Tidal Waves a nonadiabatic microscopic descr of the
Tidal Waves – a non-adiabatic microscopic descr of the yrast states in near-spherica Stefan Frauendorf Yongquin Gu Jie Sun
The soft Quadrupole mode Spherical nuclei: Vibrators Transitional nuclei Deformed nuclei: Rotors, β, γ-vibrators Phenomenological: Bohr Hamiltonian, Interacting Boson Model Micoscopic: Spherical mean field Bohr Hamiltonian +RPA GCM Non-adiabatic Adiabatic deformed rotating mean field (Cranking) + RPA Non-adiabatic
E qp. excitations n=2 n=1 n=0 I Only very few vibrational levels are well separated from the two quasiparticle excitations.
A second look on quadrupole vibrations E qp. excitations e av s w l a d Ti I Multiphonon states
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Generation of angular momentum Angular velocity Rotor increases Tidal wave Vibrator stays constant Deformation (Other degrees of freedom) stays constant increases 3
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You can describe the Tidal Wave mode by means of a rotating mean field The mean field description works for vibrational, transitional, rotational nuclei
Microscopic treatment of the yrast states • Cranking model: Micro-macro method (Nilsson+ fixed pairing). • Find the equilibrium shape for the rotating mean field. Gives the energy and deformation. • Calculate the E 2 transition probability for the deformed charge distribution. • Calculate magnetic moments (g-factors) • ….
Minimizing at fixed frequency problematic: Minimizing
E I=8 I=4 I=2 I=0 I=6
Diabatic tracing of the configuration
A “good” vibrator F. Corminboeuf et al. PRC 63, 014305 Strong coupling between qp and quadrupole degrees of freedom. theory experiment er” d u r t “in ar. Xiv: 0709. 0254
Remarkable reproduction of data by calculations Development of tidal waves from vibrational Z=48 toward rotational with decreasing Z at low I. Energies of “vibrational nuclei” strongly anharmonic, valence neutrons react non-adiabatically Z=48, N=60 -66: after neutron alignment, smaller deformation approach of antimagnetic rotation Z=46, N=56, 60 and Z=44, N=62, 64 angular velocity nearly constant during neutron alignment – tidal wave with quasiparticle degrees of freedom More B(E 2) values to check theory Low-lying 0+ (“intruders”) naturally incorporated 9
g-factors of the + 2 states Sensitive to the proton-neutron composition of the state. Data (new and from literature): S. K. Chamoli, 1 A. E. Stuchbery, 1 S. Frauendorf, 2 Jie Sun, 2 Y. Gu, 2 P. T. Moore, 1 A. Wakhle, 1 M. C. East, 1 T. Kib¶edi, 1 A. N. Wilson, 1 and Any Others? 3 1 Department of Nuclear Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia 2 Department of Physics, University of Notre Dame, IN 46556, USA To be published
g-factors around A=100 Z/A theory
N-dependence of g-factors • The N-dependence of gfactors not accounted for by the phenomenological collective models. • In the A=100 region it reflects the increase of the neutron fraction. • The increase results from the neutron Fermi level entering the h 11/2 shell. 108 106 102 104 100 98 94 92 96 full
-g is very sensitive to pairing -for I=6, 8, g-depends sensitively on the competing configurations
Perspectives • Odd mass transitional nuclei • More cases / other regions /predicted the position of 2+, 4+, … far from stability • Better mean field (MM for WS or FY, RMF, S • Problems: 1) missing zero point motion of deformation 2) transition operators semiclassical 3) crossings between quasiparticle orbitals • Possible remedy for 1 and 2: generalized density matrix approach, • 3 is the toughest angular momentum projection + diagonalization ?
Mass on string/spring In rotating frame, the spring force balances the centrifugal force for any l, which thus cannot be found by minimizing the energy in the rotating frame.
A “good” vibrator F. Corminboeuf et al. PRC 63, 014305 Strong coupling between qp and quadrupole degrees of freedom. theory I 10 5 experiment 0. 4 0. 2 ar. Xiv: 0709. 0254
g-factors around A=100 Z/A theory
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