RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-2. Nuclear Physics (Theory)

Enhanced collectivity of γ vibration in the neutron-rich Dy isotopes
around N = 108 †∗1∗2Yoshida,∗1and H.
H. Watanabe
Watanabe∗2
K. Yoshida
andThe γ vibrational mode of excitation is an acknowledged collective mode in deformed nuclei. Quite recently, a sudden decrease in the excitation energyof the γ vibration was observed at RIKEN for theneutron-rich Dy (Z = 66) isotopes at N = 1061) . In
the present report, by systematically studying the microscopic structure of the γ vibration in the neutronrich Dy isotopes with N = 98 − 114, we try to understand the mechanism of the observed softening. The
low-frequency modes of excitation in the neutron-richrare-earth nuclei are described on the basis of nuclear
density-functional theory.
Atomic nuclei reveal spontaneous breaking of rotational symmetry in both real space and gauge space in
stepping away from magic numbers. Most of the deformed nuclei still retain the axial symmetry. In axiallydeformed nuclei, a low-frequency quadrupole mode ofexcitation, known as the γ vibration, emerges. The γvibrational mode of excitation is regarded as a precursory soft mode of the permanent non-axial deformation. It would be interesting to investigate the possibility of occurrence of the γ vibration in exotic nuclei,
and to achieve a deep understanding of the microscopic
mechanism for the generation of collective vibrationsin atomic nuclei.
Figure 1 shows the excitation energy of the γ vibration in the neutron-rich Dy isotopes. Here, we employ
the Skyrme energy-density functionals (EDF’s) in theHartree-Fock-Bogoliubov calculation for the groundstates and in the Quasiparticle Random-Phase Approximation (QRPA) for the excitations. The results of the calculation are compared with experimendata1)1–3)
Boththethe
SkM*,2).,3). BothSkM*andandSLy4
SLy4 functionals
functionals
tal data
reproduce the isotopic trend in energy well; lowering
when N increases from 104 to 106.
Based on the analysis of the wave functions, wefound that the coherent contribution of the ν[512]3/2⊗
ν[510]1/2, ν[510]1/2 ⊗ ν[512]5/2, and ν[512]3/2 ⊗ν[514]7/2 excitations satisfying the selection rule of thenon-axial quadrupole matrix element,
ΔN = 0 or 2, Δn3 = 0, ΔΛ = ΔΩ = ±2,Fig. 1. QRPA frequency of γ vibration obtained by using
SkM* and SLy4 EDF’s. Also shown are the experimen1–3). .
tal data1)2)3)

the γ vibration decreases toward N = 110(108) in thecase of the calculation employing the SkM* (SLy4)functional. This is because the Fermi level of neutrons
lies among the orbitals that play an important role ingenerating the collectivity around N = 106.
We found a similar isotopic dependence of the excitation energy in the neutron-rich Er (Z = 68) and Yb(Z = 70) isotopes. We can thus conclude that themicroscopic mechanism governing the enhanced collectivity around N = 108 in the Dy isotopes is robust in the neighboring nuclei. Note that we obtained
the strongest collectivity for Z = 66 because the 2qp
excitations of π[411]1/2 ⊗ π[411]3/2 and π[411]1/2 ⊗π[413]5/2, located around the Fermi level of protons
and satisfying the selection rule (1), make a coherent
contribution to generation of the γ vibration together
with the excitation of neutrons.
The numerical calculations were performed onSR16000 and CRAY XC40 at the Yukawa Institute for
Theoretical Physics, Kyoto University, and on COMA(PACS-IX) at the Center for Computational Sciences,
University of Tsukuba.

(1)plays a major role in generating the collectivity, i.e.
lowering of the frequency and enhancement in the transition strength.
One can see in Fig. 1 that the excitation energy of†∗1∗2References
1) H. Watanabe et al: Phys. Lett. B760, 641 (2016).
2) National Nuclear Data Center. “Evaluated NuclearStructure Data File”, http://www.nndc.bnl.gov/ensdf.
3) P.-A. Söderström et al: Phys. Lett. B762, 404 (2016).

Condensed from the article in Prog. Theor. Exp. Phys.
(2016), 123D02 (2016)
Graduate School of Science and Technology, Niigata University
School of Physics and Nuclear Energy Engineering, Beihang
University,- 96 -