Hi Stan, which version of Peaksight is running there? I don't see the equations in the 6.x users guide, but I think you should still have the initial version of the SXfive users guide somewhere there. The equations relevant to the Ancey method are given in the guide to Results. I have a pdf of the original paper from the famous St-Martin-d'Heres Summer School on Microanalysis and Scanning Electron Microscopy in 1978 if you need it. We also outlined the basic things in our IOP paper ( Jercinovic, M.J., Williams, M.L., Allaz, M.J., and Donovan, J.J. (2012) Trace analysis in EPMA. IOP Conference Series: Materials Science and Engineering 32 (J.L. Labar, C.T. Walker, F. Brisset, O. Dugne, and F. Robaut eds.). Institute of Physics Publishing, Bristol, UK. Doi:10.1088/1757-899X/32/1/012012. P.1-22).
I am not sure of the exact Goldstein equation Cameca might be using now, but I would presume it is the one used in Goldstein (1967) which is also outlined in the Goldstein et al textbook (editions 1-3, not v4!). You can also find the Ziebold approximation in that book also, which gives a result pretty similar to the Goldstein calculation. Might check on that implementation with Carl Henderson at Ametek.
Anyway, a lot of this depends importantly on the confidence level you need (to get the student's T value) and the number of measurements involved in the test. We like the statistics of the Ancey approach overall. Remember you are just manipulating X-ray counting statistics based on Poisson stats and relating that to concentration. The question of detectability is somewhat subjective (i.e. 3x the standard deviation of the background). This means the concept of "correct" is not so straightforward. Detection limit sounds like it should be a hard number, but it is really just a statistical estimate from a confidence envelope that makes no presumption of accuracy. When does a signal emerge from the noise? You can say probably this value or that value depending on your assumptions and how you define that magical signal level. I am just making this worse now, sorry. One thing for sure, these sorts of measurements imply that, as your peak intensity approaches the background intensity, the precision on the background measurement needs to be excellent. As you will see in the equations, the calculation of detection limit depends mostly on the precision of the background.
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