Estimating Relative Uncertainty of Radiative Transition Rates

Abstract

We consider a method to estimate relative uncertainties of radiative transition rates in an atomic spectrum. Few of these many transitions have had their rates determined by more than two reference-quality sources. One could estimate uncertainties for each transition, but analyses with only one degree of freedom are generally fraught with difficulties. We pursue a way to empirically combine the limited uncertainty information in each of the many transitions. We “pool” a dimensionless measure of relative dispersion, the “Coefficient of Variation of the mean,” \(C_{V}^{n} \equiv s/(\bar{x}\sqrt{n})\). Here, for each transition rate, “s” is the standard deviation, and “\(\bar{x}\)” is the mean of “n” independent data sources. \(C_{V}^{n}\) is bounded by zero and one whenever the determined quantity is intrinsically positive.) We scatter-plot the \(C_{V}^{n} \)as a function of the “line strength” (here a more useful radiative transition rate than transition probability). We find a curve through comparable \(C_{V}^{n} \)as that envelops a specified percentage of the \(C_{V}^{n} \)s (e.g. 95%). We take this curve to represent the expanded relative uncertainty of the mean. The method is most advantageous when the number of determined transition rates is large while the number of independent determinations per transition is small. The transition rate data of Na III serves as an example.

Keywords

• line strengths
• normalized
• relative uncertainty
• transition probabilities