Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 48 (2015)

Tops-on-top model applied to TSD bands in 164 Lu†
K. Sugawara-Tanabe,∗1,∗2 K. Tanabe,∗1,∗3 and N. Yoshinaga∗3
The top-on-top model with moments of inertia(MoI) dependent on angular-momentum (I) works
quite well in describing triaxial strongly deformed(TSD) bands in odd-mass nuclei.1–3) In this paper, thetop-on-top model is extended to the tops-on-top modelfor an odd-odd nucleus 164 Lu, in which one proton andone neutron in each single-j orbital are coupled to thetriaxial rotor.
Both positive- and negative- parity TSD bands in
164
Lu are well reproduced by taking account of attenuation factors in the Coriolis interaction, which includes the eﬀect of the partially ﬁlled single-j shell. In
order to observe the eﬀect of the attenuation factor,
we compared numerical results with and without theattenuation factor and conﬁrmed its importance forthe excitation energies relative to the reference, i.e.,E ∗ − aI(I + 1) with a = 0.0075 MeV.4,5)
For a pure-rotor case without single-particle potentials, an explicit algebraic formula for the TSD band
levels is obtained. The level is classiﬁed by three quantum numbers (nα , nβ , nγ ), where nα is related to therotor wobbling quantum number, and nβ and nγ to theprecession quantum numbers for a proton and a neutron. Under the condition of D2 -invariance,6) threequantum numbers take limited integers depending on
the value of I − j1 − j2 and nα − nβ − nγ . As anexample, we assume j1 = j2 = 13/2, and compare
the energy eigenvalues from this boson model with theresult obtained from the exact diagonalization of therotor Hamiltonian in Fig. 1 for odd number I whereI − j1 − j2 is even. In this case nβ and nγ appear as
the combination np = nβ + nγ . The yrast has quantum numbers (0, 0) and the yrare (0, 2)3 . On the otherhand, for even number I where I − j1 − j2 is odd, theyrast has quantum numbers (1, 0) and the yrare (2, 1)2 .
The boson model reproduces the exact results in goodaccuracy.
It is easy to derive the stability condition for a purerotor case. We found that there is no wobbling aroundthe axis with the intermediate MoI. The wobbling motion exists only around the axis with the maximum orminimum MoI, which agrees with the result in classicalmechanics.7) Consequently, we can state that there isno stable rotation around the axis with the intermediate MoI, and that stable rotational motion exists onlyaround the axis with the maximum or minimum MoI.
The diﬀerence in quantum numbers between theyrast and yrare TSD bands in 164 Lu, in which single†∗1∗2∗3Condensed from the article in Prog. Theor. Exp. Phys.,Vol.2014, 063D01 (2014)
RIKEN Nishina Center
Otsuma Women’s University
Department of Physics, Saitama UniversityEMeV
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-0.5Fig. 1. Comparison of the energy levels of odd spin I(13 ≤ I ≤ 31) between the boson model (solid lines) andthe exact result (dashed lines). Quantum numbers anddegeneracy of levels (np + 1) are given by (nα , np )np +1
below each rotational band. Angular momentum values
are assigned to the lowest two levels and the highest
level in the right-hand side of each band.

particle potentials are included, is conﬁrmed by direct
estimation of spin alignments. It is conﬁrmed that theyrast TSD band with even I−j1 −j2 has quantum numbers (nα , nβ , nγ )=(0,0,0), while the yrare TSD bandwith odd I − j1 − j2 has (1,0,0).
The electromagnetic transition rates of B(M 1) are
reduced by a factor of 1/20 because the signs of gfactors of a proton and a neutron are diﬀerent in comparison with the odd-A case, while the electromagnetictransition rates of B(E2) are in the same order but
reduced by a factor of 1/2. These reductions of electromagnetic transition rates will make the observationof TSD bands in even-even nuclei diﬃcult.
References
1) K. Tanabe and K. Sugawara-Tanabe: Phys. Rev. C 73,034305 (2006).
2) K. Tanabe and K. Sugawara-Tanabe: Phys. Rev. C 77,064318 (2008).
3) K. Sugawara-Tanabe and K. Tanabe: Phys. Rev. C 82,051303(R) (2010).
4) S. Törmänen et al.: Phys. Lett. B 454, 8 (1999).
5) P. Bringel et al.: Phys. Rev. C 75, 044306 (2007).
6) A. Bohr: Mat. Fys. Medd. Dan. Vidensk. Selsk. 26,
no. 14 (1952).
7) L. D. Landau and E. M. Lifshitz:
Mechanics(Butterworth-Heinemann, Oxford, 1976), 3rd ed.,Sect. 37.

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