Power-Law Distribution of Line Intensity in Complex Many-Electron Atoms

It has long been known that the number of weak lines from many-electron atoms follows a power-law distribution of intensity. This property has been observed by both experiments and computer simulations for several atomic systems. However, its origin has not yet been clarified. Here we report that the combination of two statistical models ---an exponential increase in the level density of many-electron atoms and local thermal equilibrium of the excited state population--- produces a surprisingly simple analytical explanation for this power-law dependence. We find that the exponent of the power-law is proportional to the electron temperature. This dependence may provide a useful diagnostic tool to extract the temperature of plasmas of complex atoms without line assignments.