Information entropy and number of principal components in shell model transition strength distributions

The bivariate Gaussian form for smoothed strength densities given by statistical spectroscopy (equivalently by the embedded Gaussian orthogonal ensemble EGOE) is used to derive formulas for information entropy and number of principal components, which are measures of complexity and choas, in transition strength distributions. They describe, in terms of the bivariate correlation coefficient (ζ), shell model results and reduce to GOE results for ζ=0.