Energy averages and fluctuations in the decay out of superdeformed bands

Abstract

We derive analytic formulae for the energy average (including the energy average of the fluctuation contribution) and variance of the intraband decay intensity of a superdeformed band. Our results may be expressed in terms of three dimensionless variables: $Γ^{\downarrow}/Γ_S$, $Γ_N/d$, and $Γ_N/(Γ_S+Γ^{\downarrow})$. Here $Γ^{\downarrow}$ is the spreading width for the mixing of a superdeformed (SD) state $|0>$ with the normally deformed (ND) states $|Q>$ whose spin is the same as $|0>$'s. The $|Q>$ have mean level spacing $d$ and mean electromagnetic decay width $Γ_N$ whilst $|0>$ has electromagnetic decay width $Γ_S$. The average decay intensity may be expressed solely in terms of the variables $Γ^{\downarrow}/Γ_S$ and $Γ_N/d$ or, analogously to statistical nuclear reaction theory, in terms of the transmission coefficients $T_0(E)$ and $T_N$ describing transmission from the $|Q>$ to the SD band via $|0\angle$ and to lower ND states. The variance of the decay intensity, in analogy with Ericson's theory of cross section fluctuations depends on an additional variable, the correlation length $Γ_N/(Γ_S+Γ^{\downarrow})=\frac{d}{2π}T_N/(Γ_S+Γ^{\d ownarrow})$. This suggests that analysis of an experimentally obtained variance could yield the mean level spacing $d$ as does analysis of the cross section autocorrelation function in compound nuclear reactions. We compare our results with those of Gu and Weidenmüller.