Parametrizations of triaxial deformation andE2transitions of the wobbling band

Abstract

There are various different definitions for the triaxial deformation parameter "γ ". It is pointed out that the parameter conventionally used in the Nilsson (or Woods-Saxon) potential, γ (pot:Nils) [or γ (pot:WS)], is not appropriate for representing the triaxiality γ defined in terms of the intrinsic quadrupole moments. The difference between the two can be as large as a factor two in the case of the triaxial superdeformed bands recently observed in Hf and Lu nuclei, i.e., γ (pot:Nils) ≈ 20 • corresponds to γ ≈ 10 • . In our previous work, we studied the wobbling excitations in Lu nuclei using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation. The most serious problem was that the calculated B(E2) value is about factor two too small. It is shown that the origin of this underestimate can mainly be attributed to the small triaxial deformation parameter γ ≈ 10 • that corresponds to γ (pot:Nils) ≈ 20 • . If the same triaxial deformation parameter is used as in the analysis of the particle-rotor model, γ ≈ 20 • , the calculated B(E2) gives correct magnitude of the experimental data.

Wobbling motion in Pr135 within a collective Hamiltonian

“…Therefore, the wobbling bands in the Lu and Ta isotopes are interpreted as transverse wobbling bands. Theoretically, the triaxial particle rotor model (PRM) [1,[15][16][17][18][19][20][21][22] and the cranking model plus random phase approximation (RPA) [23][24][25][26][27][28][29][30][31][32] have been widely used to describe the wobbling motion. Recently, based on the cranking mean field and treating the nuclear orientation as collective degree of freedom, a collective Hamiltonian was constructed and applied for the chiral [33] and wobbling modes [34].…”

Quantal rotation and its coupling to intrinsic motion in nuclei

“…There are still many open issues in these fields which are waiting for future studies. potentials in reference [76]. Introducing ǫ = The situation is the same for the self-consistent mean-field calculation.…”

“…This was first pointed out in the Appendix B of reference [34] and more recently discussed again in relation to the wobbling motion in reference [76]. The most basic definition is γ(den) ≡ − tan −1 ( Q 22 / Q 20 ) by using the intrinsic quadrupole moments, which is directly related to the E2 transition probability.…”

“…The γ(den) is defined with respect to the intrinsic quadrupole moments calculated from the density distribution. Here, it should be noted that the triaxial parameter γ for the potential shape is significantly different from γ(den) [76] (See Appendix A for details). As far as we know, at present, none of the microscopic calculations are able to reproduce the triaxiality of γ(den) ≈ 20 • .…”

“…The two pictures are schematically illustrated in figure 8. The microscopic QRPA calculations were first performed with the Nilsson potential and the separable quadrupole interactions [72,73,74,75,76]. Later, it has been done with the Woods-Saxon potential and an separable interaction which is determined by the symmetry restoration condition [11].…”