On the Relationship between the Natural Line Width and Lifetime of X-Ray Transitions?

In developing advanced spectrum fitting analysis engines for Hybrid K-Edge Densitometry (HKED), parameters to describe the natural energy distribution of x-ray fluorescence lines, K-shell absorption edges, and the gamma-ray sources sometimes used to study them are needed. The relationship ?? · ?? = h between the Natural Line Width (NLW), ??, and the mean lifetime, ??, of the transition is widely quoted in the related literature. Indeed it is the basis for experimentally finding one from the other, the direction of the inference, depending on whether ?? or ?? is more readily and accurately accessible. However, the plausibility arguments usually used to justify this energy-time relation seem to be inadequate, raising a number of deep and difficult basic physics issues. In this article we set out to explain the specific energytime equation ???? = h so that nondestructive assay professionals can both use it correctly and also better appreciate the modern physics behind it, physics which remains incompletely understood.