1. A microscopic investigation on magnetic and antimagnetic rotations in 110 Cd Jing Peng Beijing Normal University Collaborators:P.W.Zhao, Jie Meng, and S. Q. Zhang

2. Peng J. 2 Content Introduction Formulation Numerical details Results and discussions Summary

3. Peng J. 3 Introduction Backbending Alignment phenomena Superdeformed bands Wobbling motion Magnetic rotation Chiral phenomena ……

4. Peng J. 4 Introduction S. Frauendorf, et al., Report LBL35687,Vol. II:52 (1994) Magnetic rotation(90’s) : different from the electric rotation

5. Peng J. 5 Introduction Magnetic Rotation Frauenfor,Meng, Reif, 1994 near spherical or weakly deformed nuclei strong M1 and very weak E2 transitions rotational bands with  I = 1 shears mechanism two blades of shears perpendicular closing of the shears

6. Peng J. 6 Magnetic rotation Ferromagnet near spherical nuclei rotational bands with ΔI = 1; strong M1 transitions, weak E2 transitions B(M1) decrease with spin shears mechanism Frauendorf 1995 Introduction Antimagnetic rotation Antiferromagnet near spherical nuclei rotational bands with ΔI = 2 no M1 transitions B(E2) decrease with spin two “shears-like” mechanism

7. Peng J. 7 Introduction Experiment for MR ① clear evidence:lifetime measurements for four M1-bands in 198,199 Pb Clark PRL1997 ② in A~60, A~80, A~110, A~140 and A~190 regions (85 nuclei, ~200MR) Amita ADNDT2000…

8. Peng J. 8 ① first evidence 106 Cd ： small B(E2) (decrease with spin) large  (2) /B(E2) (increase with spin) Simons PRL2003 ② 105,106,107,108,109,110 Cd, 100,101,104 Pd Simons PRL2003,Choudhury PRC2010, Roy PLB2011, Choudhury PRC2013, Chiara PRC2000 ， Zhu PRC2001, Sugawara PRC2012, Rather PRC2014, Li PRC2012, Sugawara PRC2009 Introduction Experiment for AMR

9. Peng J. 9 Introduction: theory Semiclassical particle plus rotor model Macchiavelli PRC1998; Clark ARNPS2000 Pairing-plus-quadrupole tilted axis cranking (TAC) model Frauendorf NPA1993; Frauendorf NPA2000 TAC based on Skyrme Density Functional Theory 3-D Cranking: Olbratowski PRL2004 for chirality 2-D Cranking: Olbratowski APPB 2002 for MR

10. Peng J. 10 In this presentation The self-consistent TAC-CDFT with PC interaction Investigation of MR and AMR in 110 Cd Introduction: theory TAC based on Covariant Density Functional Theory Meson exchange version: 3-D Cranking: Madokoro, Meng, Matsuzaki, Yamaji, PRC 62, 061301 (2000) 2-D Cranking: Peng, Meng, Ring, Zhang, PRC 78, 024313 (2008) Point-coupling version: Simple and more suitable for systematic investigations 2-D Cranking: PWZ, Zhang, Peng, Liang, Ring, Meng, PLB 699, 181 (2011)

11. Peng J. 11 Formulation:tilted axis cranking CDFT  General Lagrangian density x z  two dimensional rotation Koepf NPA1989; Kaneko PLB1993; Madokoro PRC1997

12. Peng J. 12  Dirac Equation Potential Formulation:tilted axis cranking CDFT Spatial components of vector field are involved due to the time-reversal invariance broken → binding energy, the total angular momentum, quadrupole moments and magnetic moments, BM1 and BE2.

13. Peng J. 13 Numerical details Harmonic oscillator shells: Nf = 10 Effective interaction: PC-PK1 Zhao PRC2010

14. Peng J. 14 Numerical details Gamma-ray spectroscopy of 110 Cd Juutinen NPA1994 Shears mechanism in the A  110 Region Clark PRL1999: Band 12: an example of MR Systematics of antimagnetic rotation in even–even Cd isotopes Roy PLB2011:Band 7: a strong interplay between the antimagnetic and core rotations

15. Peng J. 15 EI-band 7 the data at I=16ħ  reference the TAC-CDFT results reproduce the data. convergent results of config1 are only up to ~20 ħ Juutinen NPA1994

16. Peng J. 16 Results and discussions

17. Peng J. 17 EI-band 7 Juutinen NPA1994 the same reference for config1 † level crossing between proton g7/2 and d3/2  config1 † reproduce the data ~20-24 ħ

18. Peng J. 18 EI-band 7 Juutinen NPA1994 the same reference for config1 * level crossing between neutron g9/2 and g7/2  config1 * reproduce the data ~24-30 ħ

19. Peng J. 19 EI-band 12 Juutinen NPA1994 the lower spin part ← config2 the higher spin part ← config3

20. Peng J. 20 IħIħ [11]Roy PLB2011 [28]Clark PRL1999 filled symbols ~ the data red, blue, black ~ the TAC-CDFT results green ~ results in Refs.[11,28]

21. Peng J. 21 IħIħ [11]Roy PLB2011 [28]Clark PRL1999 the TAC-CDFT results are in very good agreement with the data. The upbending at ħΩ = 0.65 MeV: one neutron excitation:g7/2→d3/2 The upbending at ħΩ = 0.72 MeV: two-particle-hole excitation neutron: g7/2 → d3/2 proton: g9/2 → g7/2 along the band, config1  config1 †  config1* results in [11] reproduce the upbending region

22. Peng J. 22 IħIħ [11]Roy PLB2011 [28]Clark PRL1999 the calculated results reproduce the data. config2 → the lower spin config3 → the higher spins

23. Peng J. 23 deformation a rapid decrease in  together with a small and nearly constant triaxial deformation.

24. Peng J. 24 two-shears-like mechanism config1 ： j  pointing opposite to each other j  is almost perpendicular to J two j  and J form the blades of two shears. alignment of j  → higher J the two-shears-like mechanism config1 † ： The third unpaired neutron hole in g7/2 contributes 2.4ħ along z-axis. J deviate from x-axis. two j  and J form two inclined shears. config1* ： The third unpaired proton hole in g7/2 and proton in g7/2 make contribution.

25. Peng J. 25 Shears mechanism The proton and neutron angular momentum are mainly from high-j orbitals. They form the two blades of the shears. The angular momentum is increased due to the alignment of J  and J. The two shears mechanism is well presented

26. Peng J. 26 B(E2) and B(M1)

27. Peng J. 27 B(E2)

28. Peng J. 28 B(M1) The B(E2) values of config2 and config3 < 0.05e 2 b 2 The attenuate factor of 0.3 has been used here to reproduce the tendency of the data. The B(M1) values for config2 show a roughly constant trend ( ∼ 11  2 N ). The B(M1) values of config3 reproduce the falling tendency of observed B(M1) values. a. the pairing correlations b. the meson exchange currents…

29. Peng J. 29 The tilted-axis-cranking covariant density functional theory could describe MR and AMR in one nucleus self-consistently Summary the energy spectra (upbending in band 7), the I-ħ  the two-shears-like mechanism for band 7 the shears mechanism for band 12 the M1 and E2 values support AMR for band 7 and MR for band 12

30. Peng J. 30

31. Observables Binding energy Angular momentum

32. Observables Quadrupole moments and magnetic moments Where B(M1) and B(E2) transition probabilites

33. Peng J. 33

34. Peng J. 34 166 Re

35. Peng J. 35 110 Cd

36. Peng J. 36

37. Peng J. 37 jx and jz contributions