Decay out of superdeformed bands in the mass region $A\approx 190$ within a cluster approach

A cluster model is applied to the description of the decay out phenomenon of the yrast superdeformed states in the nuclei ${}^{190,192,194}\mathrm{Hg}$ and ${}^{192,194,196}\mathrm{Pb}$. The model is based on the assumption that highly deformed cluster-type shapes are produced by a collective motion of the nuclear system in the charge asymmetry coordinate. As follows from our analysis, the sudden transition from the superdeformed minimum to the normal deformed minimum occurs because of the crossing of superdeformed band with the nearest neighboring excited normal deformed band and spreading of collective states among the compound states.

Figure 1

Potential energy of ${}^{194}\mathrm{Hg}$ as a function of $Z_2$ at spins $I=0$ and 10. Squares of the wave functions of the ground (solid curve) and first excited (dashed curve) ND bands, and ground (dash-dotted curve) and first excited SD (dotted curve) bands are shown.

Figure 2

The same as in Fig. 1, but for nucleus ${}^{194}\mathrm{Pb}$ at spins $I=0$ and 6.

Figure 3

Experimental (expt.) and calculated (theor.) energies of the states of the ground ND and first SD (SD-1) bands in ${}^{194}\mathrm{Hg}$. Experimental data are taken from Ref. 4.

Figure 4

The same as in Fig. 3, but for nucleus ${}^{192}\mathrm{Hg}$. Experimental data for the energies of transitions are taken from Ref. 9. The experimental energies of the SD states are adjusted to have $E_{SD}^{theor}(I=8)=E_{SD}^{expt}(I=8)$.

Figure 5

The same as in Fig. 3, but for nucleus ${}^{190}\mathrm{Hg}$. Experimental data for the energies of transitions are taken from Ref. 8. The experimental energies of the SD states are adjusted to have $E_{SD}^{theor}(I=12)=E_{SD}^{expt}(I=12)$.

Figure 6

The same as in Fig. 3, but for nucleus ${}^{196}\mathrm{Pb}$. Experimental data for the energies of transitions are taken from Ref. 10. The experimental energies of the SD states are adjusted to have $E_{SD}^{theor}(I=6)=E_{SD}^{expt}(I=6)$.

Figure 7

The same as in Fig. 3, but for nucleus ${}^{194}\mathrm{Pb}$. Experimental data are taken from Ref. 6.

Figure 8

The same as in Fig. 3, but for nucleus ${}^{192}\mathrm{Pb}$. Experimental data are taken from Ref. 5.

Figure 9

Calculated energies of the states of the first excited ND band in ${}^{196}\mathrm{Pb}$ and ${}^{194}\mathrm{Hg}$.

Figure 10

Experimental (expt.) and calculated (theor.) energies of the states of the second and third SD bands (SD-2 and SD-3) in ${}^{194}\mathrm{Hg}$. Experimental data are taken from Ref. 4.

Figure 11

The calculated (squares) and experimental (circles) [1] transition quadrupole moments $Q_t$ in the ground (solid symbols) and first excited (open symbols) SD bands of nuclei ${}^{190,192,194}\mathrm{Hg}$ as a function of spin $I$.

Figure 12

The same as in Fig. 11, but for nuclei ${}^{192,194,196}\mathrm{Pb}$.

Figure 13

The energies of ground (solid line) and first excited (dashed line) ND states with positive parity, and first SD states (dotted line) as functions of spin $I$ for the isotopes of mercury.

Figure 14

The same as in Fig. 13, but for the isotopes of lead.

Figure 15

The calculated ND admixture $c^2$ of the yrast SD states as a function of spin for the nuclei ${}^{190,192,194}\mathrm{Hg}$. The experimental decay out spins are $I_{out}=14$, 10, and 10 for ${}^{190,192,194}\mathrm{Hg}$, respectively [4, 8, 9].

Figure 16

The same as in Fig. 15, but for the nuclei ${}^{192,194,196}\mathrm{Pb}$. The experimental decay out spins are $I_{out}=10$, 6, and 8 for ${}^{192,194,196}\mathrm{Pb}$, respectively [6, 5, 10].

Figure 17

The ratio (solid squares) between the decay width ${\Gamma }_{ND}$ in the ND well and the decay width ${\Gamma }_{SD}$ in the SD well as a function of spin $I$ for nuclei ${}^{190,192,194}\mathrm{Hg}$. The solid line is to guide the eye.

Figure 18

The same as in Fig. 17, but for the isotopes of lead.

Figure 19

The calculated (solid circles) probability $P_{out}$ that the SD state decays into the ND states as a function of spin $I$ for different isotopes of mercury. Experimental data (solid squares) are taken from Refs. 4, 8, 9. The solid and dashed lines are to guide the eye.

Figure 20

The same as in Fig. 19, but for the isotopes of lead. Experimental data (solid squares) are taken from Refs. 6, 5, 10.