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

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

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

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

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

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

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…

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

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

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, (2000) 2-D Cranking: Peng, Meng, Ring, Zhang, PRC 78, (2008) Point-coupling version: Simple and more suitable for systematic investigations 2-D Cranking: PWZ, Zhang, Peng, Liang, Ring, Meng, PLB 699, 181 (2011)

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

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.

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

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

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

Peng J. 16 Results and discussions

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

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

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

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]

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

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

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

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.

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

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

Peng J. 27 B(E2)

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…

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

Peng J. 30

Observables Binding energy Angular momentum

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

Peng J. 33

Peng J Re

Peng J Cd

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Peng J. 37 jx and jz contributions