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: $\Gamma^{\downarrow}/\Gamma_S$, $\Gamma_N/d$, 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

Intensity profiles of superdeformed bands in Pb isotopes in a two-level mixing model

“…[8][9][10][11][12][13]), in the present paper we consider only the simple, two-level mixing model first proposed by Stafford and Barrett [1]. In subsequent work, Cardamone, Stafford, and Barrett built on this initial proposal to develop a better physical understanding of the parameters of the model and to introduce statistical approaches leading to the extraction of ND-SD coupling strengths [2].…”

Multi-level and two-level models of the decay out of superdeformed bands

“…In practice calculations proceed by choosing a representation -the optical background representation of Kawai, Kerman and McVoy [30] -which is defined such that the couplings V NS have statistical properties which are convenient for analytical calculation. [21] to calculate F S . [31] that the properties of the V NS which are normally assumed do indeed obtain from the underlying random Hamiltonian.)…”

“…An advantage of the energy averaging technique is that it also yields an analytical expression for the variance of the decay intensity [21]: From Eqs. (6), (7), (8) and (12) it is seen that F S depends only on the two dimensionless variables Γ Γ S and Γ N D. However it is possible to construct three independent dimensionless variables from the input variables Γ, Γ S , Γ N and D. In Ref.…”

“…[20,21] which exploit analogies of the SD decay with the theory of compound nucleus reactions [22] and the two-level model of Refs. [20,21] which exploit analogies of the SD decay with the theory of compound nucleus reactions [22] and the two-level model of Refs.…”

Energy Averages over Regular and Chaotic States in the Decay Out of Superdeformed Bands

“…In Section 2 we present analytic formulae for the energy average (including the energy average of the fluctuation contribution) and variance of the intraband decay intensity of a SD band in terms of variables which usefully describe the decayout. 13)- 15) In agreement with Gu and Weidenmüller 14) (GW) we find that average of the total intraband decay intensity can be written as a function of the dimensionless variables Γ ↓ /Γ S and Γ N /D where Γ ↓ is the spreading width for the mixing of an SD state with ND states of the same spin, D is the mean level spacing of the latter and Γ S (Γ N ) are the electromagnetic decay widths of the SD (ND) states. Our formula for the variance of the total intraband decay intensity, in addition to the two dimensionless variables just mentioned, depends on the dimensionless variable…”