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Abstract

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.