Intrinsic quantum chaos and spectral fluctuations within the protactinium atom

Recently, spectroscopic investigations of the protactinium atom applying resonant laser ionization spectroscopy revealed high-resolution data of the single-excitation spectrum of protactinium, reaching slightly beyond the first ionization potential [P. Naubereit et al., preceding paper, Phys. Rev. A 98, 022505 (2018)]. The more than 1500 recently detected energy levels contain several complete sequences of levels. In this work we study the spectral fluctuations of these data exhibiting clear signatures of intrinsic quantum chaos within the protactinium atom. In order to obtain an estimate on possibly missing levels, simulations were performed based on large ensembles of random matrices from the Gaussian orthogonal ensemble. Our experimental results show that tabulated data in the literature are far from completeness and atomic structure calculations severely underestimate the density of states in the spectral range of highly excited states. However, the statistical analysis of our data as well as of the data from literature and calculations predict a level statistics close to that of fully developed chaos at energies well below the single-ionization threshold.