How large is the spreading width of a superdeformed band?

Recent models of the decay out of superdeformed (SD) bands can broadly be divided into two categories. One approach is based on the similarity between the tunneling process involved in the decay and that involved in the fusion of heavy ions, and it builds on the formalism of nuclear reaction theory. The other arises from an analogy between the superdeformed decay and transport between coupled quantum dots. These models suggest conflicting values for the spreading width of the decaying superdeformed states. In this paper, the decay of superdeformed bands in the five even-even nuclei in which the SD excitation energies have been determined experimentally is considered in the framework of both approaches, and the significance of the difference in the resulting spreading widths is considered. The results of the two models are also compared to tunneling widths estimated from previous barrier height predictions and a parabolic approximation to the barrier shape.

Figure 1

Decay profiles of the yrast superdeformed bands in ${}^{190}\mathrm{Hg}$, ${}^{192}\mathrm{Hg}$, ${}^{194}\mathrm{Hg}$, ${}^{192}\mathrm{Pb}$, ${}^{194}\mathrm{Pb}$, and ${}^{196}\mathrm{Pb}$. The right-hand panel shows the profiles shifted in spin so that the last point represents the lowest spin level from below which some intensity remains in the band, regardless of the absolute spin.

Figure 2

Schematic illustration of the SD and ND levels at the point of decay.

Figure 3

(a) In the statistical models, the SD level mixes with many ND levels of average separation D. The resulting interaction $\langle V\rangle$ is an average over all of these interactions. (b) In the two-level mixing model, the SD level mixes predominantly with one ND level. The resulting interaction V is extracted assuming an average separation of the SD and ND states by energy $\Delta =D/4$.

Figure 4

(a) Comparison of various model predictions of the height of the barrier separating the SD and ND wells in ${}^{192}\mathrm{Pb}$ and ${}^{194}\mathrm{Hg}$: Strutinsky method with Woods-Saxon potential (SM-WS) [19], mean field using the Skyrme interaction (HFB-S) [20], and mean field using a Gogny interaction (HFB-G) [21]. (b) Comparison of the barrier heights predicted using the HFB method and a Gogny force for ${}^{192}\mathrm{Pb}$ and ${}^{194}\mathrm{Hg}$ at various different spins.

Figure 5

Values of the ratio ${\Gamma }^{\downarrow }/{\Gamma }_S$ as a function of the in-band intensity I calculated for ${\Gamma }_N/D$ appropriate for the ${10}^{+}$ and ${12}^{+}$ levels in ${}^{192}\mathrm{Hg}$.