Many-body quantum chaos and actinide ions: Testing the predictions of random matrix theory with high-Zions

Abstract

In this study, we present a statistical analysis of the level structures of four highly charged actinide ions: Bk xii, Cf xii, No xiii, and Md xiv. In these ions, $5f$ wave-function contraction gives rise to a manifold of levels arising from configurations with partially filled $5f$ and $6p$ subshells. The cumulative effects of configuration interaction (CI) between these configurations results in a complete breakdown of the independent particle model used in the labeling of the states and leads to the formation of so-called ``compound'' states. Properties of the calculated level structures have been analyzed using the techniques of random-matrix theory (RMT). Standard statistical measures, such as the repulsion parameter $q$, the covariance of adjacent spacings $\text{cov}({s}_{i},{s}_{i+1})$, and the Dyson-Mehta statistic ${\mathrm{\ensuremath{\Delta}}}_{3}(L)$, have been computed for specific ${J}^{\ensuremath{\pi}}$ interacting sets belonging to the four aforementioned ion stages. In the majority of cases, these calculations are found to be in very good agreement with the RMT-predicted values for these quantities. This study therefore extends previous identifications of RMT-like level fluctuations in the level spectra of lanthanide ions to high-$Z$, moderately charged actinide ions.