a non-adiabatic microscopic description Tidal Waves – a non-adiabatic microscopic description of the yrast states in near-spherical nuclei Stefan Frauendorf Yongquin Gu Jie Sun

The soft Quadrupole mode Deformed nuclei: Rotors, β, γ-vibrators Spherical nuclei: Vibrators Transitional nuclei Phenomenological: Bohr Hamiltonian, Interacting Boson Model Micoscopic: Spherical mean field Bohr Hamiltonian deformed rotating mean field +RPA GCM (Cranking) + RPA Non-adiabatic Adiabatic Non-adiabatic

Only very few vibrational levels are well separated qp. excitations n=0 n=1 n=2 Only very few vibrational levels are well separated from the two quasiparticle excitations.

E A second look on quadrupole vibrations I Multiphonon states qp. excitations Tidal waves A second look on quadrupole vibrations Multiphonon states

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Generation of angular momentum Angular velocity Deformation Rotor increases stays constant Tidal wave Vibrator stays constant increases (Other degrees of freedom) 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 E2 transition probability for the deformed charge distribution. Calculate magnetic moments (g-factors) ….

Minimizing at fixed frequency problematic:

E I=8 I=6 I=4 I=2 I=0

Diabatic tracing of the configuration

A “good” vibrator Strong coupling between qp and quadrupole degrees F. Corminboeuf et al. PRC 63, 014305 Strong coupling between qp and quadrupole degrees of freedom. theory experiment “intruder” arXiv: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(E2) 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 1Department of Nuclear Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200, Australia 2Department of Physics, University of Notre Dame, 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 g-factors 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 h11/2 shell. full 92 98 94 96 100 104 102 106 108 19

-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 Strong coupling between qp and quadrupole degrees F. Corminboeuf et al. PRC 63, 014305 Strong coupling between qp and quadrupole degrees of freedom. experiment theory I 10 0.4 0.2 5 arXiv:0709.0254

g-factors around A=100 Z/A theory