RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-2. Nuclear Physics (Theory)

135
Application of top-on-top model to 11/2Pry†
11/2− band in 135
Pr∗1,∗2
K. Sugawara-Tanabe
Sugawara-Tanabe,∗1,∗2andK.
andK.
K.Tanabe
Tanabe∗3∗3

We have proved that a transverse wobbling mode
does not exist in the particle-rotor model with hydrodynamical moment of inertia (MoI).1) Consequently,
stable rotation around the middle MoI does not exist
in the particle-rotor model as well as in the pure rotor
case. Then, a question arises as to how the experimental data of the 11/2− band in 135 Pr2) can be explained.
This yrast 11/2− band starts near the ground state andshows backbending thrice,3) and the levels discussed inRef. 2 are concerned with those before the ﬁrst backbending. Thus, the pairing eﬀect is essentially important in such low-excitation states. We have proposed
an analytic formula for the angular-momentum (I) dependence of MoI originating from the Coriolis antipairing eﬀect (CAP).4) This formula is derived fromthe second-order perturbation to the Coriolis term inthe self-consistent HFB equation under I and nucleonnumber constraints. The I dependence of the MoI is
related to the rigid MoI with a functional dependenceof the pairing gap together with the blocking eﬀect.
We have also achieved good success with the top-ontop model, i.e., the particle-rotor model with the Idependent rigid MoI, for the high spin and highly excited levels in Lu isotopes in describing not only theenergy scheme but also the electromagnetic transitions
B(E2) and B(M 1).5–7) Similarly, we apply the top-ontop model for the 11/2− band in 135 Pr. In reference
to the I-dependence curve as displayed in Fig. 9 inRef. 4, we assume a simpliﬁed functional form for theI dependence of MoI for those low-excitation levels,J0.
1 + exp(−(I − b)/a)(1)

We choose two parameters a = 7.5 and b = 15.5. The
asymptotic value of the MoI in the limit of I → ∞ isassumed to be J0 =25 MeV−1 , and the deformation
parameters β2 = 0.18 and γ = 18◦ .
In Fig. 1, we compare E(I) − 0.02I(I + 1) as functions of I between theoretical values and experimental
ones2) . The theoretical value is normalized at I = 11/2
in Band 1 where I − j is even, while Bands 2 and 4
have odd values of I − j. For the backbending curveof Band 1, we choose a larger J0 = 35 MeV−1 , which
reproduces the experimental data from I=35/2 up to57/2, indicating the CAP eﬀect is well simulated by
two common parameters a and b. The energies ofE(I) − 0.02I(I + 1) are not sensitive to γ, but γ = 18◦†∗1∗2∗3Condensed from the article in Phys. Rev. C, Vol.95, 064315(2017).
RIKEN Nishina Center
Department of Information Design, Otsuma Women’s University
Department of Physics, Saitama University- 100 -ω

Fig. 1. Comparison of E(I)−0.02I(I +1) between theoretical results and experimental data in Ref.2) . Theoreticalvalues are shown by ﬁlled triangles for Band 1 and ﬁlled
circles for Bands 2 and 4, while experimental data areshown for Band 1 by open triangles and for Bands 2and 4 by open circles. Band 2 is from I=13/2 to 25/2,
while Band 4 is from I=17/2 to 33/2.

seems to be favorable mainly from the electromagnetictransitions. It also gives good ﬁt to the experimental
data2) not only in the electomagnetic transition rates
but also in the mixing ratio δ.
In conclusion, the experimental data of the 11/2−
band in 135 Pr2) is interpreted as the normal wobblingband inﬂuenced by the CAP eﬀect, rather than thetransverse wobbling mode. We point out a possibilityof the violation of Bohr symmetry to a small extent,
which explains the existence of Band 2, i.e., the signature partner band.
References1) K. Tanabe, K. Sugawara-Tanabe, Phys. Rev. C 95,064315 (2017).
2) J. T. Matta et al., Phys. Rev. Lett. 114, 082501 (2015).
3) E. S. Paul et al., Phys. Rev. C 84, 047302 (2011).
4) K. Tanabe, K. Sugawara-Tanabe, Phys. Rev. C 91,034328 (2015).
5) K. Tanabe, K. Sugawara-Tanabe, Phys. Rev. C 73,034305 (2008); Phys. Rev. C 77, 064318 (2008);
6) K. Sugawara-Tanabe, K. Tanabe, Phys. Rev. C 82,051303(R) (2010).
7) K. Sugawara-Tanabe, K. Tanabe, N. Yoshinaga, Prog.
Theor. Exp. Phys. 2014, 063D01 (2014).