Simple Explanation for the Observed Power Law Distribution of Line Intensity in Complex Many-Electron Atoms

It has long been observed that the number of weak lines from many-electron atoms follows a power law distribution of intensity. While computer simulations have reproduced this dependence, 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 the need to assign lines.