Regular and Chaotic Vibrations of Deformed Nuclei with Increasing $\gamma$ Rigidity

We study classical trajectories corresponding to $L=0$ vibrations in the geometric collective model of nuclei with stable axially symmetric quadrupole deformations. It is shown that with increasing stability against the onset of triaxiality the dynamics passes between a fully regular and semiregular limiting regime. In the transitional region, an interplay of chaotic and regular motions results in complex oscillatory dependence of the regular phase space on the Hamiltonian parameter and energy.

Figure 1

Classical trajectories (second and fourth rows) and Poincaré phase-space sections (first and third rows) corresponding to Hamiltonian (2) with $K=-A=C=1$ and $E=0$. The value of $B$ increases as indicated in panels (a)–(f). Only a few examples of regular trajectories were selected (the outer curve marks the border of the energetically accessible area) while each Poincaré section involves a total number of 20 000 crossings of 52 randomly chosen trajectories.

Figure 2

The regular fraction of the Poincaré phase-space section as a function of $B$ for $E=0$.

Figure 3

The regular fraction of the Poincaré section as a function of energy for values of $B$ corresponding to maxima of the curve in Fig. 2. The horizontal axis is split into linear and logarithmic parts. The inset expands the $E\sim 0$ region.

Figure 4

The same as in Fig. 3, but at three minima of Fig. 2.