Energy averages and fluctuations in the decay out of superdeformed bands.

Abstract

We derive analytic formulas 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: G#/GS , GN /d, and GN /(GS1G#). Here G# is the spreading width for the mixing of a superdeformed ~SD! state u0& with the normally deformed ~ND! states uQ& whose spin is the same as u0&’s. The uQ& have mean lever spacing d and mean electromagnetic decay width GN whilst u0& has electromagnetic decay width GS. The average decay intensity may be expressed solely in terms of the variables G#/GS and GN /d or, analogously to statistical nuclear reaction theory, in terms of the transmission coefficients T0(E) and TN describing transmission from the uQ& to the SD band via u0& 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 GN /(GS1G#)5(d/2p)TN /(GS1G#). This suggests that analysis of an experimentally determined variance could yield the mean level spacing d as does analysis of the cross section autocorrelation function in compound nucleus reactions. We compare our results with those of Gu and Weidenmu¨ller.