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Study of nuclear excited states through quantised angular momentum

Study of nuclear excited states through quantised angular momentum. Makito Oi Senshu University, Tokyo. Study of “rotation”. Eudoxus. 3D. Hipparcus. Apparent retrograde motion of Saturn in 2011 (Apr-July) … observation by MO. 1D. Nuclear rotation. “Yrast” states (1D).

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Study of nuclear excited states through quantised angular momentum

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  1. Study of nuclear excited states through quantised angular momentum MakitoOi Senshu University, Tokyo

  2. Study of “rotation” Eudoxus 3D Hipparcus Apparent retrograde motion of Saturn in 2011 (Apr-July) … observation by MO 1D

  3. Nuclear rotation “Yrast” states (1D) • Static rotation • Uniform rotation • One-dimensional rotation Rcoll

  4. Collectivity: many-body Physics • Microscopic and Macroscopic viewpoints • Degrees of freedom: collectivity

  5. prolate oblate triaxial ND SD sphere 0.2 0.6 0.0 Quadrupole deformation

  6. Wobbling motion as a 3D rotation Bohr and Mottelson (1975) • Triaxial rotor • High spin (J >> 1) • Quasi-1D rotation (Jx ~ J)

  7. Non-abelian algebra: QM flucutation Classical: J2 Quantum: J2 + J

  8. Definition of K quantum number K : quantisaion axis | J K >

  9. QM flucutation (II) Example: state |J K=J >

  10. Nuclear chiral rotation Three Spin Vectors Jparticle Jtotal PRL84 (2000), Dimitrov, Frauendorf, Donau • Valence neutron (hole) • Valence proton (particle) • Triaxial rotor (collective) Jhole Rcoll

  11. Angular momentum projection Norm overlap kernels NPA 80 (1966), Onishi and Yoshida

  12. The Onishi formula Square root of determinant NPA 80 (1966), Onishi and Yoshida

  13. Nodal lines PLB 606 (2005), M.Oi and Tajima A collection of singular points

  14. A Pfaffian formula of Robledo Pfaffian: polynomials Robledo, PRC 79 (2009)

  15. Another Pfaffian formulafor odd-A systems Chirality needs a particle and a hole M. Oi and Mizusaki, PLB 707 (2012)

  16. A Pfaffian formulaof Oi and Mizusaki Several unfamiliar bipartite matrices… M. Oi and Mizusaki, PLB 707 (2012)

  17. Meaning of X-1 Antisymmetrised density matrix (with a bipartite form) Mizusaki and M.OI, arXiv:1204.6531(2012)

  18. Extended Pfaffian formulaof Mizusaki and Oi Mizusaki and M.OI, arXiv:1204.6531(2012)

  19. “Lewis Carroll” formulafor Pfaffian Mizusaki and M.OI, arXiv:1204.6531(2012) Avez and Bender, PRC 85 (2012)

  20. Summary • Nuclear excited states through angular momentum • Structural transitions to exotic shape and 3D rotation • Quantization of classical / semi-classical 3D models • New formulae were discovered • Ready for numerical analysis!

  21. LB２０４５： NaI scintillator University of Tokyo

  22. “Global warming effect”

  23. “Next big ones to come…”

  24. “Centre of the world”

  25. “Demonic” least common multiple

  26. Fukushima No.4 reactor

  27. Apr, 2012

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