NIST Physical Measurement Laboratory X-Ray Form Factor, Attenuation, and Scattering Tables Main Page

[skip navigation] National Institute of Standards and Technology NIST Physical Measurement Laboratory

4. Reliability of Experimental and Theoretical Results

This paper addresses a key theoretical issue behind this dilemma, focusing on the soft x-ray near-edge region. We derive new results based on the formalism of C95. We primarily compare our new theoretical results to those of C95 and refs. [28] and [29], because of the detailed and extensive discussion of these references over the last few years. A moderately detailed discussion of databases of Henke et al. [32,33], Cromer and Liberman [25], and Brennan and Cowan [30] has been made earlier in comparison to C95 [1] and [31].

The primary experimental references for comparison in this paper will be Henke et al. [32,33] and those contained in Saloman, Hubbell, and Scofield [34]. Compilations of experimental data for photoabsorption and total cross-sections are widespread [34], particularly for common elements over the central x-ray energies. These are particularly useful in evaluating the reliability of a particular measurement, or the difficulty of an experiment in a given energy regime. The range of the imaginary coefficient in such compilations often varies by 10 % to 30 %. This implies in general that claimed experimental accuracies of 1 % to 2 % are not reliable. The effect of a 10 % error is equivalent to a 10 % error in the thickness of the sample, or a 10 % error in the exponent of the probability of photoabsorption through a sample.

The second primary source for an experimental best-fit line is given by the Center for X-Ray Optics, Lawrence Berkeley Laboratory [32,33]. A recent successor in this series is presented by Cullen, Hubbell and Kissel [35], but we do not discuss it further in the current context. These references present experimental-theoretical syntheses for the complex form factor in the softer x-ray regime. As a weighted evaluation of experimental data, they are extremely useful. However, no variation or error bar is associated with this single fit, and in soft x-ray regimes, near-edge regimes and other areas the result may be in sharp discrepancy with theory and expected results, or with the best available data. Observed deviations lie at the same 10 % to 30 % level as the variation of less critical compilations.

For medical and diagnostic applications, reliance on either theory or idealized "narrow beam" experiment is dangerous: an "ideal" procedure is to measure relative fluxes of energy distributions in situ, with and without filters, in "broad beam" geometry, as they would be used in practice. This then ignores the relative significance of scattering, absorption, harmonic contamination and divergence effects, and yields a purely empirical calibration subject to the detector calibration itself. The danger of this approach is that lack of subsequent control of flux distribution with angle and energy, and of the orientation and uniformity of filters and optical elements, will lead to arbitrary and potentially severe changes (over time, or between exposures) in administered doses or derived structural distributions.

Given this situation, it is sensible to turn to theoretical computations. One of the most recent and comprehensive theoretical approaches was developed to explicitly eliminate these difficulties (C95). Useful recent general reviews of other theoretical and experimental compilations are given by Hubbell [36] and Creagh and McAuley [17]. These also discuss scattering contributions which are not the primary concern of this paper.

Comparing the new theoretical approach with other commonly used theoretical refs. [28,29] and [34] reveals surprising variation and uncertainty in the theory. Many references have been made to Scofield theory in unrenormalized and normalized forms, and we discuss some of the variations between these two results. Scofield presents only atomic photoabsorption cross-sections, τPE, so this discussion will be limited to the imaginary component of the atomic form factor. The real component will be discussed for comparison to Henke et al. [33].

It is difficult to accurately assign uncertainty to theoretical results, and the uncertainty varies dramatically across energy ranges for well-defined reasons. A number of authors give useful estimates based on convergence criteria [28], on self-consistency or consistency with experiment [4] and [34], or on a combination of these criteria (C95). A figure of 0.1 % to 1 % is often quoted away from edges and in the medium energy range. This paper highlights and addresses the largest apparent single source of discrepancy currently observed.

Back to Main Page
Table of Contents - 2000
previous page next page