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

TL;DR

This paper explains the power law distribution of line intensities in many-electron atoms by combining statistical models, revealing that the distribution's exponent depends on electron temperature, aiding plasma diagnostics.

Contribution

It provides a simple analytical explanation for the observed power law distribution, linking it to level density and thermal equilibrium in complex atoms.

Findings

Power law exponent is proportional to electron temperature.

The model explains the distribution without line assignment.

Potential use as a plasma diagnostic tool.

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.