic effects ・validity of uniform distribution of <K-> and baryons ・ambiguity of kaon - baryon attractive interaction （ s-wave scalar attractionΣKn term） ・ baryon-baryon interactions at high densities (c.f. three-body repulsion between YNN, YYN, YYY) [ S. Nishizaki, Y. Yamamoto and T. Takatsuka, Prog. Theor.Phys. 108 (2002) 703. ] Connection to (strange) quark matter Relativistic framework Formation mechanisms of kaon-condensed nuclei in the laboratory ・ By the use of high-intensity K- beam, K- shouldbe trapped in a nucleus with total strangeness: |S | 〜A( > 10) ー (double K nuclear clusters . . . )

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