Ⅰ. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 56 (2023)
RIKEN
Accel. Prog. Rep. 56 (2023)

Large amplitude collective motion in 44 S†
Y. Suzuki,∗1 W. Horiuchi,∗2,∗3,∗4,∗5 and M. Kimura∗5
It is well known that neutron-rich N ≃ 28 nuclei exhibit strong quadrupole collectivity.1,2) Using antisymmetrized molecular dynamics (AMD), we have discovered many interesting features such as triaxial deformation and shape coexistence in 42 Si and neighboring
nuclei.3,4) Herein, we report the large-amplitude collective motion (LACM) in 44 S.
Figure 1 shows the comparison between the energy
curves and collective amplitudes of 40 Mg and 44 S.
40Mg possesses the prolately-deformed energy minimum and the collective amplitude of the ground stateis localized around it, whereas the 0+
2 state is localized
in the oblately-deformed region. Thus, 40 Mg depicts
the coexistence of the prolate and oblate rigid rotors.
In contrast, 44 S exhibits a signiﬁcantly diﬀerent structure: The energy curve is extremely ﬂat as a function ofγ and the collective amplitudes of the ground, and the0+2 states demonstrate broad and non-localized distributions, which imply that 44 S possesses no rigid shapedue to the LACM.
Energy (MeV)

02+ amp.

01+ amp.

40.50240Mg

Energy0020

(deg)

=0.3501+ amp.

4
200
=0.3

0+2 amp.
00.5

44S

Energy20

(deg)

40-0.5-160

Fig. 1. Energy curves and collective amplitudes of the 0+1and 0+
2 states as functions of the quadrupole deformation parameter γ. The values of quadrupole parameterβ are set to 0.35 and 0.30 for 40 Mg and 44 S, respectively.

A general question is as follows: Based on which
type of physical quantity, can we distinguish rigid-rotor
and LACM? The monopole transition is the solution
to this question. The monopole transition strength(Table 1) is strongly hindered in 40 Mg, whereas it is†
∗1
∗2
∗3
∗4
∗5Mg
0.0
0.0

44

S (calc.)
0.04
0.38

44

S (expt.)5)
0.022(2)non-negligible in 44 S.5) This feature can be explainedusing a two-conﬁguration mixing model.6) 40 Mg possesses prolate ground state and oblate 0+
2 state; hence,the monopole matrix element is given as ⟨obl.|M|pro.⟩,where |pro.⟩ and |obl.⟩ denote the prolate and oblate
conﬁgurations, respectively, and M denotes the transition operator (1p1h operator). This matrix element
vanishes because single-particle conﬁgurations of |pro.⟩and |obl.⟩ diﬀer by 2p2h. This is the reason why thetransition is strongly hindered in 40 Mg.
Owing to LACM, we approximate 44 S as a mixtureof prolate and oblate shapes with equal amplitudes,√|0+(1)1 ⟩ = (|pro.⟩ + |obl.⟩)/ 2,√+|02 ⟩ = (|pro.⟩ − |obl.⟩)/ 2.
(2)+⟨0+2 |M|01 ⟩ =Collective amp.

140+B(E0; 0+1 → 02 )+B(IS0; 01 → 0+2 )In this case, the transition matrix read-0.5
60-1406Energy (MeV)1

Collective amp.

6Table 1. Electric (E0) and isoscalar (IS0) monopole transition strengths in Weisskopf unit (Wu).

Condensed from the article in Phys. Rev. C 104, 024327(2021) and Prog. Theor. Exp. Phys. 2022, 063D02 (2022)
Research Center for Nuclear Physics, Osaka University
Department of Physics, Osaka Metropolitan UniversityNambu Yoichiro Institute of Theoretical and Experimental
Physics (NITEP), Osaka Metropolitan University
Department of Physics, Hokkaido University
RIKEN Nishina Center- S20 -}1{⟨pro.|M|pro.⟩ − ⟨obl.|M|obl.⟩
2(3)Thus, the transition matrix is proportional to the difference in the squared-radii of the prolate and oblate
shapes. Consequently, 44 S possesses non-negligible
monopole transition strength. Using the single AMD
wave functions with prolate and oblate deformationand Eq. (3), we obtain B(E0) = 0.05 Wu and B(IS0)= 0.4 Wu, which are close to the results of the fullmodel space calculation listed in Table 1.
Thus, there is an interesting relationship between
the monopole transition and LACM. In 40 Mg, the prolate and oblate rotors coexist, and the monopole transition is hindered as they do not mix with each other.
In 44 S, there is a considerable mixture of prolate andoblate shapes due to LACM. This leads to the nonnegligible monopole transition, which is roughly proportional to the diﬀerence in the squared-radii of thetwo shapes.
References
1) O. Sorlin et al., Prog. Part. Nucl. Phys. 61, 602 (2008).
2) S. Takeuchi et al., Phys. Rev. Lett. 109, 182501 (2012).
3) Y. Suzuki et al., Phys. Rev. C 104, 024327 (2021).
4) Y. Suzuki et al., Prog. Theor. Exp. Phys. 2022, 063D02(2022).
5) S. Grévy et al., Eur. Phys. J. A 25, 111 (2005).
6) S. Shimoura et al., Phys. Lett. B 654, 87 (2007).