Comment on “Stability of the wobbling motion in an odd-mass nucleus and the analysis of ${}^{135}\mathrm{Pr}$”

The claim of Tanabe and Sugawara-Tanabe [Phys. Rev. C 95, 064315 (2017)] that transverse wobbling is unstable is contradicted. Examples for stable transverse wobbling are provided. It is demonstrated that the alternative scenario suggested in the commented paper violates fundamental properties of the nuclear many-body system.

Figure 1

The moments of inertia of the three principal axes as function of the triaxiality parameter $\gamma$. Thick black curves: irrotational flow values Eq. (2); thick dashed curves: rigid body values Eq. (1); colored (grey) curves: microscopic values obtained by cranking calculations. In (a) “'hydro” denotes the irrotational flow values and “cranking” the cranking values, which are scaled by the factor ${\mathcal{J}}_m^{\mathrm{hyd}}\left(\gamma \right)/{\mathcal{J}}_m^{\mathrm{crank}}\left(\gamma \right)$. The numbers in the legends quote the pairing strength. J1110 means ${\mathrm{\Delta }}_p=1.1\mathrm{MeV},{\mathrm{\Delta }}_n=1.0\mathrm{MeV}$; J0309 means ${\mathrm{\Delta }}_p=0.3\mathrm{MeV},{\mathrm{\Delta }}_n=0.9\mathrm{MeV}$; etc. (a) and (b) show the same calculations for $Z=68,N=96,\varepsilon =0.25$; (c) for $Z=38,N=76,\varepsilon =0.2$; and (d) for $Z=68,N=96,\varepsilon =0.4$. In (b)–(d) the three moments of inertia are shown in the three $\gamma$ intervals: long $-{120}^{\circ }\le \gamma \le -{60}^{\circ }$ with $\gamma \to \gamma +{120}^{\circ }$; medium $-{60}^{\circ }\le \gamma \le 0^{\circ }$ with $\gamma \to -\gamma$; short $0^{\circ }\le \gamma \le {60}^{\circ }$; compare (a) with (b). The intersections of the red (grey) vertical lines indicate the moments of inertia of the three axes for $\gamma ={20}^{\circ }$.