Ⅰ. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 53

Dineutron correlation and rotational excitations in neutron-rich Mg
isotopes
M. Yamagami ∗1
The spatial two-neutron correlation between two
weakly-bound neutrons, called dineutron correlation, is
one of the unique features of nuclei around the neutron
drip line. It is considered to be a universal phenomenon
that appears over all mass-number regions. However,experimental probes for this phenomenon are still underintense debate, except for light-mass nuclei such as 11 Li.
In this study, the inﬂuences of the novel pairing eﬀect
on rotational excitations in neutron-rich Mg isotopes areclariﬁed.
The experimental moment of inertia (MOI), which
can be extracted from the excitation energy E(2+1 ), issmaller than the rigid-body values by a factor of 2 to 3.
The most important inﬂuences in this respect are pairing correlations. I calculate the Thouless-Valatin (TV)
MOI, which includes the pairing correlations and residual interactions within the framework of the quasiparticle random phase approximation (QRPA).
The Hartree-Fock-Bogoliubov (HFB) equation with
the Skyrme energy density functional (EDF) is solvedin the three-dimensional wave-number mesh space.1) On
top of the HFB states, the QRPA equation in the A-Bmatrix form1) is solved for the TV MOI:∑′(1)(Jx )∗kk′ (A + B)−1
ITV = 2kk′ ,ll′ (Jx )ll .

Fig. 2. Same as Fig. 1 but for the Thouless-Valatin (TV),Belyaev, and experimental MOIs. They are divided by
the empirical value.

and 0.15 respectively. Figure 1 shows the neutron pairing gaps ∆n in neutron-rich Mg isotopes. The pairing gaps ∆n are almost constant in calculation using
the surface-type pairing force. This pairing force has astrong continuum-coupling eﬀect and creates dineutron
correlation around 40 Mg.1,2) The continuum-coupling effect is weak in the volume-type pairing force, and theneutron pairing gaps ∆n decrease as a function of mass
number A.
Figure 2 shows the TV MOIs in neutron-rich Mg
isotopes. The Belyaev MOIs, in which the residualinteractions in QRPA are neglected, are also shown.
They are divided by the empirical value Iemp =β 2 A7/3 /400 [MeV−1 ]. The TV MOIs using the surfacetype pairing force agree well with the experimental values, whereas the Belyaev MOIs underestimate the experimental values by about 20%.
The ratios of TV MOIs ITV /Iemp are almost constantin Mg isotopes with A ≤ 40, but they are substantiallyenhanced in 42, 44 Mg owing to the weak-binding eﬀect.
In conclusion, it is emphasized that the experimental
MOIs in neutron-rich Mg isotopes are well reproduced bythe TV MOIs using the surface-type pairing force, which
creates dineutron correlations. The diﬀerence between
the TV MOIs using the surface-type and volume-type
pairing forces increases on approaching the neutron drip
line, and the diﬀerence is 20.7% in 44 Mg.

kk′ ,ll′

The Skyrme SkM* EDF predicts the neutron drip
line at 44 Mg.
The quadrupole deformations of34, 36, 38, 40, 42, 44
Mg are β = 0.35, 0.30, 0.28, 0.28, 0.21,

Fig. 1. Neutron pairing gaps ∆n in neutron-rich Mg isotopes.
The results obtained using the surface-type and volumetype pairing forces are compared with the experimentaldata.
∗1

References

1) M. Yamagami, Phys. Rev. C 100, 054302 (2019).
2) M. Yamagami et al., Phys. Rev. C 77, 064319 (2008).

Department of Computer Science and Engineering, Universityof Aizu-8-