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超重原子核的结构

超重原子核的结构. 孙 扬 上海交通大学 合作者：清华大学 龙桂鲁， F. Al-Khudair 中国原子能研究院 陈永寿，高早春. 济南，山东大学 , 2008 年 9 月 20 日. Island of stability. What are the next magic numbers, i.e. most stable nuclei? Predicted neutron magic number: 184 Predicted proton magic number: 114, 120, 126. Explore the island.

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超重原子核的结构

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  1. 超重原子核的结构 孙 扬 上海交通大学 合作者：清华大学 龙桂鲁，F. Al-Khudair 中国原子能研究院陈永寿，高早春 济南，山东大学, 2008年9月20日

  2. Island of stability • What are the next magic numbers, i.e. most stable nuclei? • Predicted neutron magic number: 184 • Predicted proton magic number: 114, 120, 126

  3. Explore the island • Single particle states for SHE • Important for locating the island • Little experimental information available • Indirect ways to find information on single particle states • Study of rotation alignment of yrast states in very heavy nuclei • Study of quasiparticle K-isomers in very heavy nuclei • Deformation effects, collective motions in SHE • gamma-vibration • (Triaxial) octupole effect

  4. Single-particle states protons neutrons

  5. The projected shell model • Shell model based on deformed basis • Take a set of deformed (quasi)particle states (e.g. solutions of HFB, HF + BCS, or Nilsson + BCS) • Select configurations (deformed qp vacuum + multi-qp states near the Fermi level) • Project them onto good angular momentum (if necessary, also parity) to form a basis in lab frame • Diagonalize a two-body Hamiltonian in projected basis

  6. Model space constructed by angular-momentum projected states • Wavefunction: with a.-m.-projector: • Eigenvalue equation: with matrix elements: • Hamiltonian is diagonalized in the projected basis

  7. Building blocks: a.-m.-projected multi-quasi-particle states • Even-even nuclei: • Odd-odd nuclei: • Odd-neutron nuclei: • Odd-proton nuclei:

  8. Hamiltonian and single particle space • The Hamiltonian • Interaction strengths • c is related to deformation e by • GM is fitted by reproducing moments of inertia • GQ is assumed to be proportional to GM with a ratio ~ 0.13 • Single particle space • Three major shells for neutrons or protons For very heavy nuclei, N = 5, 6, 7 for neutrons N = 4, 5, 6 for protons

  9. Yrast line in very heavy nuclei • No useful information can be extracted from low-spin g-band (rigid rotor behavior) • First band-crossing occurs at high-spins (I = 22 – 26) • Transitions are sensitive to the structure of the crossing bands • g-factor varies very much due to the dominant proton or neutron contribution

  10. Band crossings of 2-qp high-j states • Strong competition between 2-qp pi13/2 and 2qp nj15/2 band crossings (e.g. in N=154 isotones)

  11. MoI, B(E2), g-factor in Cf isotopes p-crossing dominant p-crossing dominant p-crossing dominant p-crossing dominant

  12. MoI, B(E2), g-factor in Fm isotopes p-crossing dominant p-crossing dominant

  13. MoI, B(E2), g-factor in No isotopes p-crossing dominant n-crossing dominant n-crossing dominant

  14. K-isomers in 254No • The lowest kp = 8- isomeric band in 254No is expected at 1–1.5 MeV • Ghiorso et al., Phys. Rev. C7 (1973) 2032 • Butler et al., Phys. Rev. Lett. 89 (2002) 202501 • Recent experiments confirmed two isomers: T1/2 = 266 ± 2 ms and 184 ± 3 μs • Herzberg et al., Nature 442 (2006) 896 • Tandel, et al., Phys. Rev. Lett. 97 (2006) 082502

  15. Projected shell model calculation • A high-K band with Kp = 8- starts at ~1.3 MeV • A neutron 2-qp state: (7/2+ [613] + 9/2- [734]) • A high-K band with Kp = 16+ at 2.7 MeV • A 4-qp state coupled by two neutrons and two protons: n (7/2+ [613] + 9/2- [734]) + p (7/2- [514] + 9/2+ [624])

  16. Prediction: K-isomers in No chain • Positions of the isomeric states depend on the single particle states • Nilsson states used: • T. Bengtsson, I. Ragnarsson, Nucl. Phys. A 436 (1985) 14

  17. A superheavy rotor can vibrate • Take triaxiality as a parameter in the deformed basis and do 3-dim. angular-momentum-projection • Microscopic version of the g-deformed rotor of Davydov and Filippov, Nucl. Phys. 8 (1958) 237 • e~0.25, e’~0.1 (g~22o) Data: Hall et al., Phys. Rev. C39 (1989) 1866

  18. g-vibration in very heavy nuclei • Prediction: g-vibrations (bandhead below 1MeV) • Low 2+ band cannot be explained by qp excitations

  19. Bands in odd-proton 249Bk Nilsson parameters of T. Bengtsson-Ragnarsson Slightly modified Nilsson parameters Ahmad et al., Phys. Rev. C71 (2005) 054305

  20. Bands in odd-proton 249Bk

  21. Octupole correlation: Y30 vs Y32 • Strong octupole effect known in the actinide region (mainly Y30 type: parity doublet band) • As mass number increases, starting from Cm-Cf-Fm-No, 2- band is lower • Y32 correlation may be important

  22. Triaxial-octupole shape in superheavy nuclei • Proton Nilsson Parameters of T. Bengtsson and Ragnarsson • i13/2 (l = 6, j = 13/2), f7/2 (l = 3, j = 7/2) degenerate at the spherical limit • {[633]7/2; [521]3/2}, {[624]9/2; [512]5/2} satisfy Dl=Dj=3,DK=2 • Gap at Z=98, 106

  23. Yrast and 2- bands in N=150 nuclei

  24. Summary • Study of structure of very heavy nuclei can help to get information about single-particle states. • The standard Nilsson s.p. energies (and W.S.) are probably a good starting point, subject to some modifications. • Testing quantities (experimental accessible) • Yrast states just after first band crossing • Quasiparticle K-isomers • Excited band structure of odd-mass nuclei • Low-lying collective states (experimental accessible) • g-band • Triaxial octupole band

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