奇質量核での２フォノン・ガンマ振動バンド

1. 奇質量核での２フォノン・ガンマ振動バンド Thanks to 松柳さん、清水さん

2. if really collective, multiple excitations (possibly with anharmonicity) Bohr and Mottelson, “Nuclear Structure II”

3. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80)

4. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. (‘80) --- s,dボソン harmonic vib. のみ

5. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. ('80) general framework Bohr and Mottelson ('82)

6. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. ('80) general framework Bohr and Mottelson ('82) macro and micro Dumitrescu and Hamamoto (‘82) --- γ変形

7. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. ('80) general framework Bohr and Mottelson ('82) macro and micro Dumitrescu and Hamamoto ('82) QPM Soloviev and Shirikova (‘81) --- “2 phonon ない”

8. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. ('80) general framework Bohr and Mottelson ('82) macro and micro Dumitrescu and Hamamoto ('82) QPM Soloviev and Shirikova ('81) SCCM Matsuo and Matsuyanagi ('85) MPM Piepenbring and Jammari ('88) 実験を再現

9. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. (‘80), Yoshinaga et al. (’86) --- s,d,gボソン general framework Bohr and Mottelson ('82) macro and micro Dumitrescu and Hamamoto ('82) QPM Soloviev and Shirikova ('81) SCCM Matsuo and Matsuyanagi ('85) MPM Piepenbring and Jammari ('88)

10. 2 phonon states in even-even nuclei ・Exp. observ. 168Er Davidson et al. ('80) ・Theories IBM Warner et al. ('80), Yoshinaga et al. ('86) general framework Bohr and Mottelson ('82) macro and micro Dumitrescu and Hamamoto ('82) QPM Soloviev and Shirikova ('81) SCCM Matsuo and Matsuyanagi ('85) MPM Piepenbring and Jammari ('88) ・Exp. --- some are as predicted 166Er, 164Dy, 232Th, 106,104Mo, ... TPSM Sun et al. ('00) also K=0

11. 2 phonon states in odd-A nuclei

12. 1γ 1γ G. Gervais et al., NPA624, 257 ('97)

13. 2 phonon states in odd-A nuclei ・Theo. MPM Durand and Piepenbring ('96) ・Exp. observ. fission fragments of 252Cf 105Mo Ding et al. ('06) 103Nb Wang et al. ('09) 107Tc Long et al. ('09) 10 years

14. 2 phonon states in odd-A nuclei --- interplay between single-particle and collective modes ・Theo. MPM Durand and Piepenbring ('96) ・Exp. observ. fission fragments of 252Cf 105Mo Ding et al. ('06) 103Nb Wang et al. ('09) 107Tc Long et al. ('09) ・Theo. TPSM Sheikh et al. ('10)

15. ground(1qp) 2γ ?? 1γ

16. Mean field Residual interaction RPA particle-vibration coupling

20. Mean field Residual interaction RPA particle-vibration coupling

21. Eigenstates 1qp (0γ) 1γ 2γ

22. Eigenstates --- signature dependence M.M., Shimizu, Matsuyanagi, PTP 77 ('87) 1qp (0γ) 1γ --- intensity relation Gervais et al. ('97) 2γ

23. parameters from literatures and to fit signature splitting in 1qp, to fit γ bandhead in 104Mo

24. probabilities of in the wave function at each vs routhian two 1γ and three 2γ are collective !!

25. K scheme vs signature scheme States with lower Khave lower intrinsic energies than those with higher K and the same I.

27. probabilities of in the wave function at each vs routhian two 1γ and three 2γ are collective !!

28. K=Ω+4 K=Ω K=|Ω-4| K=Ω+2 K=Ω+4 K=Ω+2 curves are exp. data converted to the rot. frame K=|Ω-2|

30. Summary (1) ・ 2γ bands in odd-A 103Nb are calculated by means of the particle-vibtration coupling model in the signature scheme ・ K=Ω+4 state is the most collective at zero rotation, but small rotation immediately delivers its collectivity to other two sequences (K=Ω, |Ω-4|) ・ Three 2γ bands keep collectivity up to high spins ・ Excitation energies of 2γ bands are higher than observed  3γ basis states are necessary

31. Triaxial 変形  wobbling motion ---

32. TSD1: 0 phonon TSD2: 1 phonon TSD3: 2 phonon TSD4: another conf.

33. 2 phonon 1 phonon

35. 163 Lu Not ∝ω Automatically ! rot ω -dependent rot MM, Y.R.Shimizu and K.Matsuyanagi, PRC 65, 041303(R) (2002)

36. γ deformation in rotating systems

37. γ～+20゜ contradicts irrotational ?

39. Irrotational + QP align  Jx > Jy

40. 163 162 Lu (1QP) Yb (0QP) 角運動量ベクトルの向きの関数としてのエネルギー z y x Shallow Tilted ! M. M. and S. –I. Ohtsubo, PR C69, 064317 (‘04)

41. 2 phonon 1 phonon

42. 平均場の相転移

43. 146 Gd 相転移後 shallow θ

44. 相転移後 stiff M. Matsuo and K. Matsuyanagi, PTP 74, 1227 (‘85)

45. Summary (2) • Instability of wobbling leads to tilted axis rotation --- “Phase transition” • Correspondence between RPA and TAC is good • Anharmonicity in 2 phonon wobbling suggests softening of potential surface

46. のみ Dumitrescu and Hamamoto, NPA383, 205 (‘82)