RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-2. Nuclear Physics (Theory)

QRPA calculations with Skyrme energy density functional forrotating unstable nuclei∗2,∗3M.
andK.
K.Matsuyanagi
Matsuyanagi∗2,∗3M. Yamagami,
Yamagami∗1∗1andthat the B(IS2) value decreases with small ωrot . Thisis because the K π = 0+ excitation strongly depends
on the pairing properties, while pairing is sensitive to
breaking of time-reversal symmetry. Here, the neutronpairing gap is Δn = 2.2 MeV at ωrot = 0, and 1.4
MeV at ωrot = 0.6 MeV/ corresponding to the total
angular momentum Jz = 2.6. We also found the same
results for 36 Mg, as shown in Fig. 2.
In conclusion, we developed a new computer codefor the QRPA calculations with Skyrme EDF. By using this code, we emphasized the role of pairing andcollective rotation for K π = 0+ quadrupole excitationsin 34 Mg and 36 Mg. This is a unique phenomenon thatcan emerge only in atomic nuclei as ﬁnite quantumsystems.

The energy density functional (EDF) theory is theonly tractable microscopic theory that can be applied
across the entire table of nuclides. The EDF has been
optimized using the basic nuclear properties, and theextension to various collective dynamics in unstable
nuclei is a current hot issue.
We have developed a new computer code for thequasiparticle random phase approximation (QRPA)
calculations. As an input, we adopt the Skyrme EDF.
At ﬁrst, we solve the Hartree-Fock-Bogoliubov(HFB) equation in the matrix form h −λΔUk
Uk= Ek. (1)−Δ∗ −h + λVk
VkThe single-particle Hamiltonian h = h − ωrot jx describes the independent-particle motion in the triaxially deformed potential that is uniformly rotatingwith the rotational frequency ωrot about the x-axis.
The Skyrme SkM* parametrization and the mixedtype density-dependent zero-range pairing force areemployed. The Fourier-series expansion method isused to eﬃciently represent wave functions (WFs) ofunbound and weakly bound states1) .
We solve the QRPA equation in the matrix form
with WFs obtained by the HFB calculation. The
particle–hole residual interaction is derived from theSkyrme force through the Landau–Migdal approximation, while the pairing residual interaction is selfconsistently treated.
As a ﬁrst application, we studied the rotational effect on the K π = 0+ isoscalar quadrupole excitations
in neutron-rich nuclei, 34 Mg and 36 Mg. Figure 1 shows
the strength function at ωrot = 0 in 34 Mg. Here, theground state has a prolate deformation β2 = 0.22.
We obtained a collective state at the vibrational energy Evib = 3.31 MeV with the transition strength
B(IS2) = 11.4 w.u..
In Fig. 1, the result without the residual pairing interaction (δΔ = 0) is also shown. Without the ﬂuctuation of the pairing ﬁeld, this excited state can notemerge. As a main conﬁguration, the ﬂuctuation of
the neutron-pair occupation between the oblate-type[202]3/2 orbit and the prolate-type [321]3/2 one acrossthe N = 22 shell gap induces vibration of the particlenumber density.
In Fig. 2, the B(IS2) value of the lowest collective
states in 34 Mg is shown as a function of ωrot . We found∗1∗2∗3(δΔ=0)

Fig. 1. Strength function of K π = 0+ isoscalar quadrupole
excitation at ωrot = 0 in 34 Mg. The resut of QRPA calculation without the residual pairing interaction (δΔ =0) is also shown.

Fig. 2. B(IS2) values of the lowest K π = 0+ excitationsin 34 Mg and 36 Mg as a function of ωrot .

Department of Computer Science and Engineering, University of Aizu
RIKEN Nishina Center
Yukawa Institute for Theoretical Physics, Kyoto University

References
1) M. Yamagami
Yamagami etet al.:al., JPSJPS Conf.
Conf. Proc.
Proc. 6,6, 030051
030051(2015).
(2015).
2) K. Yoshida et al.:al., Phys. Rev. C 77,77, 044312 (2008).

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