Top-on-top mechanism in triaxial strongly deformed bands

We have derived the algebraic solution to the particle-rotor model with high j nucleon coupled to a triaxially deformed core, which elucidates the top-on-top mechanism without numerical analysis [1,2]. It can clarify not only the energy level scheme, but also give approximate selection rules in the strength of B(E2) and B(M1) transitions. As Coriolis term is explicitly taken into account, that composes a difference from the wobbling model [3], the algebraic solution is represented by two quantum numbers, corresponding to the precession of total angular momentum and the single-particle angular momentum, respectively. The invariance of the nuclear states under Bohr symmetry restricts the range of quantum numbers depending on I - j, and the level is denoted by a set of I and quantum numbers. We also found the rigid-body moments of inertia are favourable to simulate TSD (triaxial strongly deformed) bands observed in odd-A Lu isotopes [4] both from the energy level and from the transition rates. Thus, TSDl in odd-A Lu is denoted by (I, 0, 0) for favored / bands, and TSD2 by (I,1,0) for unfavored I bands around γ ∼ 20o. If the single-particle angular momentum j is assumed to be the sum of two angular momenta as j = j1 + j2 and the value of integer j keeps constant over some range of I, then the algebraic solution is easily extended to the even-even nucleus with alignment of j. Although several candidates of TSD bands are observed in Hf isotopes, no linking transitions between (0,0) and (1,0) are found. The rough estimation of the transition rates gives a factor of (G0000G1010)2 both in the B(E2) and B(M1) values for the transitions with ΔI = 1 among the favored (0,0) and the unfavored (1,0) bands. The value oil - j is smaller for even-A case than odd-A case, which makes the observation of the other partner band difficult