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重い不安定核における集団運動

重い不安定核における集団運動. 山上　雅之　 ( 理化学研究所 ). トピックス. 　新しい独立粒子運動 　集団運動の質的変化：超流動、低励起振動状態 　中性子過剰 Ni 同位体（球形核） 　中性子過剰 Mg 同位体（変形核）. 集団運動 - 多彩な“形”の物理 -. 原子核 ⇒ 様々な“形”が出現する最小の量子多体系. 粒子密度の変形（実空間回転対称性の破れ）. エキゾチック変形 ( 非軸対称８重極変形） !?. ４重極変形. オブレート. プロレート.

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重い不安定核における集団運動

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  1. 重い不安定核における集団運動 山上　雅之　(理化学研究所) トピックス • 　新しい独立粒子運動 • 　集団運動の質的変化：超流動、低励起振動状態 • 　中性子過剰Ni同位体（球形核） • 　中性子過剰Mg同位体（変形核）

  2. 集団運動 -多彩な“形”の物理- 原子核 ⇒ 様々な“形”が出現する最小の量子多体系 粒子密度の変形（実空間回転対称性の破れ） エキゾチック変形(非軸対称８重極変形）!? ４重極変形 オブレート プロレート Refs. S.Takami, K.Yabana, and M.Matsuo: Phys. Lett. B431, 242 (1998) M.Y., K.Matsuyanagi, and M.Matsuo, Nucl. Phys. A693, 579 (2001) 超流動性（ゲージ空間・実空間回転対称性の破れ） 対称性の破れと集団モードの発生 • 自発的対称性の破れ（β、Δ）を回復する集団モード（回転、対回転） • 様々な振動モード（形、対振動） vibration （各モードのエネルギースケール、モード結合） zero-freq. mode

  3. Gammasphere: www-gam.lbl.gov

  4. Motivation 理研RIBF 軽い不安定核 重い不安定核 どのような新しい物理の可能性が拓けるか？ 重い不安定核における新しい集団運動の物理に焦点を当てる。 キーワード：弱束縛、連続状態、対相関

  5. Pairing correlation in borromean nucleus 11Li Two-particle density in 11Li n n 9Li Soft E1 excitation K.Hagino, H.Sagawa, Phys.Rev. C 72, 044321 (2005) New data: T. Nakamura, et al., Phys. Rev. Lett. 96, 252502 (2006) Appreciable two neutron spatial correlation Di-neutron correlation is implied.

  6. NN force and di-neutron formation D.M.Brink, R.A.Broglia, Nuclear Superfluidity, Cambridge University Press, 2005

  7. Questions In heavy n-rich nuclei with many weakly-bound neutrons, • Formation of multi di-neutrons and their condensation? • Collective excitations? “Core” 11Li ??

  8. Pairing correlation in weakly-bound nuclei Pair scattering into continuum states Break down of BCS approximation • Pairing correlation dose NOT change the spatial structure. • Neutron gas problem J.Dobaczewski, H.Flocard, J.Treiner, Nucl. Phys. A422, 103 (1984)

  9. Coordinate space Hartree-Fock-Bogoliubov theory A. Bulgac, FT-194-1980, CIP-IPNE, Bucharest Romania, 1980 (nucl-th/9907088) J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A422, 103 (1984) Asymptotic behavior at infinity Pairing correlation changes the spatial structure Different asymptotic behavior

  10. Quasiparticle states in weakly-bound nuclei No neutron gas HFB HF+BCS HFB HF+BCS Pairing anti-halo effect K. Bennaceur, et al., Phys. Lett. 496B, 154 (2000)

  11. New features of collective excitations In weakly-bound superfluid nuclei,... New type independent particle motions Novel features? Collective excitations Coherent motions involving many two-quasiparticle states

  12. First 2+ states in neutron rich Ni isotopes • Comparison (Skyrme SLy4) • HFB + QRPA • HF-resonant BCS + QRPA • HF + RPA Ref. M.Y. Phys. Rev. C72, 064308 (2005)

  13. z = 0 plane 2 z-axis 1 High-l non-resonant continuum states h11/2 res. (l=5) HFB Vpair fixed High-l continuum states Spatial localization of correlated pair (di-neutron picture) Ref. M.Matsuo, et. al., Phys. Rev. C 71, 064326 (2005)

  14. Role of high-l continuum lmax → larger Steeper slope

  15. Neutron rich Mg isotopes Collaborators • K. Matsuyanagi (Kyoto) • K. Yoshida (Kyoto)

  16. N=28 HFB (Gogny DIS) Z=12 J.Terasaki, H.Flocard, P.-H.Heenen, P.Bonche Nucl.Phys. A621, 706 (1997) HFB (Skyrme SIII) R.Rodriguez-Guzman, J.L.Egido, L.M.Robledo Phys. Rev. C65, 024304 (2002) Deformed multi-weakly-bound nucleon system N=28 X 40Mg region 44S X X X 42Si 40Mg 38Mg 36Mg Z=12 X X X

  17. Ingredients taken into account in this calculation Continuum Deformation Pairing 0 HFB, QRPA calculation simultaneously taking into account Directly solve HFB eq. in coordinate-space mesh-representation X H.O. basis Spatially extended structure

  18. Neutron two-body correlation density in 40Mg External region High-W states are required for convergence Reference neutron Indication of spatial localization of the correlated pair (di-neutron picture)

  19. Di-neutron correlation in 36,38Mg

  20. Quadrupole vibrations in n-rich Mg isotopes (1W.u.=6 - 8fm4)

  21. Microscopic structure of the low-lying K=0+ mode [310]1/2 3.16% 5.86% [321]3/2 35.7% [202]3/2 [330]1/2 [330]1/2 32.2% [200]1/2 3.19% [202]3/2 1.07% [202]5/2

  22. Soft K=0+ mode in deformed nuclei 2 1 Two-level model (Bohr and Mottelson) Transition matrix element opposite sign Enhancement Deformation of pairing field

  23. Two neutron pair transition strengths Monopole pairing Quadrupole pairing

  24. More exotic soft K=0+ mode in 36Mg Configurations (e) (a) (b) (c) (d) (e) (c) (a) (b) (d) … Violation of selection rule valid for H.O. like w.f. If is good quantum number for non-zero transition matrix elements with

  25. Octupole vibrations

  26. Microscopic structure of the K=0- mode at β=0.3 ~8 W.u. (intrinsic) [321]3/2 Single 2qp excitation is dominant, but [202]3/2 contribution of many 2qp excitations Enhancement of transition strength (1W.u.=60fm6)

  27. Microscopic structure of the K=0- mode atβ=0.55 Strikingly enhanced transition strengths ~100 W.u. (intrinsic) Coherent coupling of many 2qp excitations Striking enhancement of transition strength (1W.u.=60fm6) Good indicator of large deformation

  28. Systematic features Soft octupole vib. associated with SD shell structure cf. Soft K=0- and 1- modes on SD state in 40Ca and 44Ti T.Inakura et al., NPA768(2006)61 Gamma vibration Coupling between pair fluctuation and beta vibration Z=12 Excitation of protons Soft K=0+ mode

  29. Continuum Deformation Pairing まとめ 中性子過剰Ni、Mg同位体を例に、重い不安定核での新しい物理の可能性の“一端”を議論した。 • 新しい独立粒子運動 • 新しい超流動性（BCSからBEC（ダイニュートロン凝縮）の可能性） • 低励起振動状態の質的変化（連続状態、対相関、対ポテンシャルの変形） 展望 • より系統的な計算（中性子過剰Si、S、Arなど、正負パリティ振動、回転運動） • 理論計算の精密化（変形Skyrme-QRPA、連続状態の取り扱い、など）

  30. 5-D quadrupole zero point energy corrections for 32Mg GOA X S.Peru, M.Girod, J.F.Berger, Eur.Phys.J. A 9, 35 (2000)

  31. 空間回転対称性の回復： 32Mgの場合 HFB X X X X X X R.Rodriguez-Guzman, J.L.Egido, L.M.Robledo, Nucl.Phys. A709, 201 (2002) 概念図 Intrinsic frameが上手く定義できない 0 Generator Coordinate Method (GCM)

  32. Angular correlation z = 0 plane 2 1 z-axis (symmetry axis)

  33. Our approach Ground state Coordinate-space HFB Mean-field Deformed Woods-Saxon potential Pair-field Excited states QRPA in matrix formulation Residual interaction p-h channel p-p channel

  34. Difference of K=0+ mode between 34Mg and 40Mg proton excitations

  35. Spatial structure of 2qp excitations in 40Mg

  36. Quadrupole1p-1h states in 86Ni Decoupling region Quadrupole 1p-1h states Quadrupole 1p-1h states No pairing 3s1/2 → d3/2 (res) 2d5/2 → d3/2 (res) 2d5/2 → g7/2 (res) Correlated region

  37. Quadrupole two-quasiparticle statesin 86Ni Neutrons in 86Ni • Increase of available configurations: p-h, p-p, h-h channels • Correlations between s1/2, d3/2 and d5/2 states in spatially extended region • Competition between the pairing anti-halo effect in the lower components and the broadening effect in the upper components

  38. θ O Di-neutron correlation in medium mass region Extensive discussion for spherical nuclei (O, Ca, and Ni) M.Matsuo, K.Mizuyama, and Y.Serizawa, Phys. Rev. C 71, 064326 (2005) Two-body correlation density (spin anti-parallel) Coordinate space HFB • High-l states → Spatial localization of the correlated pair • Di-neutron correlation becomes stronger as approaching the neutron drip line

  39. Deformations of neutron-rich Mg isotopes “Skyrme-HFB deformed nuclear mass table” K.Yoneda et al., PLB499(2001)233 M.Stoitsov et al.,PRC68(2003),054312 Gogny-HFB calculation using D1S R. Rodríguez-Guzmán et al., NPA709(2002)201 34Mg is well deformed.

  40. Convergence of two-body correlation density High-W states are required in nuclei close to the neutron drip line Spatial localization of the correlated pair (di-neutron picture)

  41. Size of neutron Cooper pair M.Matsuo, nucl-th/0512021

  42. BCS-BEC crossover in fermionic 40K atoms Experiment: Regal et al., 2004 Analytically solvable BCS-BEC crossover model BEC BCS BEC BCS

  43. Courtesy of M. Matsuo

  44. Schematic level schemes for 40Mg

  45. 36Mg24周辺（変形した中性子過剰核） HFB (Skyrme SIII): J.Terasaki, H.Flocard, P.-H.Heenen, P.Bonche, Nucl.Phys. A621, 706 (1997)

  46. RIKEN RIBF r-process pass N=2Z Neutron drip line http://www.rarf.riken.go.jp/RIBF/nuclearchart-e.htm

  47. Onset of weak binding in nuclear structure M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D. J. Dean, Phys. Rev. C 68, 054312 (2003)

  48. J. Dobaczewski, M.V. Stoitsov, W. Nazarewicz, nucl-th/0404077

  49. Characteristic Pattern of Excited Spectrum 80Zr : Spherical + Y32 deformation (Td group) Rigid rotation… sequence of levels 0+, 3-, 4+, 6+, 7-, … with rotational energy relation Octupole vibration… low-lying Jπ=3- state 68Se : Oblate + Y33 deformation (D3h group) Octupole vibration low-lying Jπ=3- state Kπ=0+ rotational band (associated with the ground state) 0+, 2+, 4+, … Kπ=3- rotational band (associated with the low-lying 3- state) 3-, 4-, 5-, … Ref. S. Takami, K. Yabana, M. Matsuo: Phys. Lett. B431 (1998) 242

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