Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 56 (2023)
RIKEN
Accel. Prog. Rep. 56 (2023)

Enhanced moments of inertia for rotation in neutron-rich nuclei†
K. Yoshida∗1†∗1

MeV-1

120120

SkM*

Proton number

100

100

80

80

60

60

40

40

20

20

0
1200Exp.

100

Proton number

Nuclear rotational motion emerges due to the spontaneous breaking of rotational symmetry. As steppingaway from the magic numbers, the ﬁrst I π = 2+ state
becomes lower in energy: The collective mode of excitation changes its character from vibration to rotation
as the deformation develops.
Recently, various spectroscopic studies have been
conducted to explore unique structures in neutron-rich+nuclei. The excitation energy of the 2+
1 state, E(21 ),is often among the ﬁrst quantities accessible in experiments and systematic measurements have revealed theevolution of the shell structure. Besides the change ofthe shell structure associated with the onset of deformation, the E(2+1 ) value may provide rich information
on exotic nuclei. A signiﬁcant lowering of E(2+1 ), observed in a near-drip-line nucleus 40 Mg, could be asignal of new physics in drip-line nuclei,1) as the theoretical calculations have predicted that the magnitudeof deformation is not enhanced in 40 Mg compared tothe Mg isotopes with fewer neutrons.2)
There are 657 even-even nuclei with known E(2+1 ).
In the present study, I limit the scope by excluding
the very light nuclei (Z < 10), for which mean-ﬁeld
theory is least justiﬁed. This eliminates 22 nuclei. The
experimental data evaluated as 3/E(2+1 ) for 635 nuclei
are displayed in Fig. 1 as ‘Exp.’ There is no collective
rotation in spherical nuclei where the MoI is zero. I
deﬁned the spherical nuclei if the calculated MoI wasless than 0.1 MeV−1 . An additional 273 nuclei havebeen eliminated for that reason, leaving 362 nuclei inthe present analysis.
To quantitatively measure the theoretical accuracy,
I compared theory and experiment, and examined thestatistical properties of the quantity R = Jth /Jexp .
Here, Jth and Jexp are the theoretical and experimental MoI. For the SkM* functional, the average isR̄ = 1.02. Here, the Yamagami-Shimizu-Nakatsukasa
pairing functional3) was adopted. When excluding theweakly deformed nuclei with the deformation parameter β < 0.1, R̄ = 1.07 for 332 data. Therefore, thepresent model overestimates the MoI by about 10%.
This analysis indicates that the 2+
1 state is mostly governed by the rotational MoI of the ground state, andthe self-consistent cranking model describes the MoI
surprisingly well for nuclei with a ﬁnite β value.
I investigate the MoI of neutron-rich nuclei, and discussed the unique features near the drip line. A striking feature observed in the result shown in Fig. 1 isthat the deformation is strong in the neutron-rich lanthanide nuclei around N = 100 and the MoI is large

806040200020406080

100120140

Neutron number160180Fig. 1. Calculated moments of inertia J for the SkM* functional. The experimental data are taken from NNDC,
which is evaluated as 3/E(2+1 ).

accordingly. Furthermore, the MoI in nuclei near thedrip line is comparable to that of heavy actinide nuclei, despite a mass number diﬀerence of about 40. TheMoI in the lanthanides with N ∼ 150 is about twiceas large as that in the N ∼ 100 region, although thedeformation of protons is almost the same. Because
the neutrons are spatially extended, β of neutrons andmatter are both smaller than those in the N ∼ 100 region, which is against a simple perspective for a large
MoI. The density dependence of a pairing functional
employed in the calculation is the origin of this uniquefeature near the drip line, and that weak binding plays
a minor role.
References
1) H. L. Crawford et al., Phy. Rev. Lett. 122, 052501(2019).
2) J. Terasaki et al., Nucl. Phys. A 621, 706 (1997).
3) M. Yamagami et al., Phys. Rev. C 80, 064301 (2009).

Condensed from the article in Phys. Lett. B 834, 137458(2022)
Research Center for Nuclear Physics, Osaka University- 40 -