Statistical properties of hollow atoms

We investigate the statistical properties of a prototype of a “hollow atom,” i.e., an atom having a large number of empty inner shells. In particular, we have carried out ab initio calculations of the positions and widths of the 1s²4l⁵ states of nitrogen. These states give rise to a dense spectrum of strongly overlapping resonances. Due to the large number of open channels, the statistical description of the system simplifies considerably. We find that the distribution of the nearest-neighbor energy-level spacings follows a Wigner distribution, while the widths of the states are narrowly distributed about the average perturbative width.