1 / 69

K - 中間子原子核、最近の状況

Prototype of kaonic nuclei “K - pp”. KEK Theory center J-PARC branch /IPNS Akinobu Doté. K - 中間子原子核、最近の状況. Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN). Introduction Expanding the nuclear world Exotic properties of kaonic nuclei with

liseli
Download Presentation

K - 中間子原子核、最近の状況

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Prototype of kaonic nuclei “K-pp” KEK Theory center J-PARC branch /IPNS AkinobuDoté K-中間子原子核、最近の状況 Y. Akaishi (Nihon/RIKEN), T. Yamazaki (RIKEN) Introduction Expanding the nuclear world Exotic properties of kaonic nuclei with a phenomenological KbarN potential Variational calculation of K-ppwith a chiral SU(3)-based KbarN potential Current status of the K-ppstudy Experiments related to Kbar nuclear physics Summary and future plan T. Hyodo (TITech), W. Weise (TU Munich) 東大駒場セミナー ’12.05.23 @ 東京大学駒場キャンパス

  2. 1. Introduction

  3. Expanding the nuclear world 原子核 ＝ 陽子・中性子からなる有限量子多体系、　安定核　…　約３００種 Large isospin 不安定核…約3000種、RIBF＠理研で展開 http://www.rarf.riken.go.jp/newcontents/contents/facility/RIBF.html

  4. Expanding the nuclear world 原子核 ＝ 陽子・中性子からなる有限量子多体系、　安定核　…　約３００種 Large isospin 不安定核…約3000種、RIBF＠理研で展開 Strangeness ハイパー核 … J-PARC (JAEA+KEK) で展開

  5. K- Kaonic nuclei Another form of nuclear system with strangeness Nucleus containing K- meson

  6. What is Kaonic nucleus? Hypernuclei… u s d Hyperon baryon = qqq Nucleus Strangeness is introduced through baryons.

  7. What is Kaonic nucleus? Strangeness is introduced through mesons … ubar s K- meson meson = qqbar quark (q) and anti-quark (qbar) pair Nucleus Kaonic nuclei !

  8. p + K- p + K- 1435 1435 Λ(1405) Λ(1405) 1405 1405 Σ + π Σ + π 1325 1325 Λ + π Λ + π 1250 1250 Energy [MeV] Energy [MeV] Σ Σ 1190 1190 Λ Λ 1115 1115 940 940 p,n p,n Actors in Kbar nuclei Leading actors Key person Excited state of Λ Supporting players

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

  10. p + K- p + K- 1435 1435 Λ(1405) Λ(1405) 1405 1405 Σ + π Σ + π 1325 1325 Λ + π Λ + π 1250 1250 Energy [MeV] Energy [MeV] Σ Σ 1190 1190 Λ Λ 1115 1115 I=0 Proton-K-bound state with 30MeV binding energy? Not 3 quark state? 　　←　can’t be explained with a simple quark model… 940 940 p,n p,n Actors in Kbar nuclei Leading actors q ubar q s Key person Excited state of Λ q Supporting players u d u

  11. p + K- 1435 Λ(1405) 1405 Σ + π 1325 Λ + π 1250 Energy [MeV] Σ 1190 Λ 1115 Σπchannel is open at about 100 MeV below the Proton-K- threshold. 940 p,n Actors in Kbar nuclei Leading actors Key person Excited state of Λ Supporting players

  12. Deeply bound below πΣthreshold • (main decay channel) KNNN… Possible to exist as a quasi-bound state with narrow width ΣπNN… K nuclear state Interests of Kaonic nuclei Kaonic nucleus K- K- Proton • Self-bound • Kbar-nuclear system = • Nuclear structure change. • Highly dense state. • if the interaction is so attractive… Λ(1405)

  13. Studies with a phenomenological KbarN potential • Y. Akaishi and T. Yamazaki, PRC 52, 044005 (2002) Phenomenological KbarN potential (AY KbarN potential) Strongly attractive • Free KbarNscattering data • 1s level shift of kaonic hydrogen atom • Binding energy and width of Λ(1405) Λ(1405) = I=0K- p quasi-bound state with 27 MeV binding energy 3HeK- … 100MeV binding with a narrow width of 20MeV. (a simple model calculation) Deeply bound kaonic nuclei ! • A. D., H. Horiuchi, Y. Akaishi and T. Yamazaki, PLB 590, 51 (2004); PRC 70, 044313 (2004) Systematic study of light kaonic nuclei (3HeK- to 11CK-) with AMD + G-matrix (effective NN potential ) + AY KbarN potential shows their interesting properties…

  14. ①Deeply bound and Dense ②Drastic change of structure 8Be 8BeK- ③Isovector deformation ④Proton satellite pppK- Kaonic nuclei ＝ exotic system

  15. Theoretical studies of nuclear system with anti-kaons • Light nuclei with a single antikaon 3HeK-～ 11CK- studied with AMD + G-matrix + AY potential E(K)≒100MeV • Light nuclei with double antikaons 3HeK-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, 055204 (2007); • PRC77, 045206 (2008) - T. Muto, T. Maruyama and T. Tatsumi, PRC79, 035207 (2009) … Antikaon part is based on non-linear chiralLagrangian Strongly repulsive KbarKbar interaction Saturation for the number of antikaons In case of 15O+xK-, central nuclear density and –B/x are saturated for x>8. • Nuclear matter with antikoans Neutron star, kaon condensation…

  16. 2. Variational calculation of K-ppwith a chiral SU(3)-based KbarN potential

  17. Are kaonic nuclei really exotic? • The phenomenological KbarN potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. AY potential Chiral SU(3) KbarN πΣ ηΛ KΞ

  18. Are kaonic nuclei really exotic? • The phenomenological KbarN potential is all right? πΣ-πΣ potential is completely neglected, although it is somewhat strongly attractive in chiral SU(3) theory. • The G-matrix treatment is adequate? NN repulsive core is too smoothed out? As a result, such a dense state is formed??

  19. More theoretical study of the most essential kaonic nucleus K-pp system “Prototype of kaonic nuclei” studied with a chiral SU(3)-based KbarN potential

  20. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). 1E Strong repulsive core (3 GeV)

  21. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential

  22. Local KbarN potential based on Chiral SU(3) In Chiral unitary model, Resonance position in I=0 KbarN channel 1420 MeV not 1405 MeV ! T. Hyodo and W. Weise, PRC77, 035204(2008) I=0 KbarNscattering amplitude Chiral Unitary Effective potential 1420 Chiral unitary;T. Hyodo, S. I. Nam, D. Jido, and A. Hosaka, Phys. Rev. C68, 018201 (2003)

  23. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV • Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. Kbar N N

  24. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential • Av18 NN potential … a realistic NN potential with strong repulsive core (3GeV). • Effective KbarN potential based on Chiral SU(3) theory … reproduce the original KbarN scattering amplitude obtained with coupled channel chiral dynamics. Single channel, Energy dependent, Complex, Gaussian-shape potential I=0 KbarN resonance “Λ(1405)”appears at 1420 MeV, not 1405 MeV • Variational method … Trial wave function contains NN/KbarN correlation functions. The NN repulsive core can directly be treated. × Four variants of chiral unitary modes Shallow binding and large decay width Total B. E. : 20 ± 3 MeV G（KbarN→pY） : 40 ～ 70 MeV

  25. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar N N

  26. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, NNdistance in normal nuclei～ 2 fm Size of deuteron～ 4 fm Kbar K-pp中の二核子は普通の原子核の断片！ 通常核密度に対応していると思える。 1.97 fm N N 2.21 fm

  27. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar 1.97 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  28. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, I=0 KbarN 1.82 fm Kbar N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  29. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, Kbar I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  30. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, “Λ(1405)” as I=0 KbarN calculated with this potential 1.86 fm I=0 KbarN I=1 KbarN 1.82 fm 2.33 fm Kbar Almost “Λ(1405)” N N • NN distance = 2.21 fm KbarN distance = 1.97 fm • Mixture of TN=0 component = 3.8 %

  31. Structure of K-pp KbarN potential based on “HNJH” “Corrected”, “Λ(1405)” N Kbar Density distribution: KbarN pair in K-ppvs“L(1405)” Isospin 0 Isospin 0 KbarN pair “K-pp” N N Kbar Isospin 1 KbarN pair Isospin 0 and 1 mixed “L(1405)”almost survives in K-pp!

  32. A. Doté, T. Hyodo and W. Weise, Nucl. Phys. A804, 197 (2008) Phys. Rev. C79, 014003 (2009) Variational calculation of K-pp with a chiral SU(3)-based KbarN potential B .E. Width • s-wave KbarN potential • (Variational calculation) 20 ± 3 MeV 40 ～ 70 MeV • Dispersive correction • (Effect of imaginary part) +6～ +18 MeV • p-wave KbarN potential ～ -3 MeV 10 ～ 35 MeV • Two nucleon absorption 4～ 12 MeV K-pp … Total B .E. Total Width 20 ～ 40 MeV 55 ～ 120 MeV Rough estimation Very large…

  33. 3. Current status of the K-pp study

  34. Kbarnuclei = Exotic system !? To make the situation more clear … K-pp= Prototye of Kbar nuclei Studied with various methods, because it is a three-body system: • Doté, Hyodo, Weise Variational with a chiral SU(3)-based KbarN potential PRC79, 014003(2009) • Akaishi, Yamazaki ATMS with a phenomenological KbarN potential PRC76, 045201(2007) • Ikeda, Sato Faddeev with a chiral SU(3)-derived KbarN potential PRC76, 035203(2007) • Shevchenko, Gal , Faddeev with a phenomenological KbarN potential PRC76, 044004(2007) • Mares • Wycech, Green Variational with a phenomenological KbarN potential (with p-wave) PRC79, 014001(2009) • Arai, Yasui, OkaΛ* nuclei model PTP119, 103(2008) • continued by Uchino, Hyodo, Oka • Nishikawa, Kondo Skyrme model PRC77, 055202(2008) All calculations predict that K-pp can be bound. There are several experiments: Experiments concerned to this topics: FINUDA (Frascatti), KEK, DISTO (Sacley), OBELIX (CERN) Planned or undergoing experiments: FOPI (GSI), J-PARC, AMADEUS (Frascatti)

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

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

  37. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) Exp. FINUDA 115±7 67±14 K-absorption, Λp inv. mass DISTO 103±3±5 118±8±10 p+p→K++Λ+p, Λp inv. mass (Finalized) All four calculations shown above are constrained by experimental data. … KbarN scattering data, Kaonic hydrogen atom data, “Λ(1405)” etc. Only s-wave KbarN potential is used.

  38. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) DHW vs AY Difference of the used KbarN interactions.

  39. Comparison of AY potential and Chiral-based potential Coupled channel Chiral dynamics AY potential Weinberg-Tomozawa term derived from Chiral SU(3) effective Lagrangian Two poles (double pole); one couples strongly to KbarN, the other couples strongly to πΣ. Λ(1405) (experimentally observed) appears in I=0 πΣ-πΣchannel. I=0 KbarN resonance @ 1420MeV. KbarN πΣ ηΛ KΞ Λ(1405) = a quasi-bound state of I=0 KbarN at 1405MeV. Appears in I=0 KbarN channel. I=0 KbarN resonance @ 1405MeV. • Energy dependent potential • Somewhat strongly attractive • πΣ-πΣ interaction • Energy independent potential • No πΣ-πΣ interaction

  40. Quite different in the sub-threhold region Almost same in the on-shell region Comparison of AY potential and Chiral-based potential I=0 KbarN full scattering amplitude

  41. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) DHW vs AY In Chiral SU(3) theory, the πΣ-πΣ interaction is so attractive to make a resonance, while AY potential doesn’t have it. “Λ(1405)” is I=0KbarN bound state at 1420 MeV or 1405 MeV? AY potential is twice more attractive than Chiral-based one.

  42. Recent results with various calculations of K-pp Channels at final step B. E. Γ (mesonic) KbarN Int. Method DHW 20 ± 3 40 ～ 70 VariationalChiral SU(3) KbarN AY 47 61 VariationalPhenom. KbarN IS 60 ～ 95 45 ～ 80 FaddeevChiral SU(3) KbarN, πY (AGS) (Separable) SGM 50～70 90 ～ 110 FaddeevPhenom. KbarN, πY (AGS) (Separable) DHW vs IS Although both are based on Chiral SU(3) theory, results are very different from each other. • Separable approximation? • Different energy dependence of interaction kernel Vij? • πΣNthree-body dynamics • … may not be included in DHW. (Y. Ikeda and T. Sato, PRC79, 035201(2009))

  43. Variational cal. vsFaddeev A possible reason is Y. Ikeda and T. Sato, PRC79, 035201(2009) πΣN thee-body dynamics Three-body system calculated with the effective KbarN potential In the variational calculation (DHW), πΣ channel is eliminated and incorporated into the effective KbarN potential. π π K K K … K = + … N N N N Σ Σ conserved N N N N N N

  44. 4. Experiments related to Kbar nuclear physics

  45. Ｋ原子核に関係する実験 • Ｋ原子 (Kaonic atom) • Kaonic4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570) • S. Okada et. al., Phys. Lett. B653, 387 (2007) • Kaonic3He atom, 2pレベルシフト (3d→2p X線測定) • @ J-PARC (E17, DAY-1) • Kaonic hydrogen atom, 1sレベルシフト @ DEARgroup, DAΦNE, • G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al., Phys. Lett. B704, 113 (2011) • Λ(1405) γ + p → K+ + Λ(1405), Λ(1405) → π Σ πΣ invariant mass測定 • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A835, 329 (2010) • CLAS / JLab K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010) π-Σ+, π0Σ0, π+Σ-が全て押さえられた

  46. Ｋ原子核に関係する実験 • Ｋ原子 (Kaonic atom) • Kaonic4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570) • S. Okada et. al., Phys. Lett. B653, 387 (2007) • Kaonic3He atom, 2pレベルシフト (3d→2p X線測定) • @ J-PARC (E17, DAY-1) • Kaonic hydrogen atom, 1sレベルシフト @ DEARgroup, DAΦNE, • G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al., Phys. Lett. B704, 113 (2011) • Λ(1405) γ + p → K+ + Λ(1405), Λ(1405) → π Σ πΣ invariant mass測定 • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A835, 329 (2010) • CLAS / JLab K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010) π-Σ+, π0Σ0, π+Σ-が全て押さえられた

  47. DEAR exp. for kaonic hydrogen atom G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005) Kaonic hydrogen atom, 1sのレベルシフト @ DEARCollaboration, DAΦNE, Frascati National Laboratories cf) KEK exp. M.Iwasakiet al., Phys. Rev. Lett. 78, 3067 (1997) シフトの符号は同じだが、ＫＥＫの前回の実験（ＫｐＸ）と重ならない！ KEK exp. Coupled channel chiral dynamics (Chiral unitary model) で DEARの結果を合わすのには苦労する。 かろうじてギリギリ合わせられる程度。。。 DEAR B. Borasoyet al., Phys. Rev. Lett. 94, 213401 (2005)

  48. SHIDDARTA exp. for kaonic hydrogen atom M. Bazzi et al., Phys. Lett. B704, 113 (2011) Kaonic hydrogen atom, 1sのレベルシフト @ SHIDDARTACollaboration, DAΦNE, Frascati National Laboratories K-p散乱長が精密に決定 理論計算にとって重要な インプットに強い拘束条件 KbarNsubthresholdでの 散乱振幅の振る舞い、 Λ(1405)のポールの位置、 が制限される。 Y. Ikeda, T. Hyodo and W. Weise, Phys. Lett. B706, 63 (2011) KEK実験（ＫｐＸ）とコンシステントな結果

  49. Ｋ原子核に関係する実験 • Ｋ原子 (Kaonic atom) • Kaonic4He atom, 2pレベルシフト (3d→2p X線測定) @ KEK (E570) • S. Okada et. al., Phys. Lett. B653, 387 (2007) • Kaonic3He atom, 2pレベルシフト (3d→2p X線測定) • @ J-PARC (E17, DAY-1) • Kaonic hydrogen atom, 1sレベルシフト @ DEARgroup, DAΦNE, • G. Beer et al., Phys. Rev. Lett. 94, 212302 (2005)Frascati National Laboratories • Kaonic hydrogen, deuterium @ SIDDHARTA group M. Bazzi et al., Phys. Lett. B704, 113 (2011) • Λ(1405) γ + p → K+ + Λ(1405), Λ(1405) → π Σ πΣ invariant mass測定 • LEPS / SPring-8 J. K. Ahn, Nucl. Phys. A835, 329 (2010) • CLAS / JLab K. Moriya and R. Schumacher, Nucl. Phys. A835, 325 (2010) π-Σ+, π0Σ0, π+Σ-が全て押さえられた

  50. KEK E570 for kaonic4He atom S. Okada et. al., Phys. Lett. B653, 387 (2007) Kaonic4He atom, 2pのレベルシフト 3d→2p X線測定 @ KEK, E570 “Kaonic helium puzzle” 理論の予言がほぼ0eVに対して、 過去の実験ではシフトは平均-43 eV シフトは 0 eVとconsisitent パズルは解けた！ S. Hirenzaki et al., Phys. Rev. C61, 055205 (2000)

More Related