Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Enhancement of pairing fluctuation in neutron-rich Mg isotopes
studied by Skyrme QRPA calculation
M. Yamagami ∗1
ferent spatial shapes. In 34 Mg, the prolate-type orbits [330]1/2 and [321]3/2 and the oblate-type orbit[202]3/2 are involved. In 38,40 Mg, the prolate-type orbits [310]1/2 and [301]1/2 and the oblate-type orbit[303]7/2 are the main contributors. The large pairingﬂuctuation enhances the B(IS2) around 40 Mg. Actually, the ratio of B(IS2) in 40 Mg and 34 Mg is 1.32 with
Ecut = 12 MeV, while 1.01 with Ecut = 6 MeV.
In conclusion, we discussed the pairing ﬂuctuationand the induced B(IS2) values of K π = 0+ isoscalar
quadruple excitations in neutron-rich Mg isotopes. We(ad)predicted the enhancement of B(P20 ) by the continuum eﬀect in 38,40 Mg. This phenomenon suggests thepresence of dineutron correlation and can be observed
by a two-neutron transfer experiment. The B(IS2)values also contain indispensable information about
the shell structure and pairing properties.

Nuclei close to the drip line often exhibit novel features that do not appear in stable nuclei. An example is dineutron correlation, which is the strong spatial correlation between two neutrons of a Cooper pair.
The pair excitation into continuum states (continuumeﬀect) plays a key role to create the strong correlation. Dineutron correlation has been extensively investigated both experimentally and theoretically in lightmass nuclei such as 11 Li. We also expect dineutron correlation in medium-heavy neutron-rich nuclei, for example, around 40 Mg,1) which are accessible in RIKEN
RIBF. However, no evidence has been obtained thusfar. In this study, we discuss K π = 0+ isoscalar
quadrupole excitations in neutron-rich Mg isotopes as
a probe of dineutron correlation. We emphasize thecontinuum eﬀect for the collectivity of excitations.
At ﬁrst, we solve the Hartree-Fock-Bogoliubov(HFB) equation by using the Fourier-series expansion
method. The Skyrme SkM* parametrization and themixed-type density-dependent zero-range pairing force
are employed. The pairing correlation is active among
single-particle states with the energies εk satisfying|εk − λ| < Ecut . Here, λ is the chemical potential andEcut is the cut-oﬀ energy. On top of the HFB states,
we solve the quasiparticle random phase approximation (QRPA) equation in the matrix form.2)
The ground states of 34,36,38,40 Mg have quadrupole
deformations β2 = 0.243, 0.262, 0.265, and 0.259,
and neutron pairing gaps ∆n = 2.13, 2.05, 2.02,
and 2.04 MeV in our calculation. Figure 1 (upper)
shows the excitation energies E of the K π = 0+
isoscalar quadrupole excited states |ν⟩. Figure 2 shows
the transition strength of quadruple-pair excitations(ad)†B(P20 ) = | ⟨ν| P20|0⟩ |2 with the quadrupole-pair ad†. The results with Ecut = 6, 8,
ditional operator P20
10, and 12 MeV are compared. Here, Ecut = 6 is a typical value in stable nuclei. A larger Ecut increases thecoupling to continuum states. We found the large en(ad)hancement of B(P20 ) as a function of Ecut in 38,40 Mg,
the neutron chemical potentials of which λn = −1.57(ad)and −0.77 MeV satisfy |λn | < ∆n . Here, the B(P20 )with Ecut = 12 MeV is small at approximately 10% in40
Mg from the converged value of 215 fm4 from extrapolation with the exponential-type function of Ecut .
Figure 1 (lower) shows the isoscalar transition
strength B(IS2) = | ⟨ν| r2 Y20 |0⟩ |2 . This vibrationof matter density is induced by the ﬂuctuation ofneutron-pair occupation among Nilsson orbits with dif∗1Fig. 1. Excitation energies E and B(IS2) values of theK π = 0+ excitations in neutron-rich Mg isotopes.

Fig. 2. Transition strength of quadruple-pair excitations(ad)
B(P20 ) of the K π = 0+ excitations. The results with
Ecut = 6, 8, 10, and 12 MeV are compared.

References
1) M. Yamagami et al., Phys. Rev. C 77, 064319 (2008).
2) M. Yamagami et al., RIKEN Accel. Prog. Rep. 50, 92(2017).

Department of Computer Science and Engineering, University of Aizu

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