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: $\Gamma^{\downarrow}/\Gamma_S$, $\Gamma_N/d$,
and $\Gamma_N/(\Gamma_S+\Gamma^{\downarrow})$. Here $\Gamma^{\downarrow}$ 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
$\Gamma_N$ whilst $|0>$ has electromagnetic decay width $\Gamma_S$.
The average decay intensity may be expressed solely in terms of the variables
$\Gamma^{\downarrow}/\Gamma_S$ and $\Gamma_N/d$ 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
$\Gamma_N/(\Gamma_S+\Gamma^{\downarrow})=\frac{d}{2\pi}T_N/(\Gamma_S+\Gamma^{\d
ownarrow})$. 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 Weidenm\"uller.Comment: revtex4, 14 pages, 4 figures, to appear in Physical Review
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to m GOEs.
The attenuation of the intraband intensity of a superdeformed band, which
results from mixing with normally deformed configurations, is calculated using
reaction theory. It is found that the sharp increase of the attenuation is
mostly due to the tunnelling through a spin dependent barrier and not to the
chaotic nature of the normally deformed states.Comment: 10 pages, 3 figures, to appear in Phys. Rev.
Recent models of the decay out of superdeformed 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 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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.