In calculation of the mean atomic number, how do you justify the use of an arbitrary fractional exponent? What does it actually *mean*? In your 2002 paper with Nicholas Pingitore, it appears without explanation. If you are trying to construct a model that’s physically more realistic, then what, physically, does the fractional exponent represent? *Why* does it appear to produce an improvement in the fit?

I'm sorry, I just noticed this post. Been swamped with other work lately!

The exponent is simply tuned to the data (much like the PAP models themselves!) to provide the best fit. As Aurelien Moy points out in his recent paper, the best fit exponent seems vary slightly with x-ray energy.

As to why a fractional exponent, well it seems to be related to a geometric charge screening effect of the distribution of coulombic charge, e.g., Yukawa Potential. This would imply a Z^0.66 response. We are currently working on this idea...

In the case for a fractional Z exponent for backscatter production, we explain in some of our publications that the fractional exponent seems to relate to the decrease in backscatter production at higher average Z, due to well known screening of the nuclear charge by the increase in inner orbital electrons. Essentially another geometric screening effect.

In that same paper, in your plots on p. 434 (Fig. 3), it looks like the curves represent 2nd-degree polynomials. Is there a physical explanation for why continuum intensity should vary with mean atomic number or mass in such a manner? This approach seems not to work for some high mean Z compounds (like cheralite and galena). And why is zircon problematic?

Outliers can be interesting I agree and I welcome any insight into these, though I will notice that the Monte Carlo models do not show outliers, so I suspect they are simply poor measurements, but certainly worth keeping an eye on.

But keep in mind that the original effort was solely based on the fact that backscatter, continuum (and for that matter characteristic), emissions/productions are overwhelmingly based on electrodynamics. That is already known from physics, and confirmed by the isotope data measurements.

Atomic mass is a best only a rough proxy for these electrodynamic effects, so why not simply exclude mass, since we already know mass has essentially no effect on these productions? In fact, because A/Z generally increases as a function of Z, merely due to reasons of nuclear stability, including neutrons into these electrodynamic calculations, introduces a mass bias into our calculations. As my friends analyzing interstellar dust would say: atomic number is universal, but atomic mass is local.

In summary, what I'm saying is this: You expend some effort in creating a new model that you say has a more physically realistic basis, but then, regardless of Reed's criticisms, you render that physical basis null and void by introducing an unexplained, empirical fractional exponent and polynomial fit. Even the relatively complex PAP model is still semi-empirical, noting that two parabolas are used to model φ(ρz) rather than a seemingly more appropriate "surface-centered Gaussian" model.

We are not committed to the polynomial fit in any way. It just happens that earlier continuum models utilized a straight line fit and the polynomial fit seems to better represent the data. If you can suggest a better method for fitting continuum production as a function of average Z we can certainly try that also.

Also, like Reed points out in his earlier comment (from 2000), the atomic number averaging only produces a marginal apparent improvement over mass averaging in the plots shown in Fig. 2 of Pingitore et al. (1999). This also appears to be true in the plots presented in Fig. 3 of your 2002 paper.

I think we all prefer scientific models that are more physically realistic *and* produce an improvement in our predictions of measurements. Even if the effect is relatively small, it's still an improvement. Shouldn't we welcome improvements in our physical models?

Why not use a model such as PAP to predict continuum intensity relative to that of an analyzed reference material that produces only continuum radiation at the wavelength of the X-ray line of interest?

I think that is an interesting idea. I look forward to seeing your results from this. Just remember, mass doesn't affect any of the emissions/production we observe in the microprobe. Of course if we utilized a 1 MeV electron beam, that would be another story!

I do have to add one comment. Whenever I discuss this atomic mass versus atomic number issue with "card carrying" physicists, they all respond the same way: "Well duh, it's all electrodynamics!". But for some reason in the field of EPMA there is this obsession with atomic mass. I suspect it's just historical inertia as chemists are used to reporting results in mass fractions, because "wet chemistry."

That and also that we started out using some mass normalized expressions (i.e., mass absorption coefficients), even though we know that density is unrelated to EPMA physics, except for considerations of non-infinitely thick specimen geometry of course.